Appendices A-C NAEP 2021 Supplemental Documents

^{NATIONAL CENTER} FOR EDUCATION STATISTICS

NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS

National Assessment of Educational Progress (NAEP) 2021

Appendices A-C

Appendix A: External Advisory Committees

Appendix B: NAEP 2013 Weighting Procedures

Appendix C: NAEP 2021 Sampling Memo

OMB# 1850-0928 v.21

October 2020

Table of Contents

Appendix A: External Advisory Committees … 3

The External Advisory Committees’ list has the most current information available to the public. At this time, there is not a timeline for when the details for revised committees will be publicly available.

Appendix B: NAEP 2013 Weighting Procedures (No changes since v.10) …15

The 2013 Weighting Procedures documentation is the most current version available to the public. At this time, there is not a timeline for when the details for later assessment years will be publicly available.

Appendix C: NAEP 2021 Sampling Memo …...................................……………………………………..66

NATIONAL CENTER FOR EDUCATION STATISTICS NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS

National Assessment of Educational Progress (NAEP) 2021

Appendix A

External Advisory Committees

OMB# 1850-0928 v.21

The External Advisory Committees’ list has the most current information available to the public. At this time, there is not a timeline for when the details for revised committees will be publicly available.

Appendix A-1: NAEP Design and Analysis Committee

Name	Affiliation
Betsy Becker	Florida State University, FL
Peter Behuniak	University of Connecticut, CT
Dan Bolt	University of Wisconsin, Madison, WI
Lloyd Bond	University of North Carolina, Greensboro, NC (Emeritus)/Carnegie Foundation (retired)
Derek Briggs	University of Colorado, CO
Richard Duran	University of California, Santa Barbara, CA
Steve Elliott	Arizona State University, AZ
Ben Hansen	University of Michigan, MI
Brian Junker	Carnegie Mellon University, PA
David Kaplan	University of Wisconsin-Madison, WI
Kenneth Koedinger	Carnegie Mellon University, PA
Sophia Rabe-Hesketh	University of California, Berkeley, CA
Michael Rodriguez	University of Minnesota, MN
S.Lynne Stokes	Southern Methodist University, TX
Chun Wang	University of Minnesota, MN

Appendix A-2: NAEP Validity Studies Panel

Name	Affiliation
Peter Behuniak	University of Connecticut, CT
Jack Buckley	American Institutes for Research, Washington, DC
Jim Chromy	RTI International (Emeritus Fellow), Raleigh, NC
Phil Daro	Strategic Education Research (SERP)
Richard Duran	University of California, Berkeley, CA
David Grissmer	University of Virginia, VA
Larry Hedges	Northwestern University, IL
Gerunda Hughes	Howard University, Washington, DC
Ina Mullis	Boston College, MA
Scott Norton	Council of Chief State School Officers, Washington, DC
Jim Pellegrino	University of Illinois at Chicago/Learning Sciences Research Institute, IL
Gary Phillips	American Institutes for Research, Washington, DC
Lorrie Shepard	University of Colorado at Boulder, CO
David Thissen	University of North Carolina at Chapel Hill, NC
Gerald Tindal	University of Oregon, Eugene, OR
Sheila Valencia	University of Washington, WA
Ting Zhang	American Institutes for Research, Washington, DC

Appendix A-3: NAEP Quality Assurance Technical Panel

Name	Affiliation
Jamal Abedi	University of California, Davis, CA
Chuck Cowan	Analytic Focus LLC, San Antonio, TX
Gail Goldberg	Gail Goldberg Consulting, Ellicott City, MD
Brian Gong	National Center for the Improvement of Educational Assessment, Dover, NH
Richard Luecht	University of North Carolina-Greensboro, NC
Jim Pellegrino	University of Illinois at Chicago/Learning Sciences Research Institute, IL
Mark Reckase	Michigan State University, MI
Michael (Mike) Russell	Boston College, MA
Phoebe Winter	Consultant, Chesterfield, VA
Richard Wolfe	University of Toronto (Emeritus), Ontario, Canada

Appendix A-4: NAEP National Indian Education Study Technical Review Panel

Name	Affiliation
Doreen E. Brown	ASD Education Center, Anchorage, AK
Robert B.Cook	Native American Initiative/Teach for America, Summerset, SD
Steve Andrew Culpepper	University of Illinois at Urbana-Champaign, IL
Susan C. Faircloth	University of North Carolina Wilmington, NC
Jeremy MacDonald	Rocky Boy Elementary, Box, Elder, MT
Holly Jonel Mackey	University of Oklahoma, OK
Jeannette Muskett Miller	Tohatchi High School, Tohatchi, NM
Sedelta Oosahwee	National Education Association, DC
Debora Norris	Salt River Pima-Maicopa Indian Community
Martin Reinhardt	Northern Michigan University, MI
Tarajean Yazzie-Mintz	Wakanyeja ECE Initative/American Indian College Fund, Denver, CO

Appendix A-5: NAEP Mathematics Standing Committee

Name	Affiliation
Scott Baldridge	Louisiana State University, LA
Carl Cowen	Indiana University–Purdue University, IN
Kathleen Heid	Pennsylvania State University, PA
Mark Howell	Gonzaga College High School, Washington, DC
Carolyn Maher	Rutgers University, NJ
Michele Mailhot	Maine Department of Education, Augusta, ME
Matthew Owens	Spring Valley High School, Columbia, SC
Carole Philip	Alice Deal Middle School, Washington, DC
Kayonna Pitchford	University of North Carolina, NC
Melisa M. Ramos Trinidad	Educación Bilingüe Luis Muñoz Iglesias, Cidra, PR
Allan Rossman	College of Science and Mathematics-CalPoly, CA
Carolyn Sessions	Louisiana Department of Education, LA
Lya Snell	Georgia Department of Education, GA
Ann Trescott	Stella Maris Academy, La Jolla, CA
Vivian Valencia	Espanola Public Schools, NM

Appendix A-6: NAEP Reading Standing Committee

Name	Affiliation
Patricia Alexander	University of Maryland, MD
Alison Bailey Jensa Bushey	University of California, LA, CA Shelburne Community Schools, Shelburne, VT
Julie Coiro	University of Rhode Island, RI
Bridget Dalton Christy Howard	University of Colorado Boulder, CO East Carolina University, Greenville, NC
Jeanette Mancilla-Martinez	Vanderbilt University, TN
Pamela Mason	Harvard Graduate School of Education, MA
P. David Pearson	University of California, Berkeley, CA
Frank Serafini	Arizona State University, AZ
Kris Shaw Ana Taboada Barber	Kansas State Department of Education, KS University of Maryland, MD
Diana Townsend Brandon Wallace	University of Nevada, Reno, NV National Office of Urban Teachers, Baltimore, MD
Victoria Young	Texas Education Agency, Austin, TX

Appendix A-7: NAEP Science Standing Committee

Name	Affiliation
Alicia Cristina Alonzo	Michigan State University, MI
George Deboer	American Association for the Advancement of Science, Washington, DC
Alex Decaria	Millersville University, PA
Crystal Edwards	Lawrence Township Public Schools, Lawrenceville, NJ
Ibari Igwe	Shrewd Learning, Elkridge, MD
Michele Lombard	Kenmore Middle School, Arlington, VA
Emily Miller	Consultant, WI
Blessing Mupanduki	Department of Defense, Washington, DC
Amy Pearlmutter	Littlebrook Elementary School, Princeton, NJ
Brian Reiser	Northwestern University, Evanston, IL
Michal Robinson	Alabama Department of Education, Montgomery, AL
Gloria Schmidt	Darby Junior High School, Fort Smith, AR
Steve Semken	Arizona State University, Tempe, AZ
Roberta Tanner	Board of Science Education, Longmont, CO
David White	Lamoille North Supervisory Union School District, Hyde Park, VT

Appendix A-8: NAEP Survey Questionnaire Standing Committee

Name	Affiliation
Angela Duckworth	University of Pennsylvania, PA
Hunter Gehlbach	Harvard University, MA
Camille Farrington	University of Chicago, Chicago, IL
Gerunda Hughes	Howard University, DC
David Kaplan	University of Wisconsin-Madison, WI
Henry Levin	Teachers College, Columbia University, NY
Stanley Presser	University of Maryland, MD
Augustina Reyes	University of Houston, Houston, TX
Leslie Rutkowski	Indiana University Bloomington, IN
Jonathon Stout	Lock Haven University, PA
Roger Tourangeau	Westat, Rockville, MD
Akane Zusho	Fordham University, NY

Appendix A-9: NAEP Mathematics Translation Review Committee

Name	Affiliation
Mayra Aviles	Puerto Rico Department of Education, PR
David Feliciano	P.S./M.S 29, The Melrose School, Bronx, NY
Yvonne Fuentes	Author and Spanish Linguist, Carrollton, GA
Marco Martinez-Leandro	Sandia High School, NM
Jose Antonio (Tony) Paulino	Nathan Straus Preparatory School, NY
Evelisse Rosado Rivera	Teacher, PMB 35 HC, PR
Myrna Rosado-Rasmussen	Austin Independent School District, TX
Gloria Rosado Vazquez	Teacher, HC-02, PR
Enid Valle	Kalamazoo College, Kalamazoo, MI

Appendix A-10: NAEP Science Translation Committee

Name	Affiliation
Daniel Berdugo	Teacher, PS 30X Wilton, NY
Yvonne Fuentes	Author and Spanish Linguist, Carrollton, GA
Myrna Rosado- Rasmussen	Austin Independent School District, Austin, TX
Enid Valle	Kalamazoo College, Kalamazoo, MI

Appendix A-11: NAEP Grade 8 Social Science Translation Review Committee

Name	Affiliation
Yvonne Fuentes	Author and Spanish Linguist, Carrollton, GA
Jose Antonio Paulino	Middle School Teacher, Nathan Strauss Preparatory School, NY
Dagoberto Eli Ramierz	Bilingual Education Expert, Palmhurst, TX
Enid Valle	Kalamazoo College, Kalamazoo, MI

Appendix A-12: NAEP Grade 4 and 8 Survey Questionnaires and eNAEP DBA System Translation Committee

Name	Affiliation
Daniel Berdugo	PS 30X Wilton, Bronx, NY
Yvonne Fuentes	Carrollton, GA
Marco Martinea-Leandro	Sandia High School. Albuquerque, NM
Jose Antonio (Tony) Paulino	Nathan Straus Preparatory School, New York, NY
Evelisse Rosado Rivera	PMB 36 HC 72, Naranjito, PR
Myrna Rosado-Rasmussen	Austin Independent School District, Austin, TX
Gloria M. Rosado Vazquez	HC – 02 Barranquitas, PR
Enid Valle	Kalamazoo College, Kalamazoo, MI

Appendix A-13: NAEP Principals’ Panel Standing Committee

Name	Affiliation
David Atherton	Clear Creek Middle School, Gresham, OR
Ardith Bates	Gladden Middle School, Chatsworth, GA
Williams Carozza	Harold Martin Elementary School, Hopkinton, NH
Diane Cooper	St. Joseph’s Academy, Clayton, MO
Brenda Creel	Alta Vista Elementary School, Cheyenne, WY
Rita Graves	Pin Oak Middle School, Bellaire, TX
Don Hoover	Lincoln Junior High School, Springdale, AR
Stephen Jackson	(Formerly with) Paul Laurence Dunbar High School, Washington, DC
Anthony Lockhart	Lake Shore Middle School, Belle Glade, FL
Susan Martin	Berrendo Middle School, Roswell, NM
Lillie McMillan	Porter Elementary School, San Diego, CA
Kourtney Miller	Chavez Prep Middle School, Washington, DC
Jason Mix	Howard Lake–Waverly–Winsted High School, Howard Lake, MN
Leon Oo-Sah-We	Ch’ooshgai Community School, Tohatchi, NM
Sylvia Rodriguez Vargas	Atlanta Girls’ School, Atlanta Georgia, GA

NATIONAL CENTER FOR EDUCATION STATISTICS NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS

National Assessment of Educational Progress (NAEP)

2021

Appendix B

NAEP 2013 Weighting Procedures

OMB# 1850-0928 v.21

August 2020

No changes since v.10

The 2013 Weighting Procedures documentation is the most current version available to the public. At this time, there is not a timeline for when the details for later assessment years will be publicly available.

NAEP Technical Documentation Website

NAEP Technical Documentation Weighting Procedures for the 2013 Assessment

NAEP assessments use complex sample designs to create student samples that generate population and subpopulation estimates with reasonably high precision. Student sampling weights ensure valid inferences from the student samples to their respective populations. In 2013, weights were developed for students sampled at grades 4, 8, and 12 for assessments in mathematics and reading.

Computation of Full-Sample Weights

Computation of Replicate Weights for Variance Estimation

Quality Control on Weighting Procedures

Each student was assigned a weight to be used for making inferences about students in the target population. This weight is known as the final full-sample student weight and contains the following major components:

the student base weight;

school nonresponse adjustments; student nonresponse adjustments; school weight trimming adjustments;

student weight trimming adjustments; and student raking adjustment.

The student base weight is the inverse of the overall probability of selecting a student and assigning that student to a particular assessment. The sample design that determines the base weights is discussed in the NAEP 2013 sample design section.

The student base weight is adjusted for two sources of nonparticipation: school level and student level. These weighting adjustments seek to reduce the potential for bias from such nonparticipation by

increasing the weights of students from participating schools similar to those schools not participating; and

increasing the weights of participating students similar to those students from within participating schools who did not attend the assessment session (or makeup session) as scheduled.

Furthermore, the final weights reflect the trimming of extremely large weights at both the school and student level. These weighting adjustments seek to reduce variances of survey estimates.

An additional weighting adjustment was implemented in the state and Trial Urban District Assessment (TUDA) samples so that estimates for key student-level characteristics were in agreement across assessments in reading and mathematics. This adjustment was implemented using a raking procedure.

In addition to the final full-sample weight, a set of replicate weights was provided for each student. These replicate weights are used to calculate the variances of survey estimates using the jackknife repeated replication method. The methods used to derive these weights were aimed at reflecting the features of the sample design, so that when the jackknife variance estimation procedure is implemented, approximately unbiased estimates of sampling variance are obtained. In addition, the various weighting procedures were repeated on each set of replicate weights to appropriately reflect the impact of the weighting adjustments on the sampling variance of a survey estimate. A finite population correction (fpc) factor was incorporated into the replication scheme so that it could be reflected in the variance estimates for the reading and mathematics assessments. See Computation of Replicate Weights for Variance Estimation for details.

Quality control checks were carried out throughout the weighting process to ensure the accuracy of the full-sample and replicate weights. See Quality Control for Weighting Procedures for the various checks implemented and main findings of interest.

In the linked pages that follow, please note that Vocabulary, Reading Vocabulary, and Meaning Vocabulary refer to the same reporting scale and are interchangeable.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/naep_assessment_weighting_procedures.aspx

NAEP Technical Documentation Computation of Full- Sample W eights for the 2013 Assessment

The full-sample or final student weight is the sampling weight used to derive NAEP student estimates of population and subpopulation characteristics for a specified grade (4, 8, or 12) and assessment subject (reading or mathematics). The full-sample student weight reflects the number of students that the sampled student represents in the population for purposes of estimation. The summation of the final student weights over a particular student group provides an estimate of the total number of students in that group within the population.

The full-sample weight, which is used to produce survey estimates, is

Computation of Base Weights

School and Student Nonresponse Weight Adjustments

School and Student Weight Trimming Adjustments

Student Weight Raking Adjustment

distinct from a replicate weight that is used to estimate variances of survey estimates. The full-sample weight is assigned to participating students and reflects the student base weight after the application of the various weighting adjustments. The full-sample weight for student k from school s in stratum j (FSTUWGT_jsk) can be expressed as follows:

where

STU_BWT_jsk is the student base weight;

SCH_NRAF_js is the school-level nonresponse adjustment factor; STU_NRAF_jsk is the student-level nonresponse adjustment factor; SCH_TRIM_js is the school-level weight trimming adjustment factor; STU_TRIM_jsk is the student-level weight trimming adjustment factor; and STU_RAKE_jsk is the student-level raking adjustment factor.

School sampling strata for a given assessment vary by school type and grade. See the links below for descriptions of the school strata for the various assessments.

Public schools at grades 4 and 8 Public schools at grade 12

Private schools at grades 4, 8 and 12

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/computation_of_full_sample_weights_for_the_2013_assessment.aspx

NAEP Technical Documentation Computation of Base Weights for the 2013 Assessment

Every sampled school and student received a base weight equal to the reciprocal of its probability of selection. Computation of a school base weight varies by

type of sampled school (original or substitute); and sampling frame (new school frame or not).

Computation of a student base weight reflects

School Base Weights Student Base Weights

the student's overall probability of selection accounting for school and student sampling; assignment to session type at the school- and student-level; and

the student's assignment to the reading or mathematics assessment.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/computation_of_base_weights_for_the_2013_assessment.aspx

NAEP Technical Documentation School Base Weights for the 2013 Assessment

The school base weight for a sampled school is equal to the inverse of its overall probability of selection. The overall selection probability of a sampled school differs by

type of sampled school (original or substitute); sampling frame (new school frame or not).

The overall selection probability of an originally selected school in a reading or mathematics sample is equal to its probability of selection from the NAEP public/private school frame.

The overall selection probability of a school from the new school frame in a reading or mathematics sample is the product of two quantities:

the probability of selection of the school's district into the new-school district sample, and the probability of selection of the school into the new school sample.

Substitute schools are preassigned to original schools and take the place of original schools if they refuse to participate. For weighting purposes, they are treated as if they were the original schools that they replaced; so substitute schools are assigned the school base weight of the original schools.

Learn more about substitute schools for the 2013 private school national assessment and substitute schools for the 2013 twelfth grade public school assessment.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/school_base_weights_for_the_2013_assessment.aspx

NAEP Technical Documentation Student Base Weights for the 2013 Assessment

Every sampled student received a student base weight, whether or not the student participated in the assessment. The student base weight is the reciprocal of the probability that the student was sampled to participate in the assessment for a specified subject. The student base weight for student k from school s in stratum j (STU_BWT_jsk) is the product of seven weighting components and can be expressed as follows:

where

SCH_BWT_js is the school base weight;

SCHSsessionassignmentESWT_js is the school-level session assignment weight that reflects the conditional probability, given the school, that the particular session type was assigned to the school;

WINSCHWT_js is the within-school student weight that reflects the conditional probability, given the school, that the student was selected for the NAEP assessment;

STUSESWT_jsk is Stu_bookmarkthe student-level session assignment weight that reflects the conditional probability, given that the particular session type was assigned to the school, that the student was assigned to the session type;

SUBJFACsubjfac_jsk is the subject spiral adjustment factor that reflects the conditional probability, given that the student was assigned to a particular session type, that the student was assigned the specified subject;

SUBADJ_js is the substitution adjustment factor to account for the difference in enrollment size between the substitute and original school; and

YRRND_AF_js is the year-round adjustment factor to account for students in year- round schools on scheduled break at the time of the NAEP assessment and thus not available to be included in the sample.

The within-school student weight (WINSCHWT_js) is the inverse of the student sampling rate in the school.

The subject spiral adjustment factor (SUBJFAC_jsk) adjusts the student weight to account for the spiral pattern used in distributing reading or mathematics booklets to the students. The subject factor varies by grade, subject, and school type (public or private), and it is equal to the inverse of

the booklet proportions (reading or mathematics) in the overall spiral for a specific sample.

For cooperating substitutes of nonresponding original sampled schools, the substitution adjustment factor (SUBADJ_js) is equal to the ratio of the estimated grade enrollment for the original sampled school to the estimated grade enrollment for the substitute school. The student sample from the substitute school then "represents" the set of grade-eligible students from the original sampled school.

The year-round adjustment factor (YRRND_AF_js) adjusts the student weight for students in year- round schools who do not attend school during the time of the assessment. This situation typically arises in overcrowded schools. School administrators in year-round schools randomly assign students to portions of the year in which they attend school and portions of the year in which they do not attend. At the time of assessment, a certain percentage of students (designated as OFF _js) do not attend school and thus cannot be assessed. The YRRND_AF_js for a school is calculated as 1/(1- OFF _js/100).

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/student_base_weights_for_the_2013_assessment.aspx

NAEP Technical Documentation Website

NAEP Technical Documentation School and Student

Nonresponse Weight Adjustments for the 2013 Assessment

Nonresponse is unavoidable in any voluntary survey of a human population. Nonresponse leads to the loss of sample data that must be compensated for in the weights of the responding sample members. This differs from ineligibility, for which no adjustments are necessary. The purpose of the nonresponse adjustments is to reduce the mean square error of survey estimates. While the nonresponse adjustment reduces the bias from the loss of sample, it also increases variability among the survey weights leading to increased variances of the sample estimates. However, it is presumed that the reduction in bias more than compensates for the increase in

School Nonresponse Weight Adjustment

Student Nonresponse Weight Adjustment

the variance, thereby reducing the mean square error and thus improving the accuracy of survey estimates. Nonresponse adjustments are made in the NAEP surveys at both the school and the student levels: the responding (original and substitute) schools receive a weighting adjustment to compensate for nonresponding schools, and responding students receive a weighting adjustment to compensate for nonresponding students.

The paradigm used for nonresponse adjustment in NAEP is the quasi-randomization approach (Oh and Scheuren 1983). In this approach, school response cells are based on characteristics of schools known to be related to both response propensity and achievement level, such as the locale type (e.g., large principal city of a metropolitan area) of the school. Likewise, student response cells are based on characteristics of the schools containing the students and student characteristics, which are known to be related to both response propensity and achievement level, such as student race/ethnicity, gender, and age.

Under this approach, sample members are assigned to mutually exclusive and exhaustive response cells based on predetermined characteristics. A nonresponse adjustment factor is calculated for each cell as the ratio of the sum of adjusted base weights for all eligible units to the sum of adjusted base weights for all responding units. The nonresponse adjustment factor is then applied to the base weight of each responding unit. In this way, the weights of responding units in the cell are "weighted up" to represent the full set of responding and nonresponding units in the response cell.

The quasi-randomization paradigm views nonresponse as another stage of sampling. Within each nonresponse cell, the paradigm assumes that the responding sample units are a simple random sample from the total set of all sample units. If this model is valid, then the use of the quasi-randomization weighting adjustment will eliminate any nonresponse bias. Even if this model is not valid, the weighting adjustments will eliminate bias if the achievement scores are homogeneous within the response cells (i.e., bias is eliminated if there is homogeneity either in response propensity or in achievement levels). See, for example, chapter 4 of Little and Rubin (1987).

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/school_and_student_nonresponse_weight_adjustments_for_the_2013_assessment.aspx

NAEP Technical Documentation School Nonresponse Weight Adjustment

The school nonresponse adjustment procedure inflates the weights of cooperating schools to account for eligible noncooperating schools for which no substitute schools participated. The adjustments are computed within nonresponse cells and are based on the assumption that the cooperating and noncooperating schools within the same cell are more similar to each other than to schools from different cells. School nonresponse adjustments were carried out separately by sample; that is, by

sample level (state, national), school type (public, private), and grade (4, 8, 12).

Development of Initial School Nonresponse Cells

Development of Final School Nonresponse Cells

School Nonresponse Adjustment Factor Calculation

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/school_nonresponse_weight_adjustment_for_the_2013_assessment.aspx

NAEP Technical Documentation Development of Initial School Nonresponse Cells

The cells for nonresponse adjustments are generally functions of the school sampling strata for the individual samples. School sampling strata usually differ by assessment subject, grade, and school type (public or private). Assessment subjects that are administered together by way of spiraling have the same school samples and stratification schemes. Subjects that are not spiraled with any other subjects have their own separate school sample. In NAEP 2015, all operational assessments were spiraled together.

The initial nonresponse cells for the various NAEP 2015 samples are described below.

Public School Samples for Reading and Mathematics at Grades 4 and 8

For these samples, initial weighting cells were formed within each jurisdiction using the following nesting cell structure:

Trial Urban District Assessment (TUDA) district vs. the balance of the state for states with TUDA districts, urbanicity (urban-centric locale) stratum; and

race/ethnicity classification stratum, or achievement level, or median income, or grade enrollment.

In general, the nonresponse cell structure used race/ethnicity classification stratum as the lowest level variable. However, where there was only one race/ethnicity classification stratum within a particular urbanicity stratum, categorized achievement, median income, or enrollment data were used instead.

Public School Sample at Grade 12

The initial weighting cells for this sample were formed using the following nesting cell structure: census division stratum,

urbanicity stratum (urban-centric locale), and race/ethnicity classification stratum.

Private School Samples at Grades 4, 8 and 12

The initial weighting cells for these samples were formed within each grade using the following nesting cell structure: affiliation,

census division stratum,

urbanicity stratum (urban-centric locale), and race/ethnicity classification stratum.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/development_of_initial_school_nonresponse_cells_for_the_2013_assessment.aspx

NAEP Technical Documentation Development of Final School Nonresponse Cells

Limits were placed on the magnitude of cell sizes and adjustment factors to prevent unstable nonresponse adjustments

and unacceptably large nonresponse factors. All initial weighting cells with fewer than six cooperating schools or adjustment factors greater than 3.0 for the full sample weight were collapsed with suitable adjacent cells. Simultaneously, all initial weighting cells for any replicate with fewer than four cooperating schools or adjustment factors greater than the maximum of

0. or two times the full sample nonresponse adjustment factor were collapsed with suitable adjacent cells. Initial weighting cells were generally collapsed in reverse order of the cell structure; that is, starting at the bottom of the nesting structure and working up toward the top level of the nesting structure.

Public School Samples at Grades 4 and 8

For the grade 4 and 8 public school samples, cells with the most similar race/ethnicity classification within a

given jurisdiction/Trial Urban District Assessment (TUDA) district and urbanicity (urban-centric locale) stratum were collapsed first. If further collapsing was required after all levels of race/ethnicity strata were collapsed, cells with the most similar urbanicity strata were combined next. Cells were never permitted to be collapsed across jurisdictions or TUDA districts.

Public School Sample at Grades 12

For the grade 12 public school sample, race/ethnicity classification cells within a given census division stratum and urbanicity stratum were collapsed first. If further collapsing was required after all levels of race/ethnicity classification were collapsed, cells with the most similar urbanicity strata were combined next. Any further collapsing occurred across census division strata but never across census regions.

Private School Samples at Grades 4, 8, and 12

For the private school samples, cells with the most similar race/ethnicity classification within a given affiliation, census division, and urbanicity stratum were collapsed first. If further collapsing was required after all levels of race/ethnicity strata were collapsed, cells with the most similar urbanicity classification were combined. Any further collapsing occurred across census division strata but never across affiliations.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/development_of_final_school_nonresponse_cells_for_the_2013_assessment.aspx

NAEP Technical Documentation School Nonresponse Adjustment Factor Calculation

In each final school nonresponse adjustment cell c, the school nonresponse adjustment factor SCH_NRAF_c was computed as follows:

where

S_c is the set of all eligible sampled schools (cooperating original and substitute schools and refusing original schools with noncooperating or no assigned substitute) in cell c,

R_c is the set of all cooperating schools within S_c, SCH_BWT_s is the school base weight,

SCH_TRIM_s is the school-level weight trimming factor, SCHSESWT_s is the school-level session assignment weight, and

X_s is the estimated grade enrollment corresponding to the original sampled school.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/school_nonresponse_adjustment_factor_calculation_for_the_2013_assessment.aspx

NAEP Technical Documentation Student Nonresponse Weight Adjustment

The student nonresponse adjustment procedure inflates the weights of assessed students to account for eligible sampled students who did not participate in the assessment. These inflation factors offset the loss of data associated with absent students. The adjustments are computed within nonresponse cells and are based on the assumption that the assessed and absent students within the same cell are more similar to one another than to students from different cells. Like its counterpart at the school level, the student nonresponse adjustment is

Development of Initial Student Nonresponse Cells

Development of Final Student Nonresponse Cells

Student Nonresponse Adjustment Factor Calculation

intended to reduce the mean square error and thus improve the accuracy of NAEP assessment estimates. Also, like its counterpart at the school level, student nonresponse adjustments were carried out separately by sample; that is, by

grade (4, 8, 12),

school type (public, private), and

assessment subject (mathematics, reading, science, meaning vocabulary).

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/student_nonresponse_weight_adjustment_for_the_2013_assessment.aspx

NAEP Technical Documentation Development of Initial Student Nonresponse Cells for the 2013 Assessment

Initial student nonresponse cells are generally created within each sample as defined by grade, school type (public, private), and assessment subject. However, when subjects are administered together by way of spiraling, the initial student nonresponse cells are created across the subjects in the same spiral. The rationale behind this decision is that spiraled subjects are in the same schools and the likelihood of whether an eligible student participates in an assessment is more related to its school than the subject of the assessment booklet. In NAEP 2013, there was only one spiral, with the reading and mathematics assessments spiraled together. The initial student nonresponse cells for the various NAEP 2013 samples are described below.

Nonresponse adjustment procedures are not applied to excluded students because they are not required to complete an assessment.

Public School Samples for Reading and Mathematics at Grades 4 and 8

The initial student nonresponse cells for these samples were defined within grade, jurisdiction, and Trial Urban District Assessment (TUDA) district using the following nesting cell structure:

students with disabilities (SD)/English language learners (ELL) by subject, school nonresponse cell,

age (classified into "older"¹ student and "modal age or younger" student), gender, and

race/ethnicity.

The highest level variable in the cell structure separates students who were classified either as having disabilities (SD) or as English language learners (ELL) from those who are neither, since SD or ELL students tend to score lower on assessment tests than non-SD/non-ELL students. In addition, the students in the SD or ELL groups are further broken down by subject, since rules for excluding students from the assessment differ by subject. Non-SD and non-ELL students are not broken down by subject, since the exclusion rules do not apply to them.

Public School Samples for Reading and Mathematics at Grade 12

The initial weighting cells for these samples were formed hierarchically within state for the state-reportable samples and the balance of the country for remaining states as follows:

SD/ELL,

school nonresponse cell,

age (classified into "older"¹ student and "modal age or younger" student), gender, and

race/ethnicity.

Private School Samples for Reading and Mathematics at Grades 4, 8, and 12

The initial weighting cells for these private school samples were formed hierarchically within grade as follows: SD/ELL,

school nonresponse cell,

age (classified into "older"¹ student and "modal age or younger" student), gender, and

race/ethnicity.

Although exclusion rules differ by subject, there were not enough SD or ELL private school students to break out by subject as was done for the public schools.

¹Older students are those born before October 1, 2002, for grade 4; October 1, 1998, for grade 8; and October 1, 1994, for

grade 12.

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NAEP Technical Documentation Development of Final Student Nonresponse Cells for the 2013 Assessment

Similar to the school nonresponse adjustment, cell and adjustment factor size constraints are in place to prevent unstable nonresponse adjustments or unacceptably large adjustment factors. All initial weighting cells with either fewer than 20 participating students or adjustment factors greater than 2.0 for the full sample weight were collapsed with suitable adjacent cells. Simultaneously, all initial weighting cells for any replicate with either fewer than 15 participating students or an adjustment factor greater than the maximum of 2.0 or 1.5 times the full sample nonresponse adjustment factor were collapsed with suitable adjacent cells.

Initial weighting cells were generally collapsed in reverse order of the cell structure; that is, starting at the bottom of the nesting structure and working up toward the top level of the nesting structure. Race/ethnicity cells within SD/ELL groups, school nonresponse cell, age, and gender classes were collapsed first. If further collapsing was required after collapsing all race/ethnicity classes, cells were next combined across gender, then age, and finally school nonresponse cells. Cells are never collapsed across SD and ELL groups for any sample.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/development_of_final_student_nonresponse_cells_for_the_2013_assessment.aspx

NAEP Technical Documentation Student Nonresponse Adjustment Factor Calculation

In each final student nonresponse adjustment cell c for a given sample, the student nonresponse adjustment factor STU_NRAF_c was computed as follows:

where

S_c is the set of all eligible sampled students in cell c for a given sample, R_c is the set of all assessed students within S_c,

STU_BWT_k is the student base weight for a given student k,

SCH_TRIM_k is the school-level weight trimming factor for the school associated with student k, SCH_NRAF_k is the school-level nonresponse adjustment factor for the school associated with student k, and SUBJFAC_k is the subject factor for a given student k.

The student weight used in the calculation above is the adjusted student base weight, without regard to subject, adjusted for school weight trimming and school nonresponse.

Nonresponse adjustment procedures are not applied to excluded students because they are not required to complete an assessment. In effect, excluded students were placed in a separate nonresponse cell by themselves and all received an adjustment factor of 1. While excluded students are not included in the analysis of the NAEP scores, weights are provided for excluded students in order to estimate the size of this group and its population characteristics.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/student_nonresponse_adjustment_factor_calculation_for_the_2013_assessment.aspx

NAEP Technical Documentation School and Student Weight Trimming Adjustments for the 2013 Assessment

Weight trimming is an adjustment procedure that involves detecting and reducing extremely large weights. "Extremely large weights" generally refer to large sampling weights that were not anticipated in the design of the sample. Unusually large weights are likely to produce large sampling variances for statistics of interest, especially when the large weights are associated with sample cases reflective of rare or atypical characteristics. To reduce the impact of these large weights on variances, weight reduction methods are typically employed. The goal of employing weight reduction methods is to reduce the mean square error of survey estimates. While the

Trimming of School Base Weights

Trimming of Student Weights

trimming of large weights reduces variances, it also introduces some bias. However, it is presumed that the reduction in the variances more than compensates for the increase in the bias, thereby reducing the mean square error and thus improving the accuracy of survey estimates (Potter 1988). NAEP employs weight trimming at both the school and student levels.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/school_and_student_weight_trimming_adjustments_for_the_2013_assessment.aspx

NAEP Technical Documentation Trimming of School Base Weights

Large school weights can occur for schools selected from the NAEP new-school sampling frame and for private schools. New schools that are eligible for weight trimming are schools with a disproportionately large student enrollment in a particular grade from a school district that was selected with a low probability of selection. The school base weights for such schools may be large relative to what they would have been if they had been selected as part of the original sample.

To detect extremely large weights among new schools, a comparison was made between a new school's school base weight and its ideal weight (i.e., the weight that would have resulted had the school been selected from the original school sampling frame). If the school base weight was more than three times the ideal weight, a trimming factor was calculated for that school that scaled the base weight back to three times the ideal weight. The calculation of the school-level trimming factor for a new school s is expressed in the following formula:

where

EXP_WT_s is the ideal base weight the school would have received if it had been on the NAEP public school sampling frame, and

SCH_BWT_s is the actual school base weight the school received as a sampled school from the new school frame.

Thirty-seven (37) schools out of 377 selected from the new-school sampling frame had their weights trimmed: eight at grade 4, 29 at grade 8, and zero at grade 12.

Private schools eligible for weight trimming were Private School Universe Survey (PSS) nonrespondents who were found subsequently to have either larger enrollments than assumed at the time of sampling, or an atypical probability of selection given their affiliation, the latter being unknown at the time of sampling. For private school s, the formula for computing the school-level weight trimming factor SCH_TRIM_s is identical to that used for new schools. For private schools,

EXP_WT_s is the ideal base weight the school would have received if it had been on the NAEP private school sampling frame with accurate enrollment and known affiliation, and

SCH_BWT_s is the actual school base weight the school received as a sampled private school.

No private schools had their weights trimmed.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/trimming_of_school_base_weights_for_the_2013_assessment.aspx

NAEP Technical Documentation Trimming of Student Weights

Large student weights generally come from compounding nonresponse adjustments at the school and student levels with artificially low school selection probabilities, which can result from inaccurate enrollment data on the school frame used to define the school size measure. Even though measures are in place to limit the number and size of excessively large weights—such as the implementation of adjustment factor size constraints in both the school and student nonresponse procedures and the use of the school trimming procedure—large student weights can occur due to compounding effects of the various weighting components.

The student weight trimming procedure uses a multiple median rule to detect excessively large student weights. Any student weight within a given trimming group greater than a specified multiple of the median weight value of the given trimming group has its weight scaled back to that threshold. Student weight trimming was implemented separately by grade, school type (public or private), and subject. The multiples used were 3.5 for public school trimming groups and 4.5 for private school trimming groups. Trimming groups were defined by jurisdiction and Trial Urban District Assessment (TUDA) districts for the public school samples at grades 4 and 8; by dichotomy of low/high percentage of Black and Hispanic students (15 percent and below, above 15 percent) for the public school sample at grade 12; and by affiliation (Catholic, Non-Catholic) for private school samples at grades 4, 8 and 12.

The procedure computes the median of the nonresponse-adjusted student weights in the trimming group g for a given grade and subject sample. Any student k with a weight more than M times the median received a trimming factor calculated as follows:

where

M is the trimming multiple,

MEDIAN_g is the median of nonresponse-adjusted student weights in trimming group g, and STUWGT_gk is the weight after student nonresponse adjustment for student k in trimming group g.

In the 2013 assessment, relatively few students had weights considered excessively large. Out of the approximately 840,000 students included in the combined 2013 assessment samples, 226 students had their weights trimmed.

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NAEP Technical Documentation Student Weight Raking Adjustment for the 2013 Assessment

Weighted estimates of population totals for student-level subgroups for a given grade will vary across subjects even though the student samples for each subject generally come from the same schools. These differences are the result of sampling error associated with the random assignment of subjects to students through a process known as spiraling. For state assessments in particular, any

Development of Final Raking Dimensions Raking Adjustment Control Totals

Raking Adjustment Factor Calculation

difference in demographic estimates between subjects, no matter how small, may raise concerns about data quality. To remove these random differences and potential data quality concerns, a new step was added to the NAEP weighting procedure starting in 2009. This step adjusts the student weights in such a way that the weighted sums of population totals for specific subgroups are the same across all subjects. It was implemented using a raking procedure and applied only to state-level assessments.

Raking is a weighting procedure based on the iterative proportional fitting process developed by Deming and Stephan (1940) and involves simultaneous ratio adjustments to two or more marginal distributions of population totals. Each set of marginal population totals is known as a dimension, and each population total in a dimension is referred to as a control total. Raking is carried out in a sequence of adjustments. Sampling weights are adjusted to one marginal distribution and then to the second marginal distribution, and so on. One cycle of sequential adjustments to the marginal distributions is called an iteration. The procedure is repeated until convergence is achieved. The criterion for convergence can be specified either as the maximum number of iterations or an absolute difference (or relative absolute difference) from the marginal population totals. More discussion on raking can be found in Oh and Scheuren (1987).

For NAEP 2013, the student raking adjustment was carried out separately in each state for the reading

and mathematics public school samples at grades 4 and 8, and in the 13 states with state-reportable samples for the reading and mathematics public school samples at grade 12. The dimensions used in the raking process were National School Lunch Program (NSLP) eligibility, race/ethnicity, SD/ELL status, and gender. The control totals for these dimensions were obtained from the NAEP student sample weights of the reading

and mathematics samples combined.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/student_weight_raking_adjustment_for_the_2013_assessment.aspx

NAEP Technical Documentation Development of Final Raking Dimensions

The raking procedure involved four dimensions. The variables used to define the dimensions are listed below along with the categories making up the initial raking cells for each dimension.

National School Lunch Program (NSLP) eligibility

1. Eligible for free or reduced-price lunch

2. Otherwise Race/Ethnicity

1. White, not Hispanic

2. Black, not Hispanic

3. Hispanic

4. Asian

5. American Indian/Alaska Native

6. Native Hawaiian/Pacific Islander

7. Two or More Races SD/ELL status

1. SD, but not ELL

2. ELL, but not SD

3. SD and ELL

4. Neither SD nor ELL Gender

1. Male

2. Female

In states containing districts that participated in Trial Urban District Assessments (TUDA) districts at grades 4 and 8, the initial cells were created separately for each TUDA district and the balance of the state. Similar to the procedure used for school and student nonresponse adjustments, limits were placed on the magnitude of the cell sizes and adjustment factors to prevent unstable raking adjustments that could have resulted in unacceptably large or small adjustment factors. Levels of a dimension were combined whenever there were fewer than 30 assessed or excluded students (20 for any of the replicates) in a category, if the smallest adjustment was less than 0.5, or if the largest adjustment was greater than 2 for the full sample or for any replicate.

If collapsing was necessary for the race/ethnicity dimension, the following groups were combined first: American Indian/Alaska Native with Black, not Hispanic; Hawaiian/Pacific Islander with Black, not Hispanic; Two or More Races with White, not Hispanic; Asian with White, not Hispanic; and Black, not Hispanic with Hispanic. If further collapsing was necessary, the five categories American Indian/Alaska Native; Two or More Races; Asian; Native Hawaiian/Pacific Islander; and White, not Hispanic were combined. In some instances, all seven categories had to be collapsed.

If collapsing was necessary for the SD/ELL dimension, the SD/not ELL and SD/ELL categories were combined first, followed by ELL/not SD if further collapsing was necessary. In some instances, all four categories had to be collapsed.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/development_of_final_raking_dimensions_for_the_2013_assessment.aspx

NAEP Technical Documentation Raking Adjustment Control Totals for the 2013 Assessment

The control totals used in the raking procedure for NAEP 2013 grades 4, 8, and 12 were estimates of the student population derived from the set of assessed and excluded students pooled across subjects. The control totals for category c within dimension d were computed as follows:

where

R_c(d) is the set of all assessed students in category c of dimension d, E_c(d) is the set of all excluded students in category c of dimension d, STU_BWT_k is the student base weight for a given student k,

SCH_TRIM_k is the school-level weight trimming factor for the school associated with student k, SCH_NRAF_k is the school-level nonresponse adjustment factor for the school associated with student k, STU_NRAF_k is the student-level nonresponse adjustment factor for student k, and

SUBJFAC_k is the subject factor for student k.

The student weight used in the calculation of the control totals above is the adjusted student base weight, without regard to subject, adjusted for school weight trimming, school nonresponse, and student nonresponse. Control totals were computed for the full sample and for each replicate independently.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/raking_adjustment_control_totals_for_the_2013_assessment.aspx

NAEP Technical Documentation Raking Adjustment Factor Calculation for the 2013 Assessment

For assessed and excluded students in a given subject, the raking adjustment factor STU_RAKE_k was computed as follows:

First, the weight for student k was initialized as follows:

where

STU_BWT_k is the student base weight for a given student k,

SCH_TRIM_k is the school-level weight trimming factor for the school associated with student k, SCH_NRAF_k is the school-level nonresponse adjustment factor for the school associated with student k, STU_NRAF_k is the student-level nonresponse adjustment factor for student k, and

SUBJFAC_k is the subject factor for student k.

Then, the sequence of weights for the first iteration was calculated as follows for student k in category c of dimension d:

For dimension 1:

For dimension 2:

For dimension 3:

For dimension 4:

where

R_c(d) is the set of all assessed students in category c of dimension d, E_c(d) is the set of all excluded students in category c of dimension d, and Total_c(d) is the control total for category c of dimension d.

k

The process is said to converge if the maximum difference between the sum of adjusted weights and the control totals is 1.0 for each category in each dimension. If after the sequence of adjustments the maximum difference was greater than 1.0, the process continues to the next iteration, cycling back to the first dimension with the initial weight for student k equaling STUSAWT ^adj(4) from the previous iteration. The process continued until

convergence was reached.

Once the process converged, the adjustment factor was computed as follows:

where STUSAWT_k is the weight for student k after convergence.

The process was done independently for the full sample and for each replicate.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/raking_adjustment_factor_calculation_for_the_2013_assessment.aspx

NAEP Technical Documentation Website

NAEP Technical Documentation Computation of Replicate Weights for the 2013 Assessment

In addition to the full-sample weight, a set of 62 replicate weights was provided for each student. These replicate weights are used in calculating the sampling variance of estimates obtained from the data, using the jackknife repeated replication method. The method of deriving these weights was aimed at reflecting the features of the sample design appropriately for each sample, so that when the jackknife variance estimation procedure is implemented, approximately unbiased estimates of sampling variance are

obtained. This section gives the specifics for generating the

Defining Variance Strata and Forming Replicates

Computing School-Level Replicate Factors

Computing Student-Level Replicate Factors

Replicate Variance Estimation

replicate weights for the 2013 assessment samples. The theory that underlies the jackknife variance estimators used in NAEP studies is discussed in the section Replicate Variance Estimation.

In general, the process of creating jackknife replicate weights takes place at both the school and student level. The precise implementation differs between those samples that involve the selection of Primary Sampling Units (PSUs) and those where the school is the first stage of sampling. The procedure for this second kind of sample also differed starting in 2011 from all previous NAEP assessments. The change that was implemented permitted the introduction of a finite population correction factor at the school sampling stage, developed by Rizzo and Rust (2011). In assessments prior to 2011, this adjustment factor has always been implicitly assumed equal to 1.0, resulting in some overestimation of the sampling variance.

For each sample, the calculation of replicate weighting factors at the school level was conducted in a series of steps. First, each school was assigned to one of 62 variance estimation strata. Then, a random subset of schools in each variance estimation stratum was assigned a replicate factor of between 0 and 1. Next, the remaining subset of schools in the same variance stratum was assigned a complementary replicate factor greater than 1. All schools in the other variance estimation strata were assigned a replicate factor of exactly 1. This process was repeated for each of the 62 variance estimation strata so that 62 distinct replicate factors were assigned to each school in the sample.

This process was then repeated at the student level. Here, each individual sampled student was assigned to one of 62 variance estimation strata, and 62 replicate factors with values either between 0 and 1, greater than 1, or exactly equal to 1 were assigned to each student.

For example, consider a single hypothetical student. For replicate 37, that student’s student replicate factor might be 0.8, while for the school to which the student belongs, for replicate 37, the school replicate factor might be 1.6. Of course, for a given student, for most replicates, either the student replicate factor, the school replicate factor, or (usually) both, is equal to 1.0.

A replicate weight was calculated for each student, for each of the 62 replicates, using weighting procedures similar to those used for the full-sample weight. Each replicate weight contains the school and student replicate factors described above. By repeating the various weighting procedures on each set of replicates, the impact of these procedures on the sampling variance of an estimate is appropriately reflected in the variance estimate.

Each of the 62 replicate weights for student k in school s in stratum j can be expressed as follows:

where

STU_BWT_jsk is the student base weight;

SCH_REPFAC_js(r) is the school-level replicate factor for replicate r; SCH_NRAF_js(r) is the school-level nonresponse adjustment factor for replicate r; STU_REPFAC_jsk(r) is the student-level replicate factor for replicate r; STU_NRAF_jsk(r) is the student-level nonresponse adjustment factor for replicate r; SCH_TRIM_js is the school-level weight trimming adjustment factor; STU_TRIM_jsk is the student-level weight trimming adjustment factor; and STU_RAKE_jsk(r) is the student-level raking adjustment factor for replicate r.

Specific school and student nonresponse and student-level raking adjustment factors were calculated separately for each replicate, thus the use of the index (r), and applied to the replicate student base weights. Computing separate nonresponse and raking adjustment factors for each replicate allows resulting variances from the use of the final student replicate weights to reflect components of variance due to these various weight adjustments.

School and student weight trimming adjustments were not replicated, that is, not calculated separately for each replicate. Instead, each replicate used the school and student trimming adjustment factors derived for the full sample. Statistical theory for replicating trimming adjustments under the jackknife approach has not been developed in the literature. Due to the absence of a statistical framework, and since relatively few school and student weights in NAEP require trimming, the weight trimming adjustments were not replicated.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/computation_of_replicate_weights_for_the_2013_assessment.aspx

NAEP Technical Documentation Defining Variance Strata and Forming Replicates for the 2013 Assessment

In the NAEP 2013 assessment, replicates were formed separately for each sample indicated by grade (4, 8, 12), school type (public, private), and assessment subject (mathematics, reading). To reflect the school-level finite population corrections in the variance estimators for the two-stage samples used for the mathematics and reading assessments, replication was carried out at both the school and student levels.

The first step in forming replicates was to create preliminary variance strata in each primary stratum. This was done by sorting the appropriate sampling unit (school or student) in the order of its selection within the primary stratum and then pair off adjacent sampling units into preliminary variance strata. Sorting sample units by their order of sample selection reflects the implicit stratification and systematic sampling features of the sample design. Within each primary stratum with an even number of sampling units, all of the preliminary variance strata consisted of pairs of sampling units. However, within primary strata with an odd number of sampling units, all but one variance strata consisted of pairs of sampling units, while the last one consisted of three sampling units.

The next step is to form the final variance strata by combining preliminary strata if appropriate. If there were more than 62 preliminary variance strata within a primary stratum, the preliminary variance strata were grouped to form 62 final variance strata. This grouping effectively maximized the distance in the sort order between grouped preliminary variance strata. The first 62 preliminary variance strata, for example, were assigned to 62 different final variance strata in order (1 through 62), with the next 62 preliminary variance strata assigned to final variance strata 1 through 62, so that, for example, preliminary variance stratum 1, preliminary variance stratum 63, preliminary variance stratum 125 (if in fact there were that many), etc., were all assigned to the first final variance stratum.

If, on the other hand, there were fewer than 62 preliminary variance strata within a primary stratum, then the number of final variance strata was set equal to the number of preliminary variance strata. For example, consider a primary stratum with 111 sampled units sorted in their order of selection. The first two units were in the first preliminary variance stratum; the next two units were in the second preliminary variance stratum, and so on, resulting in 54 preliminary variance strata with two sample units each (doublets). The last three sample units were in the 55th preliminary variance stratum (triplet). Since there are no more than 62 preliminary variance strata, these were also the final variance strata.

Within each preliminary variance stratum containing a pair of sampling units, one sampling unit was randomly assigned as the first variance unit and the other as the second variance unit. Within each preliminary variance stratum containing three sampling units, the three first-stage units were randomly assigned variance units 1 through 3.

Reading and Mathematics Assessments

At the school-level for these samples, formation of preliminary variance strata did not pertain to certainty schools, since they are not subject to sampling variability, but only to noncertainty schools. The primary stratum for noncertainty schools was the highest school-level sampling stratum variable listed below, and the order of selection was defined by sort order on the school sampling frame.

Trial Urban District Assessment (TUDA) districts, remainder of states (for states with TUDAs), or entire states for the public school samples at grades 4, 8, and 12; and

Private school affiliation (Catholic, non-Catholic) for the private school samples at grades 4, 8, and 12.

At the student-level, all students were assigned to variance strata. The primary stratum was school, and the order of selection was defined by session number and position on the administration schedule.

Within each pair of preliminary variance strata, one first-stage unit, designated at random, was assigned as the first variance unit and the other first-stage unit as the second variance unit. Within each triplet preliminary variance stratum, the three schools were randomly assigned variance units 1 through 3.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/defining_variance_strata_and_forming_replicates_for_the_2013_assessment.aspx

NAEP Technical Documentation Computing School- Level Replicate Factors for the 2013 Assessment

The replicate variance estimation approach for the mathematics and reading assessments involved finite population corrections at the school level. The calculation of school-level replicate factors for these assessments depended upon whether or not a school was selected with certainty. For certainty schools, the school-level replicate factors for all replicates are set to unity – this is true regardless of whether or not the variance replication method uses finite population corrections – since certainty schools are not subject to sampling variability. Alternatively, one can view the finite population correction factor for such schools as being equal to zero. Thus, for each certainty school in a given assessment, the school-level replicate factor for each of the 62 replicates (r = 1, ..., 62) was assigned as follows:

where SCH_REPFAC_js(r) is the school-level replicate factor for school s in primary stratum j for the r-th replicate.

For noncertainty schools, where preliminary variance strata were formed by grouping schools into pairs or triplets, school-level replicate factors were calculated for each of the 62 replicates based on this grouping. For schools in variance strata comprising pairs of schools, the school-level replicate factors,SCH_REPFAC_js(r),r = 1,..., 62, were calculated as follows:

where

min(π_j1, π_j2) is the smallest school probability between the two schools comprising R_jr,

R_jr is the set of schools within the r-th variance stratum for primary stratum j, and U_js is the variance unit (1 or 2) for school s in primary stratum j.

For noncertainty schools in preliminary variance strata comprising three schools, the school-level replicate factors SCH_REPFAC_js(r), r = 1,..., 62 were calculated as follows:

For school s from primary stratum j, variance stratum r,

while for r' = r + 31 (mod 62):

and for all other r* other than r and r' :

where

min(π_j1, π_j2,π_j3) is the smallest school probability among the three schools comprising R_jr,

R_jr is the set of schools within the r-th variance stratum for primary stratum j, and U_js is the variance unit (1, 2, or 3) for school s in primary stratum j.

In primary strata with fewer than 62 variance strata, the replicate weights for the “unused” variance strata (the remaining ones up to 62) for these schools were set equal to the school base weight (so that those replicates contribute nothing to the variance estimate).

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/computing_school_level_replicate_factors_for_the_2013_assessment_.aspx

NAEP Technical Documentation Website

NAEP Technical Documentation Computing Student- Level Replicate Factors for the 2013 Assessment

For the mathematics and reading assessments, which involved school-level finite population corrections, the student- level replication factors were calculated the same way regardless of whether or not the student was in

a certainty school.

For students in student-level variance strata comprising pairs of students, the student-level replicate factors, STU_REPFAC_jsk(r), r = 1,..., 62, were calculated as follows:

where

π_s is the probability of selection for school s,

R_jsr is the set of students within the r-th variance stratum for school s in primary stratum j, and U_jsk is the variance unit (1 or 2) for student k in school s in stratum j.

For students in variance strata comprising three students, the student-level replicate factors STU_REPFAC_jsk(r), r = 1,..., 62, were calculated as follows:

while for r' = r + 31 (mod 62):

and for all other r* other than r and r' :

where

π_s is the probability of selection for school s,

R_jsr is the set of students within the r-th replicate stratum for school s in stratum j, and U_jsk is the variance unit (1, 2, or 3) for student k in school s in stratum j.

Note, for students in certainty schools, where π_s = 1, the student replicate factors are 2 and 0 in the case of pairs, and 1.5, 1.5, and 0 in the case of triples.

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NAEP Technical Documentation Website

NAEP Technical Documentation Replicate Variance Estimation for the 2013 Assessment

Variances for NAEP assessment estimates are computed using the paired jackknife replicate variance procedure. This technique is applicable for common statistics, such as means and ratios, and differences between these for different subgroups, as well as for more complex statistics such as linear or logistic regression coefficients.

In general, the paired jackknife replicate variance procedure involves initially pairing clusters of first-stage sampling units to form H variance strata (h = 1, 2, 3, ...,H) with two units per stratum. The first replicate is formed by assigning, to one unit at random from the first variance stratum, a replicate weighting factor of less than 1.0, while assigning the remaining unit a complementary replicate factor greater than 1.0, and assigning all other units from the other (H - 1) strata a replicate factor of 1.0. This procedure is carried out for each variance stratum resulting in H replicates, each of which provides an estimate of the population total.

In general, this process is repeated for subsequent levels of sampling. In practice, this is not practicable for a design with three or more stages of sampling, and the marginal improvement in precision of the variance estimates would be negligible in all such cases in the NAEP setting. Thus in NAEP, when a two-stage design is used – sampling schools and then students – beginning in 2011 replication is carried out at both stages. (See Rizzo and Rust (2011) for a description of the methodology.) When a three-stage design is used, involving the selection of geographic Primary Sampling Units (PSUs), then schools, and then students, the replication procedure is only carried out at the first stage of sampling (the PSU stage for noncertainty PSUs, and the school stage within certainty PSUs). In this situation, the school and student variance components are correctly estimated, and the overstatement of the between-PSU variance component is relatively very small.

The jackknife estimate of the variance for any given statistic is given by the following formula:

where

represents the full sample estimate of the given statistic, and represents the corresponding estimate for replicate h.

Each replicate undergoes the same weighting procedure as the full sample so that the jackknife variance estimator reflects the contributions to or reductions in variance resulting from the various weighting adjustments.

The NAEP jackknife variance estimator is based on 62 variance strata resulting in a set of 62 replicate weights assigned to each school and student.

The basic idea of the paired jackknife variance estimator is to create the replicate weights so that use of the jackknife procedure results in an unbiased variance estimator for simple totals and means, which is also reasonably efficient (i.e., has a low variance as a variance estimator). The jackknife variance estimator will then produce a consistent (but not fully unbiased) estimate of variance for (sufficiently smooth) nonlinear functions of total and mean estimates such as ratios, regression coefficients, and so forth (Shao and Tu, 1995).

The development below shows why the NAEP jackknife variance estimator returns an unbiased variance estimator for totals and means, which is the cornerstone to the asymptotic results for nonlinear estimators. See for example Rust (1985). This paper also discusses why this variance estimator is generally efficient (i.e., more reliable than alternative approaches requiring similar computational resources).

The development is done for an estimate of a mean based on a simplified sample design that closely approximates the sample design for first-stage units used in the NAEP studies. The sample design is a stratified random sample with H strata with population weights W_h, stratum sample sizes n_h, and stratum

sample means . The population estimator and standard unbiased variance estimator are:

with

The paired jackknife replicate variance estimator assigns one replicate h=1,…, H to each stratum, so that the number of replicates equals H. In NAEP, the replicates correspond generally to pairs and triplets (with the latter only being used if there are an odd number of sample units within a particular primary stratum generating replicate strata). For pairs, the process of generating replicates can be viewed as taking a simple random sample (J) of size n_h/2 within the replicate stratum, and assigning an increased weight to the sampled elements, and a decreased weight to the unsampled elements. In certain applications, the increased weight is double the full sample weight, while the decreased weight is in fact equal to zero. In this

simplified case, this assignment reduces to replacing with , the latter being the sample mean of the sampled n_h/2 units. Then the replicate estimator corresponding to stratum r is

The r-th term in the sum of squares for is thus:

In stratified random sampling, when a sample of size n_r/2 is drawn without replacement from a population of size n_r,, the sampling variance is

See for example Cochran (1977), Theorem 5.3, using n_r, as the “population size,” n_r/2 as the “sample size,” and s_r² as the “population variance” in the given formula. Thus,

Taking the expectation over all of these stratified samples of size n_r/2, it is found that

In this sense, the jackknife variance estimator “gives back” the sample variance estimator for means and totals as desired under the theory.

In cases where, rather than doubling the weight of one half of one variance stratum and assigning a zero weight to the other, the weight of one unit is multiplied by a replicate factor of (1+δ), while the other is multiplied by (1- δ), the result is that

In this way, by setting δ equal to the square root of the finite population correction factor, the jackknife variance estimator is able to incorporate a finite population correction factor into the variance estimator.

In practice, variance strata are also grouped to make sure that the number of replicates is not too large (the total number of variance strata is usually 62 for NAEP). The randomization from the original sample distribution guarantees that the sum of squares contributed by each replicate will be close to the target expected value.

For triples, the replicate factors are perturbed to something other than 1.0 for two different replicate factors, rather than just one as in the case of pairs. Again in the simple case where replicate factors that are less than 1 are all set to 0, with the replicate weight factors calculated as follows.

For unit i in variance stratum r

where weight w_i is the full sample base weight.

Furthermore, for r' = r + 31 (mod 62):

And for all other values r*, other than r and r´,w_i(r*) = 1.

In the case of stratified random sampling, this formula reduces to replacing with for replicate r, where is the sample mean from a “2/3” sample of 2n_r/3 units from the n_r sample units

in the replicate stratum, and replacing with for replicate r', where is the sample mean from another overlapping “2/3” sample of 2n_r/3 units from the n_r sample units in the replicate stratum.

The r-th and r´-th replicates can be written as:

From these formulas, expressions for the r-th and r´-th components of the jackknife variance estimator are obtained (ignoring other sums of squares from other grouped components attached to those replicates):

These sums of squares have expectations as follows, using the general formula for sampling variances:

Thus,

as desired again.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/replicate_variance_estimation_for_the_2013_assessment.aspx

NAEP Technical Documentation Website

NAEP Technical Documentation Quality Control on Weighting Procedures for the 2013 Assessment

Given the complexity of the weighting procedures utilized in NAEP, a range of quality control (QC) checks was conducted throughout the weighting process to identify potential problems with collected student-level demographic data or with specific weighting procedures. The QC processes included

checks performed within each step of the weighting process; checks performed across adjacent steps of the weighting process; review of participation, exclusion, and accommodation rates; checking demographic data of individual schools;

comparisons with 2011 demographic data; and nonresponse bias analyses.

Final Participation, Exclusion, and Accommodation Rates

Nonresponse Bias Analyses

To validate the weighting process, extensive tabulations of various school and student characteristics at different stages of the process were conducted. The school-level characteristics included in the tabulations were minority

enrollment, median income (based on the school ZIP code area), and urban-centric locale. At the student level, the tabulations included race/ethnicity, gender, relative age, students with disability (SD) status, English language learners (ELL) status, and participation status in National School Lunch Program (NSLP).

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/quality_control_on_weighting_procedures_for_the_2013_assessment.aspx

NAEP Technical Documentation Website

NAEP Technical Documentation Final Participation, Exclusion, and Accommodation Rates for the 2013 Assessment

Final participation, exclusion, and accommodation rates are presented in quality control tables for each grade and subject by geographic domain and school type. School-level

participation rates have been calculated according to National Center for Education Statistics (NCES) standards as they have been for previous assessments.

School-level participation rates were below 85 percent for private schools at all three grades (4, 8, and 12). Student-level participation rates were also below 85 percent for grade 12 public school student sample overall and in specific states: Connecticut, Florida, Illinois, Iowa, Massachusetts, New Hampshire, New Jersey, and West Virginia. As required by NCES standards, nonresponse bias analyses were conducted on each reporting group falling below the 85 percent participation threshold.

Grade 4 Mathematics

Grade 4 Reading

Grade 8 Mathematics

Grade 8 Reading

Grade 12 Mathematics

Grade 12 Reading

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/final_participation_exclusion_and_accommodation_rates_for_the_2013_assessment.aspx

National all1

8,590

97.27

90.32

209,800

1.41

94.57

13.44

National public

8,060

99.69

99.54

202,700

1.52

94.49

14.22

NAEP Technical Documentation Website

NAEP Technical Documentation Participation, Exclusion, and Accommodation Rates for Grade 4 Mathematics for the 2013 Assessment

The following table displays the school- and student-level response, exclusion, and accommodation rates for the grade 4 mathematics assessment by school type and jurisdiction. Various weights were used in the calculation of the rates, as indicated in the column headings of the table.

The participation rates reflect the participation of the original sample schools only and do not reflect any effect of substitution. The rates weighted by the base weight and enrollment show the approximate proportion of the student population in the jurisdiction that is represented by the responding schools in the sample. The rates weighted by just the base weight show the proportion of the school population that is represented by the responding schools in the sample. These rates differ because schools differ in size.

Participation, exclusion, and accommodation rates, grade 4 mathematics assessment, by school type and jurisdiction: 2013

		School	School
		participation	participation
		rates	rates
	Number	(percent)	(percent)			Weighted
	of	before	before			student
	schools	substitution	substitution	Number	Weighted	participation
	in	(weighted	(weighted	of	percent	rates	Weighted
School type	original	by base	by base	students	of	(percent)	percent of
and	sample,	weight and	weight	sampled,	students	after	students
jurisdiction	rounded	enrollment)	only)	rounded	excluded	makeups	accommodated
All	8,760	97.30	90.45	214,900	1.40	94.57	13.55
Northeast all	1,480	95.63	85.22	34,500	1.29	93.85	15.68
Midwest all	2,190	97.27	88.80	47,300	1.32	94.84	12.87
South all	2,740	98.20	93.44	73,600	1.37	94.71	14.38
West all	2,120	96.86	91.04	51,800	1.62	94.57	10.98
Alabama	120	100.00	100.00	3,200	1.10	94.82	5.15
Alaska	200	99.48	96.56	3,100	1.14	93.18	21.85
Arizona	120	100.00	100.00	3,400	1.20	95.07	12.97
Arkansas	120	100.00	100.00	3,400	1.24	94.66	15.16
California	300	99.17	98.75	9,000	1.93	94.79	8.78
Colorado	120	100.00	100.00	3,400	1.15	92.34	12.11
Connecticut	120	97.22	97.25	3,200	1.36	93.85	15.52
Delaware	100	100.00	100.00	3,400	2.10	94.36	13.58
District of Columbia	140	100.00	100.00	2,300	1.37	95.09	17.59
Florida	240	100.00	100.00	6,900	1.84	94.11	20.24
Georgia	170	100.00	100.00	5,300	1.43	94.18	11.22
Hawaii	120	100.00	100.00	3,500	1.25	94.70	10.64
Idaho	130	100.00	100.00	3,500	1.29	95.24	9.58
Illinois	200	97.98	98.40	5,100	1.00	94.40	15.44
Indiana	120	100.00	100.00	3,300	1.52	95.18	17.03
Iowa	140	100.00	100.00	3,100	0.70	95.16	14.50
Kansas	150	100.00	100.00	3,400	1.62	94.79	15.16
Kentucky	160	100.00	100.00	4,700	1.45	94.67	11.30
Louisiana	130	100.00	100.00	3,300	1.08	94.49	18.38
Maine	160	100.00	100.00	3,400	2.11	93.95	17.44

Maryland	170	100.00	100.00	4,700	0.99	94.22	17.30
Massachusetts	190	100.00	100.00	5,200	2.03	93.74	17.18
Michigan	190	100.00	100.00	4,600	1.96	94.14	11.02
Minnesota	130	100.00	100.00	3,500	1.37	94.85	10.62
Mississippi	120	100.00	100.00	3,300	0.76	95.44	6.73
Missouri	130	100.00	100.00	3,600	1.41	95.42	11.20
Montana	200	99.85	98.28	3,400	1.68	93.92	8.56
Nebraska	170	100.00	100.00	3,500	1.72	95.37	14.37
Nevada	120	100.00	100.00	3,500	1.41	95.75	22.90
New Hampshire	130	100.00	100.00	3,400	1.22	93.74	14.78
New Jersey	120	100.00	100.00	3,300	1.17	94.85	16.62
New Mexico	150	99.69	99.48	4,200	1.22	95.06	16.90
New York	160	98.84	96.79	4,500	1.23	92.27	20.02
North Carolina	160	100.00	100.00	4,800	1.24	94.19	14.17
North Dakota	270	99.86	99.19	3,700	2.56	95.57	9.78
Ohio	210	100.00	100.00	4,700	1.33	94.29	13.52
Oklahoma	140	100.00	100.00	3,600	1.85	94.35	13.95
Oregon	130	100.00	100.00	3,500	2.12	94.18	15.23
Pennsylvania	170	100.00	100.00	4,500	1.64	94.30	12.95
Rhode Island	120	100.00	100.00	3,400	1.12	94.98	15.17
South Carolina	120	100.00	100.00	3,200	1.08	96.08	11.87
South Dakota	190	100.00	100.00	3,400	1.42	95.36	10.56
Tennessee	120	100.00	100.00	3,400	1.34	94.21	13.54
Texas	310	100.00	100.00	9,200	1.65	95.36	17.92
Utah	120	99.08	99.32	3,600	1.25	94.79	12.66
Vermont	220	100.00	100.00	3,000	1.37	95.04	15.72
Virginia	110	100.00	100.00	3,300	1.51	94.35	13.07
Washington	120	99.09	99.35	3,600	2.17	93.50	14.12
West Virginia	150	100.00	100.00	3,200	1.71	94.77	10.03
Wisconsin	190	100.00	100.00	4,400	1.79	95.42	16.21
Wyoming	200	100.00	100.00	3,500	1.01	94.65	12.76
DoDEA2	120	99.23	98.08	3,700	1.66	95.05	12.20
Trial Urban (TUDA) Districts and Other Jurisdictions
Albuquerque	50	100.00	100.00	1,700	1.15	94.71	20.47
Atlanta	60	100.00	100.00	2,000	0.98	95.42	9.76
Austin	60	100.00	100.00	1,700	2.04	93.69	30.80
Baltimore City	70	100.00	100.00	1,600	1.59	94.32	19.27
Boston	80	100.00	100.00	2,000	3.69	93.72	19.59
Charlotte	50	100.00	100.00	1,700	1.19	94.18	12.81
Chicago	100	100.00	100.00	2,500	1.07	94.85	19.30
Cleveland	90	100.00	100.00	1,500	4.26	93.62	22.29
Dallas	50	100.00	100.00	1,700	2.33	95.79	35.42
Detroit	70	100.00	100.00	1,300	4.88	90.92	14.80
Fresno	50	100.00	100.00	1,800	0.90	93.58	7.51
Hillsborough	60	100.00	100.00	1,700	1.17	95.74	23.30
Houston	80	100.00	100.00	2,600	1.88	96.62	27.25

Jefferson County, KY

50 100.00 100.00 1,700 1.74 94.66 11.61

Los Angeles 80 100.00 100.00 2,500 1.96 95.80 9.83

Miami 90 100.00 100.00 2,300 2.35 95.07 28.05

Milwaukee 70 100.00 100.00 1,500 3.40 94.68 26.55

New York City

80 100.00 100.00 2,500 1.33 91.74 27.56

Philadelphia 60 100.00 100.00 1,600 3.45 94.71 15.82

San Diego 50 100.00 100.00 1,500 1.48 95.18 11.80

National private

410

71.19

64.52

3,300

0.08

95.61

4.38

District of Columbia (TUDA)

90 100.00 100.00 1,500 1.97 95.52 18.06

Catholic 130 88.65 89.70 1,700 0.06 95.60 4.95

Non-Catholic private

280 56.94 52.97 1,600 0.11 95.62 3.92

Puerto Rico	170	100.00	100.00	5,100	0.24	94.47	27.19
Includes national public, national private, and Bureau of Indian Education schools located in the United States and all Department of Defense Education Activity schools, but not schools in Puerto Rico. Department of Defense Education Activity schools. NOTE: Numbers of schools are rounded to nearest ten, and numbers of students are rounded to nearest hundred. Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2013 Mathematics Assessment.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/participation_exclusion_and_accommodation_rates_for_grade_4_mathematics_for_the_2013_assessment.aspx

National all1

8,590

97.27

90.32

216,400

2.52

94.78

12.17

National public

8,060

99.69

99.54

209,100

2.69

94.70

12.87

NAEP Technical Documentation Website

NAEP Technical Documentation Participation, Exclusion, and Accommodation Rates for Grade 4 Reading for the 2013 Assessment

The following table displays the school- and student-level response, exclusion, and accommodation rates for the grade 4 reading assessment by school type and jurisdiction. Various weights were used in the calculation of the rates, as indicated in the column headings of the table.

The participation rates reflect the participation of the original sample schools only and do not reflect any effect of substitution. The rates weighted by the base weight and enrollment show the approximate proportion of the student population in the jurisdiction that is represented by the responding schools in the sample. The rates weighted by just the base weight show the proportion of the school population that is represented by the responding schools in the sample. These rates differ because schools differ in size.

Participation, exclusion, and accommodation rates, grade 4 r eading assessment, by school type and jurisdiction: 2013

		School	School
		participation	participation
		rates	rates
	Number	(percent)	(percent)			Weighted
	of	before	before			student
	schools	substitution	substitution	Number	Weighted	participation
	in	(weighted	(weighted	of	percent	rates	Weighted
School type	original	by base	by base	students	of	(percent)	percent of
and	sample,	weight and	weight	sampled,	students	after	students
jurisdiction	rounded	enrollment)	only)	rounded	excluded	makeups	accommodated
All	8,590	97.27	90.32	216,400	2.52	94.78	12.17
Northeast all	1,480	95.63	85.22	35,600	1.72	93.97	15.30
Midwest all	2,190	97.27	88.80	48,700	2.01	95.04	12.22
South all	2,740	98.20	93.44	76,000	3.39	95.00	12.25
West all	2,120	96.86	91.04	53,500	2.13	94.71	9.92
Alabama	120	100.00	100.00	3,400	1.14	95.49	5.39
Alaska	200	99.48	96.56	3,300	1.45	93.65	20.65
Arizona	120	100.00	100.00	3,500	1.08	95.46	13.24
Arkansas	120	100.00	100.00	3,600	1.11	95.16	15.34
California	300	99.17	98.75	9,300	2.50	94.88	7.73
Colorado	120	100.00	100.00	3,500	1.52	93.66	12.61
Connecticut	120	97.22	97.25	3,400	1.58	94.29	15.33
Delaware	100	100.00	100.00	3,500	4.70	94.34	10.38
District of Columbia	140	100.00	100.00	2,400	1.65	94.46	17.41
Florida	240	100.00	100.00	7,100	2.96	93.98	19.02
Georgia	170	100.00	100.00	5,400	4.90	95.34	8.13
Hawaii	120	100.00	100.00	3,600	1.80	93.97	10.48
Idaho	130	100.00	100.00	3,600	1.49	94.99	9.32
Illinois	200	97.98	98.40	5,200	1.24	95.13	14.76
Indiana	120	100.00	100.00	3,500	2.43	94.40	16.31
Iowa	140	100.00	100.00	3,200	1.08	95.11	14.42
Kansas	150	100.00	100.00	3,500	1.82	95.07	13.41
Kentucky	160	100.00	100.00	4,800	2.99	94.97	9.74
Louisiana	130	100.00	100.00	3,400	1.16	94.73	18.61
Maine	160	100.00	100.00	3,500	1.69	93.65	17.87
Maryland	170	100.00	100.00	4,900	12.86	94.40	5.70
Massachusetts	190	100.00	100.00	5,300	2.66	93.77	15.53
Michigan	190	100.00	100.00	4,800	3.81	94.64	9.66
Minnesota	130	100.00	100.00	3,600	2.71	94.93	9.61

Mississippi	120	100.00	100.00	3,400	0.53	94.99	6.85
Missouri	130	100.00	100.00	3,700	1.23	95.26	11.16
Montana	200	99.85	98.28	3,500	2.86	94.40	7.33
Nebraska	170	100.00	100.00	3,600	3.57	95.83	14.26
Nevada	120	100.00	100.00	3,700	1.50	95.10	22.73
New Hampshire	130	100.00	100.00	3,500	2.56	93.45	13.48
New Jersey	120	100.00	100.00	3,400	1.72	94.87	15.27
New Mexico	150	99.69	99.48	4,300	1.02	94.55	15.04
New York	160	98.84	96.79	4,600	1.35	93.06	20.15
North Carolina	160	100.00	100.00	5,000	1.80	94.88	13.06
North Dakota	270	99.86	99.19	3,800	4.06	96.28	8.73
Ohio	210	100.00	100.00	4,800	2.61	94.58	12.80
Oklahoma	140	100.00	100.00	3,700	1.72	94.58	14.35
Oregon	130	100.00	100.00	3,700	2.49	93.98	12.20
Pennsylvania	170	100.00	100.00	4,600	2.29	94.42	12.53
Rhode Island	120	100.00	100.00	3,500	1.34	94.78	14.43
South Carolina	120	100.00	100.00	3,300	1.73	94.64	9.74
South Dakota	190	100.00	100.00	3,500	2.22	95.69	9.26
Tennessee	120	100.00	100.00	3,500	3.10	95.34	12.29
Texas	310	100.00	100.00	9,500	4.90	95.50	14.40
Utah	120	99.08	99.32	3,700	3.05	93.71	10.29
Vermont	220	100.00	100.00	3,100	1.17	95.05	15.65
Virginia	110	100.00	100.00	3,400	1.54	94.93	12.21
Washington	120	99.09	99.35	3,700	2.81	93.71	12.45
West Virginia	150	100.00	100.00	3,300	1.78	93.62	8.89
Wisconsin	190	100.00	100.00	4,500	1.61	94.97	16.63
Wyoming	200	100.00	100.00	3,600	1.25	94.38	13.00
DoDEA2	120	99.23	98.08	3,800	5.95	95.48	7.39
Trial Urban (TUDA) Districts and Other Jurisdictions
Albuquerque	50	100.00	100.00	1,800	0.74	93.43	17.51
Atlanta	60	100.00	100.00	2,000	1.12	95.96	9.39
Austin	60	100.00	100.00	1,700	3.90	94.12	27.06
Baltimore City	70	100.00	100.00	1,700	15.85	93.62	4.33
Boston	80	100.00	100.00	2,000	4.33	94.03	17.64
Charlotte	50	100.00	100.00	1,700	0.90	94.49	11.72
Chicago	100	100.00	100.00	2,600	1.45	94.58	18.56
Cleveland	90	100.00	100.00	1,500	4.70	94.08	22.22
Dallas	50	100.00	100.00	1,700	17.11	96.08	24.30
Detroit	70	100.00	100.00	1,300	5.51	92.09	13.44
Fresno	50	100.00	100.00	1,800	2.36	94.94	6.04
Hillsborough	60	100.00	100.00	1,800	1.07	94.92	23.00
Houston	80	100.00	100.00	2,700	6.41	96.63	23.90
Jefferson County, KY	50	100.00	100.00	1,800	5.28	95.03	7.56
Los Angeles	80	100.00	100.00	2,500	2.10	94.63	10.75
Miami	90	100.00	100.00	2,400	4.51	95.37	26.36
Milwaukee	70	100.00	100.00	1,500	4.08	93.65	25.71
New York City	80	100.00	100.00	2,500	1.62	92.44	27.13

Philadelphia	60	100.00	100.00	1,600	3.83	94.61	15.31
San Diego	50	100.00	100.00	1,600	2.32	94.74	10.45
District of Columbia (TUDA)	90	100.00	100.00	1,600	2.26	94.50	17.21
Catholic	130	88.65	89.70	1,700	0.23	95.75	3.84
Non-Catholic private	280	56.94	52.97	1,600	0.79	95.96	4.22
Includes national public, national private, and Bureau of Indian Education schools located in the United States and all Department of Defense Education Activity schools, but not schools in Puerto Rico. Department of Defense Education Activity schools. NOTE: Numbers of schools are rounded to nearest ten, and numbers of students are rounded to nearest hundred. Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2013 Reading Assessment.

National private

410

71.19

64.52

3,400

0.53

95.85

4.05

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/participation_exclusion_and_accommodation_rates_for_grade_4_reading_for_the_2013_assessment.aspx

National all1

7,240

96.94

84.59

195,600

1.48

93.15

11.79

National public

6,760

99.48

99.61

189,400

1.59

93.02

12.25

NAEP Technical Documentation Website

NAEP Technical Documentation Participation, Exclusion, and Accommodation Rates for Grade 8 Mathematics for the 2013 Assessment

The following table displays the school- and student-level response, exclusion, and accommodation rates for the grade 8 mathematics assessment by school type and jurisdiction. Various weights were used in the calculation of the rates, as indicated in the column headings of the table.

The participation rates reflect the participation of the original sample schools only and do not reflect any effect of substitution. The rates weighted by the base weight and enrollment show the approximate proportion of the student population in the jurisdiction that is represented by the responding schools in the sample. The rates weighted by just the base weight show the proportion of the school population that is represented by the responding schools in the sample. These rates differ because schools differ in size.

Participation, exclusion, and accommodation rates, grade 8 mathematics assessment, by school type and jurisdiction: 2013

		School	School
		participation	participation
		rates	rates
	Number	(percent)	(percent)			Weighted
	of	before	before			student
	schools	substitution	substitution	Number	Weighted	participation
	in	(weighted	(weighted	of	percent	rates	Weighted
School type	original	by base	by base	students	of	(percent)	percent of
and	sample,	weight and	weight	sampled,	students	after	students
jurisdiction	rounded	enrollment)	only)	rounded	excluded	makeups	accommodated
All	7,370	96.97	84.74	201,500	1.47	93.14	11.88
Northeast all	1,160	93.53	75.06	32,700	1.60	92.00	15.85
Midwest all	1,920	97.62	85.21	44,100	1.42	93.69	11.78
South all	2,380	97.75	86.70	68,800	1.51	93.24	11.59
West all	1,720	97.42	89.08	48,000	1.41	93.28	9.25
Alabama	110	100.00	100.00	3,000	1.04	94.23	5.14
Alaska	150	99.91	98.79	3,000	1.08	91.72	18.75
Arizona	120	99.03	99.16	3,200	1.30	93.42	10.71
Arkansas	110	100.00	100.00	3,200	1.93	95.00	13.92
California	260	100.00	100.00	8,400	1.49	93.59	7.91
Colorado	120	100.00	100.00	3,100	1.12	93.47	11.50
Connecticut	110	98.00	97.87	3,100	2.05	92.44	13.92
Delaware	70	100.00	100.00	3,200	1.31	90.65	14.90
District of Columbia	90	100.00	100.00	2,100	0.96	91.26	20.71
Florida	230	100.00	100.00	6,400	1.70	91.06	15.32
Georgia	130	100.00	100.00	4,800	1.55	93.38	9.82
Hawaii	60	100.00	100.00	3,200	1.67	90.26	12.28
Idaho	100	100.00	100.00	3,100	1.06	94.15	8.42
Illinois	190	100.00	100.00	4,800	1.01	94.48	13.83
Indiana	110	97.06	96.65	3,000	1.64	92.49	13.95
Iowa	120	100.00	100.00	3,100	0.77	93.74	13.28
Kansas	130	100.00	100.00	3,300	1.67	93.94	11.23
Kentucky	140	99.04	99.21	4,300	2.08	94.54	10.09
Louisiana	150	100.00	100.00	3,200	1.06	94.14	14.26
Maine	120	100.00	100.00	2,900	1.33	92.79	15.99
Maryland	160	100.00	100.00	4,400	1.74	92.08	13.33
Massachusetts	140	100.00	100.00	4,800	2.01	91.98	16.11
Michigan	170	100.00	100.00	4,200	2.46	92.93	10.55

Minnesota	130	98.99	99.67	2,900	1.70	91.58	9.16
Mississippi	110	100.00	100.00	3,200	0.80	93.80	6.51
Missouri	130	100.00	100.00	3,100	1.28	94.25	10.57
Montana	150	99.80	98.82	3,200	1.44	92.28	9.20
Nebraska	130	100.00	100.00	3,100	1.85	93.41	12.02
Nevada	90	100.00	100.00	3,300	1.04	92.80	11.91
New Hampshire	90	100.00	100.00	3,200	1.06	91.60	15.99
New Jersey	110	100.00	100.00	3,100	1.64	92.26	16.38
New Mexico	120	99.68	99.02	4,000	1.57	93.07	12.00
New York	160	93.08	95.81	4,300	1.90	91.15	19.38
North Carolina	140	100.00	100.00	4,500	1.29	92.95	13.74
North Dakota	190	99.92	99.44	3,700	2.93	94.98	11.44
Ohio	200	100.00	100.00	4,500	1.51	93.07	13.54
Oklahoma	130	100.00	100.00	3,100	1.63	92.97	14.09
Oregon	130	100.00	100.00	3,100	1.47	92.91	10.88
Pennsylvania	160	100.00	100.00	4,300	1.70	92.17	14.66
Rhode Island	60	100.00	100.00	3,200	1.11	93.93	15.92
South Carolina	110	100.00	100.00	3,200	1.33	94.19	9.86
South Dakota	150	100.00	100.00	3,200	1.30	94.44	8.66
Tennessee	110	100.00	100.00	3,200	1.77	92.81	9.81
Texas	230	100.00	100.00	8,800	1.92	93.82	12.13
Utah	120	100.00	100.00	3,300	1.53	92.07	10.15
Vermont	120	100.00	100.00	3,000	0.83	93.91	15.36
Virginia	110	100.00	100.00	3,200	1.05	93.39	12.18
Washington	120	100.00	100.00	3,100	2.03	90.87	11.47
West Virginia	110	100.00	100.00	3,200	1.69	92.62	9.02
Wisconsin	170	100.00	100.00	4,300	1.51	94.25	14.73
Wyoming	100	100.00	100.00	3,300	1.50	93.66	12.51
DoDEA2	70	99.40	96.83	2,600	1.15	94.47	9.23
Trial Urban (TUDA) Districts and Other Jurisdictions
Albuquerque	30	100.00	100.00	1,400	1.53	90.76	14.44
Atlanta	30	100.00	100.00	1,600	0.72	91.57	11.10
Austin	30	100.00	100.00	1,600	1.88	90.97	20.60
Baltimore City	60	100.00	100.00	1,300	1.70	89.54	19.73
Boston	40	100.00	100.00	1,800	2.55	91.61	20.88
Charlotte	40	100.00	100.00	1,500	1.29	90.94	10.11
Chicago	100	100.00	100.00	2,300	1.28	94.80	17.19
Cleveland	90	100.00	100.00	1,500	2.62	91.57	28.48
Dallas	40	100.00	100.00	1,600	2.44	93.81	18.35
Detroit	50	100.00	100.00	1,100	4.29	91.58	15.07
Fresno	20	100.00	100.00	1,400	1.74	92.52	7.06
Hillsborough	50	100.00	100.00	1,600	1.35	93.78	20.46
Houston	50	100.00	100.00	2,400	2.21	92.37	14.67
Jefferson County, KY	40	100.00	100.00	1,600	1.65	93.37	12.72
Los Angeles	70	100.00	100.00	2,200	1.54	94.39	10.83
Miami	80	100.00	100.00	2,300	2.25	92.63	18.78
Milwaukee	60	100.00	100.00	1,500	4.10	91.60	25.55

New York City

90 99.00 97.58 2,400 1.72 91.78 26.10

Philadelphia 50 100.00 100.00 1,400 3.74 92.67 20.69

San Diego 30 100.00 100.00 1,300 2.32 92.60 11.81

National private

400

69.63

60.45

3,400

0.26

94.74

6.54

District of Columbia (TUDA)

40 100.00 100.00 1,100 1.69 90.15 22.20

Catholic 130 87.18 84.76 1,800 0.26 95.73 5.50

Non-Catholic private

270 53.51 48.11 1,600 0.26 93.50 7.51

Puerto Rico	130	100.00	100.00	5,900	0.03	92.75	23.05
Includes national public, national private, and Bureau of Indian Education schools located in the United States and all Department of Defense Education Activity schools, but not schools in Puerto Rico. Department of Defense Education Activity schools. NOTE: Numbers of schools are rounded to nearest ten, and numbers of students are rounded to nearest hundred. Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2013 Mathematics Assessment.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/participation_exclusion_and_accommodation_rates_for_grade_8_mathematics_for_the_2013_assessment.aspx

National all1

7,240

96.94

84.59

199,100

2.15

93.11

10.76

National public

6,760

99.48

99.61

192,900

2.32

92.93

11.16

NAEP Technical Documentation Website

NAEP Technical Documentation Participation, Exclusion, and Accommodation Rates for Grade 8 Reading for the 2013 Assessment

The following table displays the school- and student-level response, exclusion, and accommodation rates for the grade 8 reading assessment by school type and jurisdiction. Various weights were used in the calculation of the rates, as indicated in the column headings of the table.

The participation rates reflect the participation of the original sample schools only and do not reflect any effect of substitution. The rates weighted by the base weight and enrollment show the approximate proportion of the student population in the jurisdiction that is represented by the responding schools in the sample. The rates weighted by just the base weight show the proportion of the school population that is represented by the responding schools in the sample. These rates differ because schools differ in size.

Participation, exclusion, and accommodation rates, grade 8 r eading assessment, by school type and jurisdiction: 2013

		School	School
		participation	participation
		rates	rates
	Number	(percent)	(percent)			Weighted
	of	before	before			student
	schools	substitution	substitution	Number	Weighted	participation
	in	(weighted	(weighted	of	percent	rates	Weighted
School type	original	by base	by base	students	of	(percent)	percent of
and	sample,	weight and	weight	sampled,	students	after	students
jurisdiction	rounded	enrollment)	only)	rounded	excluded	makeups	accommodated
All	7,240	96.94	84.59	199,100	2.15	93.11	10.76
Northeast all	1,160	93.53	75.06	33,300	1.55	91.80	15.53
Midwest all	1,920	97.62	85.21	45,100	1.93	93.48	11.08
South all	2,380	97.75	86.70	69,900	2.60	93.39	9.99
West all	1,720	97.42	89.08	48,900	2.08	93.21	8.32
Alabama	110	100.00	100.00	3,100	1.14	94.26	4.83
Alaska	150	99.91	98.79	3,100	1.40	91.91	18.39
Arizona	120	99.03	99.16	3,300	1.47	93.67	9.67
Arkansas	110	100.00	100.00	3,200	1.96	93.21	13.36
California	260	100.00	100.00	8,500	2.52	93.42	6.74
Colorado	120	100.00	100.00	3,200	1.15	93.46	10.89
Connecticut	110	98.00	97.87	3,100	2.13	91.38	13.88
Delaware	70	100.00	100.00	3,200	3.49	91.59	12.23
District of Columbia	90	100.00	100.00	2,100	1.82	91.33	19.57
Florida	230	100.00	100.00	6,500	1.86	91.72	15.15
Georgia	130	100.00	100.00	4,900	3.80	93.67	8.18
Hawaii	60	100.00	100.00	3,300	1.93	90.58	12.33
Idaho	100	100.00	100.00	3,200	1.61	93.64	7.76
Illinois	190	100.00	100.00	4,900	1.44	93.76	12.94
Indiana	110	97.06	96.65	3,100	1.90	93.12	13.75
Iowa	120	100.00	100.00	3,100	1.27	93.44	12.16
Kansas	130	100.00	100.00	3,300	1.72	93.42	11.72
Kentucky	140	99.04	99.21	4,300	3.28	93.93	8.47
Louisiana	150	100.00	100.00	3,300	1.24	93.78	14.15
Maine	120	100.00	100.00	3,000	1.55	92.34	15.16
Maryland	160	100.00	100.00	4,400	9.41	93.77	5.45
Massachusetts	140	100.00	100.00	4,900	2.15	91.82	15.04
Michigan	170	100.00	100.00	4,300	3.53	93.66	9.68
Minnesota	130	98.99	99.67	3,000	2.33	91.30	8.43

Mississippi	110	100.00	100.00	3,200	0.70	93.72	6.55
Missouri	130	100.00	100.00	3,100	1.02	92.55	10.62
Montana	150	99.80	98.82	3,200	2.29	91.61	7.51
Nebraska	130	100.00	100.00	3,200	2.99	92.32	10.14
Nevada	90	100.00	100.00	3,400	1.00	92.19	10.91
New Hampshire	90	100.00	100.00	3,200	2.93	91.46	14.28
New Jersey	110	100.00	100.00	3,200	2.64	92.01	14.78
New Mexico	120	99.68	99.02	4,000	1.70	93.39	10.00
New York	160	93.08	95.81	4,400	0.96	90.46	20.03
North Carolina	140	100.00	100.00	4,600	1.72	92.51	12.29
North Dakota	190	99.92	99.44	3,800	4.30	94.07	9.52
Ohio	200	100.00	100.00	4,600	2.22	93.08	13.08
Oklahoma	130	100.00	100.00	3,200	1.39	93.43	12.42
Oregon	130	100.00	100.00	3,200	1.45	92.62	11.30
Pennsylvania	160	100.00	100.00	4,300	1.78	91.94	14.51
Rhode Island	60	100.00	100.00	3,300	1.37	92.96	15.18
South Carolina	110	100.00	100.00	3,200	1.88	94.03	7.48
South Dakota	150	100.00	100.00	3,300	2.95	95.01	6.02
Tennessee	110	100.00	100.00	3,200	3.13	93.54	7.75
Texas	230	100.00	100.00	8,900	3.51	93.78	10.05
Utah	120	100.00	100.00	3,400	3.05	93.00	8.36
Vermont	120	100.00	100.00	3,100	0.92	92.93	15.08
Virginia	110	100.00	100.00	3,300	1.40	92.97	10.56
Washington	120	100.00	100.00	3,200	2.46	91.22	9.78
West Virginia	110	100.00	100.00	3,200	1.82	93.10	7.60
Wisconsin	170	100.00	100.00	4,400	1.61	94.11	14.45
Wyoming	100	100.00	100.00	3,400	1.14	93.15	12.27
DoDEA2	70	99.40	96.83	2,600	3.84	94.13	7.11
Trial Urban (TUDA) Districts and Other Jurisdictions
Albuquerque	30	100.00	100.00	1,400	2.04	93.46	11.79
Atlanta	30	100.00	100.00	1,700	1.02	92.20	10.98
Austin	30	100.00	100.00	1,600	3.35	88.54	18.36
Baltimore City	60	100.00	100.00	1,300	16.39	89.73	5.14
Boston	40	100.00	100.00	1,800	3.41	93.05	18.94
Charlotte	40	100.00	100.00	1,500	1.68	92.20	9.90
Chicago	100	100.00	100.00	2,300	1.60	94.72	16.76
Cleveland	90	100.00	100.00	1,500	3.52	91.90	27.75
Dallas	40	100.00	100.00	1,600	3.51	93.98	15.20
Detroit	50	100.00	100.00	1,100	5.74	91.37	12.53
Fresno	20	100.00	100.00	1,500	3.10	93.27	5.86
Hillsborough	50	100.00	100.00	1,600	1.94	91.85	19.74
Houston	50	100.00	100.00	2,400	3.80	93.58	12.29
Jefferson County, KY	40	100.00	100.00	1,600	4.30	94.71	9.49
Los Angeles	70	100.00	100.00	2,300	2.70	94.30	9.97
Miami	80	100.00	100.00	2,400	2.88	94.21	18.45
Milwaukee	60	100.00	100.00	1,500	4.06	93.15	25.08
New York City	90	99.00	97.58	2,400	1.46	91.17	26.00

Philadelphia	50	100.00	100.00	1,400	3.79	91.35	20.91
San Diego	30	100.00	100.00	1,300	2.58	93.78	10.58
District of Columbia (TUDA)	40	100.00	100.00	1,100	2.53	90.18	22.13
Catholic	130	87.18	84.76	1,900	0.21	96.07	4.96
Non-Catholic private	270	53.51	48.11	1,600	0.39	94.67	7.56
Includes national public, national private, and Bureau of Indian Education schools located in the United States and all Department of Defense Education Activity schools, but not schools in Puerto Rico. Department of Defense Education Activity schools. NOTE: Numbers of schools are rounded to nearest ten, and numbers of students are rounded to nearest hundred. Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2013 Reading Assessment.

National private

400

69.63

60.45

3,500

0.30

95.45

6.32

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/participation_exclusion_and_accommodation_rates_for_grade_8_reading_for_the_2013_assessment.aspx

NAEP Technical Documentation Website

NAEP Technical Documentation Participation, Exclusion, and Accommodation Rates for Grade 12 Mathematics for the 2013 Assessment

The following table displays the school- and student-level response, exclusion, and accommodation rates for the grade 12 mathematics assessment. Various weights were used in the calculation of the rates, as indicated in the column headings of the table.

The participation rates reflect the participation of the original sample schools only and do not reflect any effect of substitution. The rates weighted by the base weight and enrollment show the approximate proportion of the student population in the jurisdiction that is represented by the responding schools in the sample. The rates weighted by just the base weight show the proportion of the school population that is represented by the responding schools in the sample. These rates differ because schools differ in size.

National all1

2,200

89.51

82.66

62,200

2.16

84.33

8.65

National public

2,030

92.95

93.31

60,400

2.31

84.17

8.77

Participation, exclusion, and accommodation rates, grade 12 mathematics assessment, by school type and geographic r egion: 2013

			School
		School	participation
		participation	rates			Weighted
	Number	rates (percent)	(percent)			student
	of	before	before			participation
	schools	substitution	substitution	Number	Weighted	rates	Weighted
	in	(weighted by	(weighted by	of	percentage	(percent)	percentage of
School type and geographic	original	base weight	base weight	students	of students	after	students
region	sample	and enrollment)	only)	sampled	excluded	makeups	accommodated
All	2,200	89.51	82.66	62,200	2.16	84.33	8.65
Northeast all	510	89.05	81.63	16,200	2.29	81.79	11.95
Midwest all	650	87.14	83.20	16,600	1.65	83.87	8.61
South all	710	89.42	85.99	20,300	2.31	86.52	7.98
West all	330	92.21	77.24	9,100	2.32	83.37	7.15
Arkansas	100	100.00	100.00	2,900	2.78	92.09	8.61
Connecticut	110	98.93	99.45	3,200	1.76	81.22	8.71
Florida	120	99.05	99.30	3,300	3.21	77.25	12.67
Idaho	100	100.00	100.00	3,000	1.65	89.17	6.72
Illinois	130	90.38	93.98	3,300	1.85	85.16	9.79
Iowa	120	100.00	100.00	3,300	1.13	83.05	10.78
Massachusetts	110	99.04	99.45	3,200	2.21	81.71	11.13
Michigan	140	100.00	100.00	4,000	1.90	86.94	8.78
New Hampshire	80	100.00	100.00	4,100	1.61	76.64	11.22
New Jersey	110	98.14	98.57	3,300	1.89	84.10	14.28
South Dakota	140	99.74	99.07	3,100	1.51	87.48	5.78
Tennessee	130	100.00	100.00	4,100	2.51	88.15	7.84
West Virginia	90	100.00	100.00	3,300	2.00	83.68	7.01
Remaining jurisdictions2	570	91.16	90.91	16,200	2.26	84.41	10.55
Catholic	40	68.06	79.95	1,000	0.83	85.53	5.46
Non-Catholic private	120	38.52	50.25	800	0.42	87.96	9.28
Includes national public, national private, Bureau of Indian Education, and Department of Defense Education Activity schools located in the United States. Includes national public schools not part of the state assessment. NOTE: Numbers of schools are rounded to nearest ten, and numbers of students are rounded to nearest hundred. Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2013 Mathematics Assessment.

National private

160

53.34

55.43

1,800

0.63

86.51

7.32

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/participation_exclusion_and_accommodation_rates_for_grade_12_mathematics_for_the_2013_assessment.aspx

NAEP Technical Documentation Website

NAEP Technical Documentation Participation, Exclusion, and Accommodation Rates for Grade 12 Reading for the 2013 Assessment

The following table displays the school- and student-level response, exclusion, and accommodation rates for the grade 12 reading assessment. Various weights were used in the calculation of the rates, as indicated in the column headings of the table.

The participation rates reflect the participation of the original sample schools only and do not reflect any effect of substitution. The rates weighted by the base weight and enrollment show the approximate proportion of the student population in the jurisdiction that is represented by the responding schools in the sample. The rates weighted by just the base weight show the proportion of the school population that is represented by the responding schools in the sample. These rates differ because schools differ in size.

National public

2,030

92.95

93.31

60,400

2.56

83.77

8.73

Participation, exclusion, and accommodation rates, grade 12 r eading assessment, by school type and geographic r egion: 2013

		School				Weighted
	Number	participation rates	School			student
	of	(percent) before	participation rates			participation
	schools	substitution	(percent) before	Number	Weighted	rates	Weighted
	in	(weighted by base	substitution	of	percentage	(percent)	percentage of
School type and	original	weight and	(weighted by	students	of students	after	students
geographic region	sample	enrollment)	base weight only)	sampled	excluded	makeups	accommodated
All	2,200	89.51	82.66	62,300	2.41	83.89	8.55
National all1	2,200	89.51	82.66	62,300	2.41	83.89	8.55
Northeast all	510	89.05	81.63	16,500	2.16	80.91	12.89
Midwest all	650	87.14	83.20	16,700	2.05	84.05	8.75
South all	710	89.42	85.99	20,000	2.87	85.51	7.18
West all	330	92.21	77.24	9,000	2.24	83.58	7.14
Arkansas	100	100.00	100.00	3,000	2.56	90.21	8.24
Connecticut	110	98.93	99.45	3,400	2.34	79.77	8.70
Florida	120	99.05	99.30	3,300	3.55	77.34	12.14
Idaho	100	100.00	100.00	3,200	1.66	88.68	6.42
Illinois	130	90.38	93.98	3,400	2.29	83.72	9.92
Iowa	120	100.00	100.00	3,500	1.51	84.26	10.62
Massachusetts	110	99.04	99.45	3,200	1.87	79.84	11.31
Michigan	140	100.00	100.00	3,900	4.01	87.21	6.17
New Hampshire	80	100.00	100.00	4,300	2.55	76.91	10.25
New Jersey	110	98.14	98.57	3,300	1.80	84.67	14.78
South Dakota	140	99.74	99.07	3,300	1.60	86.17	5.16
Tennessee	130	100.00	100.00	3,900	2.88	88.82	7.13
West Virginia	90	100.00	100.00	3,400	2.37	84.28	6.89
Remaining jurisdictions2	570	91.16	90.91	15,200	2.77	83.98	10.05
Catholic	40	68.06	79.95	1,100	0.92	84.67	4.01
Non-Catholic	120	38.52	50.25	800	0.75	86.75	9.41
Includes national public, national private, Bureau of Indian Education, and Department of Defense Education Activity schools located in the United States. Includes national public schools not part of the state assessment. NOTE: Numbers of schools are rounded to nearest ten, and numbers of students are rounded to nearest hundred. Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2013 Reading Assessment.

National private

160

53.34

55.43

1,900

0.84

85.52

6.67

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/participation_exclusion_and_accommodation_rates_for_grade_12_reading_for_the_2013_assessment.aspx

NAEP Technical Documentation Website

NAEP Technical Documentation Nonresponse Bias Analyses for the 2013 Assessment

NCES statistical standards call for a nonresponse bias analysis to be conducted for a sample with a response rate below 85 percent at any stage of sampling. Weighted school response rates for the 2013 assessment indicated a need for school nonresponse bias analyses for private school samples in grades 4, 8, and 12 (operational subjects). Student nonresponse bias analyses were necessary for the grade 12 public school student sample overall and in specific states, for both reading and mathematics: Connecticut, Florida, Iowa, Massachusetts, New Hampshire, and West Virginia. Additionally, a student nonresponse bias analysis was required for the grade 12 public school student sample in Illinois based on the weighted response rate for reading, while such an analysis was required for grade 12 public school student sample in New Jersey based on the weighted response rate for mathematics. Thus, three separate school-level analyses and nine separate student-level analyses were conducted.

The procedures and results from these analyses are summarized briefly below. The analyses conducted consider only certain characteristics of schools and students. They do not directly consider the effects of the nonresponse on student achievement, the primary focus of NAEP. Thus, these analyses cannot be conclusive of either the existence or absence of nonresponse bias for student achievement. For more details, please see the NAEP 2013 NRBA report (657.56 KB).

Each school-level analysis was conducted in three parts. The first part of the analysis looked

for potential nonresponse bias that was introduced through school nonresponse. The second part of the analysis examined the remaining potential for nonresponse bias after accounting for the mitigating effects of substitution. The third part of the analysis examined the remaining potential for nonresponse bias after accounting for the mitigating effects of both school substitution and school-level nonresponse weight adjustments. The characteristics examined were Census region, reporting subgroup (private school type), urban-centric locale, size of school (categorical), and race/ethnicity percentages (mean).

Based on the school characteristics available, for the private school samples at grade 4, there does not appear to be evidence of substantial potential bias resulting from school substitution or school nonresponse. However, the analyses suggest that a potential for nonresponse bias remains for the grade 8 and 12 private school samples. For grade 8, this result is evidently related to the fact that, among non- Catholic schools, larger schools were less likely to respond. Thus, when making adjustments to address the underrepresentation of non-Catholic schools among the respondents, the result is to over

represent smaller schools at the expense of larger ones. The limited school sample sizes involved means that it is not possible to make adjustments that account fully for all school characteristics. For grade 12, the analyses suggested potential bias for percentage Asian and percentage Two or more races. Please see the full report for more details.

Each student-level analysis was conducted in two parts. The first part of the analysis examined the potential for nonresponse bias that was introduced through student nonresponse. The second part of the analysis examined the potential for bias after accounting for the effects of nonresponse weight adjustments. The characteristics examined were gender, race/ethnicity, relative age, National School Lunch Program eligibility, student disability (SD) status, and English language learner (ELL) status.

Based on the student characteristics available, there does not appear to be evidence of substantial potential bias resulting from student nonresponse. Please see the full report for more details.

http://nces.ed.gov/nationsreportcard/tdw/weighting/2013/nonresponse_bias_analyses_for_the_2013_assessment.aspx

NATIONAL CENTER FOR EDUCATION STATISTICS NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS

National Assessment of Educational Progress (NAEP)

2021

Appendix C

2021 Sampling Memo

OMB# 1850-0928 v.21

October 2020

.

Date:	September 25, 2020	Memo: 2021-1.2S/1.2D
To:	William Ward, NCES Ed Kulick, ETS David Freund, ETS Amy Dresher, ETS Cathy White, Pearson Greg Binzer Lauren Byrne Lisa Rodriguez Rick Rogers Rob Dymowski	Chris Averett Kavemuii Murangi Dwight Brock Jill DeMatteis Jing Kang Yiting Long William Wall Leslie Wallace Natalia Weil Sabrina Zhang
From:	Amy Lin, John Burke, and Lloyd Hicks
Reviewer:	Keith Rust
Subject:	Sample Design for 2021 NAEP - FINAL
Comment:	This memorandum has been revised to reflect the substantial changes in the 2021 NAEP sample design due to the anticipated greater costs and complexity of administration in the COVID-19 environment. The sample sizes for each state sample have been halved, the Trial Urban District Assessment (TUDA) as well as the national US history and civics assessments have been canceled, and the three-block study has been postponed.

1. Introduction

For 2021, the NAEP assessment involves the following components:

1. National assessments in reading and mathematics in public and private schools at grades 4 and 8;

2. State-by-state assessments in reading and mathematics for public schools at grades 4 and 8;

3. An assessment of mathematics in Puerto Rico for public schools at grades 4 and 8; Below is a summary list of the features of the 2021 sample design.

1. The sample sizes for the public-school state-by-state assessments are significantly smaller than those from prior years involving state-level reporting due to increased costs associated with administering assessments during the current pandemic. This sampling plan refers to these samples as the sigma samples to distinguish them from the traditional alpha samples. The sigma state samples are half the size of the corresponding alpha samples.

2. The sample sizes for the private school assessments are relatively the same as those from past years involving state-level reporting for public schools.

3. The sigma samples for grades 4 and 8 public, and the delta samples for private schools at grades 4 and 8, will be used for the operational assessments in reading and mathematics.

4. The reading and mathematics assessments will be administered in digital form (DBA) using tablets.

5. Because of the significant reduction of the state sample sizes and the cancellation of the TUDA assessments, the school sample sizes for the sigma samples in each state are considerably smaller than in 2019 and past assessments involving state-level reporting. This can be seen by comparing the figures in Tables 1 and 3, with comparable tables from previous assessments. This also means that there are fewer schools with multiple assessment sessions assigned.

In the sigma sample at grade 4, there are 24 schools with a student sample size twice the usual student sample size, and 5 schools with a student sample size at least three times the usual student sample size. This compares with comparable counts of 234 and 38 schools in 2019. At grade 8, there are 53 schools with a double-size student sample, and 10 schools with a student sample size at least three times more than the usual student sample size. This compares with comparable counts of 588 and 336 schools in 2019.

6. The stratification for the public-school samples includes separate strata for the TUDA school districts. This is because at the time at which it was necessary to finalize the stratification, the TUDA study had not yet been cancelled.

7. There are no samples in U.S. territories other than for Puerto Rico at grades 4 and 8.

8. For 2021, the Department of Defense Schools (DoDEA) jurisdiction consists only of the DoDEA Americas schools.

9. There is no National Indian Education Study. This means that less extensive sampling of Bureau of Indian Education (BIE) schools is required than in 2019 and other years when NIES has been conducted. To ensure sound results for American Indian and Alaska Native (AIAN) students in reading and mathematics at the national level, at grades 4 and 8 BIE students were sampled at the same rate as students in Oklahoma, the state with the highest proportion AIAN population.

10. The sampling rates of private schools at grades 4 and 8 are similar to those of 2019. Response rates permitting, this will allow separate reporting for reading and mathematics for Catholic and non-Catholic schools at grades 4 and 8, but no further breakdowns by private school type.

The sample sizes of assessed students for these various components are shown in Table 1 (which also shows the approximate numbers of participating schools).

Table 1. Target sample sizes of assessed students, and expected number of participating schools, for 2021 NAEP

	Spiral	Jurisdictions		Students		Total
	Spiral Indic.	States (incl. DC, DoDEA)	Urban districts	Public school students	Private school students
Grade 4
Nat’l/state reading	DS	52	0	45,500	2,350	47,850
Nat’l/state math	DS	52	0	45,500	2,350	47,850
Puerto Rico	DP	1		3,000		3,000
Total - sigma				94,000		94,000
Total- delta					4,700	4,700
Typical max. no. students/school				50	50
Average assessed students/school				38	22
Total schools - sigma, delta				2,450	215	2,665
Total number of students grade 4				94,000	4,700	98,700
Total number of schools grade 4				2,450	215	2,665

Table 1. Target sample sizes of assessed students, and expected number of participating schools, for 2021 NAEP (Continued)

	Spiral	Jurisdictions		Students		Total
	Spiral Indic.	States (incl. DC, DoDEA)	Urban districts	Public school students	Private school students
Grade 8
Nat’l/state reading	DS	52	0	45,500	2,350	47,750
Nat’l/state math	DS	52	0	45,500	2,350	47,750
Puerto Rico	DP	1		3,000		3,000
Total - sigma				94,000		94,000
Total- delta					4,700	4,500
Typical max. no. students/school				50	50
Average assessed students/school				40	24
Total schools - sigma, delta				2,350	195	2,545
Total number of students grade 8				94,000	4,700	98,700
Total number of schools grade 8				2,350	195	2,545
GRAND TOTAL STUDENTS				188,000	9,400	197,400
GRAND TOTAL SCHOOLS				4,800	410	5,210

2. Assessment Types

The assessment spiral types are shown in Table 2. There are two spirals at both grade 4 and grade 8. Session IDs contain six characters, traditionally. The first two characters identify the assessment “type” (subjects and type of spiral in a general way). Grade is contained in the second pair of characters, and the session sequential number (within schools) in the last two characters. For example, session DS0401 denotes the first grade 4 reading and mathematics operational DBA assessment in a given school.

Table 2. NAEP 2021 assessment types and IDs

ID	Type	Subjects	Grades	Schools	Comments
DS	Operational	Reading, mathematics	4, 8	Public, Private	Schools in the sigma (except Puerto Rico) and delta samples.
DP	Operational	Mathematics	4, 8	Public	Puerto Rico sigma samples.

3. Sample Types and Sizes

In somewhat similar fashion to past years, we identified two different types of school samples: sigma and delta. These distinguish sets of schools that will be conducting distinct portions of the assessment.

1. Sigma Samples at Grades 4 and 8

These are public school samples for grades 4 and 8. They will be used for the operational state-by- state assessments in reading and mathematics, and contribute to the national samples for these subjects as well. There are sigma samples for each state, DC, DoDEA, BIE, and Puerto Rico.

The details of the target student sample sizes for the sigma samples are as follows:

1. At each grade, the assessed student target sample size is 1,750 per state. The goal in each state is to roughly assess 875 students for math and 875 students for reading. The target sample size after considering attrition is 2,050 for grade 4 and 2,100 for grade 8. The DS session type will be used.

2. In Puerto Rico, the target sample size is 3,600 per grade (grades 4 and 8), with the goal of assessing 3,000 students in mathematics only, with the DP session type.

As in past state-by-state assessments, schools with fewer than 20 students in the grade in question were sampled at a moderately lower rate than other schools (at least half, and often higher, depending upon the size of the school). This is in implicit recognition of the greater cost and burden associated with surveying these schools.

Table 3 shows the target student sample sizes, and the approximate counts of schools to be selected in the sigma samples, along with the school and student frame counts, by state for grades 4 and 8.

The table also identifies the jurisdictions where we take all schools and where we take all students.

Table 3. Total sample sizes, by state

Jurisdiction	Grade 4					Grade 8
	Schools in frame	Schools in sample	Students in frame	Overall target student sample size		Schools in frame	Schools in sample	Students in frame	Overall target student sample size
Alabama	691	43	56,826	2,050		441	43	54,908	2,100
Alaska	352	67	9,372	2,050		272	63	9,132	2,100
Arizona	1,226	44	86,545	2,050		820	45	86,796	2,100
Arkansas	473	43	37,321	2,050		308	44	36,694	2,100
Bureau Of Indian Education	136	5	3,499	138		111	5	3,170	138
California	6,127	43	458,116	2,050		3,086	44	468,753	2,100
Colorado	1,103	45	67,137	2,050		609	45	68,254	2,100
Connecticut	565	43	37,377	2,050		293	43	39,596	2,100
Delaware	120	42	10,496	2,050		68	39	10,938	2,100
District Of Columbia	128	47	6,441	2,050		78	42	5,458	2,100
DoDEA (Americas) Schools	32	32	1,850	1,850	**	15	15	1,221	1,221	**
Florida	2,273	42	216,694	2,050		1,281	44	215,429	2,100
Georgia	1,252	41	132,406	2,050		579	42	135,430	2,100
Hawaii	208	44	14,541	2,050		83	39	13,801	2,100
Idaho	389	46	23,828	2,050		214	46	24,418	2,100
Illinois	2,214	45	142,032	2,050		1,585	46	148,905	2,100
Indiana	1,039	43	78,562	2,050		485	43	79,544	2,100
Iowa	620	46	36,777	2,050		360	44	37,813	2,100
Kansas	698	48	36,425	2,050		395	47	36,977	2,100
Kentucky	718	43	50,079	2,050		416	45	51,056	2,100
Louisiana	751	44	54,491	2,050		505	44	53,001	2,100
Maine	310	55	13,131	2,050		200	49	13,542	2,100
Maryland	894	43	68,759	2,050		376	43	66,083	2,100
Massachusetts	957	43	69,662	2,050		492	43	71,983	2,100
Michigan	1,677	45	105,409	2,050		1,098	45	112,015	2,100
Minnesota	973	45	65,588	2,050		711	47	66,984	2,100
Mississippi	412	43	37,114	2,050		277	43	35,806	2,100
Missouri	1,177	47	68,717	2,050		706	47	69,209	2,100
Montana	396	64	11,723	2,050		274	58	11,652	2,100

Table 3. Total sample sizes, by state (Continued)

Jurisdiction	Grade 4					Grade 8
	Schools in frame	Schools in sample	Students in frame	Overall target student sample size		Schools in frame	Schools in sample	Students in frame	Overall target student sample size
Nebraska	514	51	23,915	2,050		293	50	23,281	2,100
Nevada	427	43	37,323	2,050		182	44	37,220	2,100
New Hampshire	268	50	13,003	2,050		147	45	13,660	2,100
New Jersey	1,368	44	97,312	2,050		796	44	99,712	2,100
New Mexico	438	46	25,324	2,050		233	46	25,200	2,100
New York	2,511	43	197,337	2,050		1,537	43	196,875	2,100
North Carolina	1,500	43	119,306	2,050		775	43	119,589	2,100
North Dakota	267	61	9,043	2,050		182	52	8,666	2,100
Ohio	1,689	44	126,278	2,050		1,062	44	129,140	2,100
Oklahoma	865	47	51,972	2,050		587	48	49,873	2,100
Oregon	751	46	44,239	2,050		422	46	44,607	2,100
Pennsylvania	1,546	42	128,810	2,050		886	43	132,393	2,100
Puerto Rico	531	149	20,203	3,600		345	145	22,853	3,600
Rhode Island	165	44	10,465	2,050		62	41	10,848	2,100
South Carolina	658	42	59,222	2,050		317	42	58,031	2,100
South Dakota	312	61	10,801	2,050		251	58	10,732	2,100
Tennessee	1,005	43	75,932	2,050		602	44	75,788	2,100
Texas	4,601	43	401,605	2,050		2,337	44	406,630	2,100
Utah	659	43	51,456	2,050		278	43	51,999	2,100
Vermont	211	69	6,015	2,050		118	53	5,900	2,100
Virginia	1,107	42	96,559	2,050		381	42	98,204	2,100
Washington	1,237	44	84,578	2,050		622	45	83,159	2,100
West Virginia	394	50	19,520	2,050		184	44	19,768	2,100
Wisconsin	1,081	47	60,115	2,050		647	45	61,629	2,100
Wyoming	189	53	7,376	2,050		95	39	7,549	2,100
Total	52,205	2,571	3,778,627	110,138		29,479	2,472	3,821,874	112,059

** identifies jurisdictions where all students for the given grade are included in the NAEP sample.

Stratification

Each state and grade was stratified separately, but using a common approach in all cases. TUDA districts were separated from the balance of their state, and each part stratified separately. This is because at the time of carrying out the stratification, TUDA assessments remained part of the program. The first level of stratification was based on urban-centric type of location. This variable has 12 levels (some of which may not be present in a given state or TUDA district), and these were collapsed so that each of the resulting location categories contained at least 15 percent of the student population (20 percent for TUDA districts).

Within each of the resulting location categories, schools were assigned a minority enrollment status. This was based on the two race/ethnic groups that were the second and third most prevalent within the location category. If these groups were both low in percentage terms, no minority classification was used. Otherwise three (or occasionally four) equal-sized groups (generally high, medium, and low minority) were formed based on the distribution across schools of the two minority groups.

Within the resulting location and minority group classes (of which there are likely to be from three to fifteen, depending upon the jurisdiction), schools were sorted by a measure derived from school level results from the most recent available state achievement tests at the relevant grade. In general, mathematics test results were used, but where these were not available, reading results were used. In the few states that do not have math or reading tests at grades 4 and 8 (or where we are unable to match the results to the NAEP school frame), instead of achievement data, schools were sorted using a measure of socio-economic status. This is the median household income of the 5-digit ZIP Code area where the school is located, based on the 2018 ACS (5-year) data. For BIE and DoDEA schools neither achievement data nor income data are available, and so grade enrollment was used in these cases.

Once the schools were sorted by location class, minority enrollment class, and achievement data (or household income), a systematic sample of schools was selected using a random start. Schools were sampled with probability proportional to size. The exact details of this process are described in the individual sampling specification memos.

2. Delta Samples

These are the private school samples at grades 4 and 8 for conducting the operational assessments in reading and mathematics. The sample sizes are large enough to report results by Catholic and non- Catholic at grades 4 and 8. Approximately half the sample at each grade is from Catholic schools.

The number of students targeted per school is 50 at each grade.

Stratification

The private schools were explicitly stratified by private school type (Catholic/Other). Within each private school type, stratification was by Census region (4 categories), type of location (12 categories), race/ethnicity composition, and enrollment size. In general, where there were few or no schools in a given stratum, categories were collapsed together, always preserving the private school type.

4. New Schools

To compensate for the fact that files used to create the NAEP school sampling frames are at least two years out of date at the time of frame construction, we supplemented the sigma and delta samples with new school samples at each grade.

The new school samples were drawn using a two-stage design. At the first stage, a minimum of ten school districts (in states with at least ten districts) were selected from each state for public schools, and ten Catholic dioceses were selected nationally for the private schools. The sampled districts and dioceses were asked to review lists of their respective schools and identify new schools. Frames of new schools were constructed from these updates, and new schools were drawn with probability proportional to size using the same sample rates as their corresponding original school samples.

The school sample sizes in the above tables do not reflect new school samples.

5. Substitute Samples

A substitute sample was selected for the delta sample. The substitute school for each original was the next “available” school on the sorted sampling frame, with the following exceptions:

1. Schools selected for any NAEP samples are not used as substitutes.

2. Private schools whose school affiliation is unknown are not used as substitutes. Also, unknown affiliated private schools in the original samples do not get substitutes.

3. A school can be a substitute for one and only one sample. (If a school is selected as a substitute school for grade 8, for example, it cannot be used as a substitute for grade 4.)

4. A Catholic school substitute is always a Catholic school, and the same for non-Catholic schools.

6. Student Sampling

Students within the sampled schools will be selected with equal probability. The student sampling parameters vary by sample type (sigma and delta) and grade, as described below.

Sigma Sample, Grades 4 and 8 Schools (Except Puerto Rico)

1. All students, up to 52, will be selected.

2. If the school has more than 52 students, a systematic sample of 50 students will be selected. In some schools, the school may be assigned more than one ‘hit’ in sampling. In these schools we will select a sample of size 50 times the number of hits, taking all students if this target is greater than or equal to 50/52 of the total enrollment.

Sigma Sample, Puerto Rico Grades 4 and 8

1. All students, up to 26, will be selected.

2. If the school has more than 26 students, a systematic sample of 25 students will be selected.

Delta Samples, Grades 4 and 8

1. All students, up to 52, will be selected.

2. If the school has more than 52 students, a systematic sample of 50 students will be selected.

7. Weighting Requirements

The Operational Reading and Mathematics Assessments, Grades 4 and 8

The sample will have weights for each subject (reading and math) applied to reflect probabilities of selection, school and student nonresponse, any trimming, and the random assignment to the particular subject. There will be separate replication schemes by grade and public/private. Weights will also be derived for the Puerto Rico assessment at grades 4 and 8.