Part B, Appendix C, Selections from Online SAS Manual

Part B Apendix C_Selections from the SAS Online Software Manual.pdf

National Agriculture Workers Survey (NAWS)

Part B, Appendix C, Selections from Online SAS Manual

OMB: 1205-0453

⚠️ Notice: This form may be outdated. More recent filings and information on OMB 1205-0453 can be found here:

Document [pdf]

Download: pdf | pdf

Overview

Page 1 of 1

The SURVEYMEANS Procedure

Overview
The SURVEYMEANS procedure produces estimates of survey population means and totals
from sample survey data. The procedure also produces variance estimates, confidence
limits, and other descriptive statistics. When computing these estimates, the procedure
takes into account the sample design used to select the survey sample. The sample design
can be a complex survey sample design with stratification, clustering, and unequal
weighting.
PROC SURVEYMEANS uses the Taylor expansion method to estimate sampling errors of
estimators based on complex sample designs. This method obtains a linear approximation
for the estimator and then uses the variance estimate for this approximation to estimate the
variance of the estimate itself (Woodruff 1971, Fuller 1975). When there are clusters, or
primary sampling units (PSUs), in the sample design, the procedure estimates variance
from the variation among PSUs. When the design is stratified, the procedure pools stratum
variance estimates to compute the overall variance estimate.
PROC SURVEYMEANS uses the Output Delivery System (ODS) to place results in output
data sets. This is a departure from older SAS procedures that provide OUTPUT statements
for similar functionality.
Previous | Next | Top of Page

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

PROC SURVEYMEANS Statement

Page 1 of 5

The SURVEYMEANS Procedure

PROC SURVEYMEANS Statement
PROC SURVEYMEANS < options > < statistic-keywords > ;

The PROC SURVEYMEANS statement invokes the procedure. In this statement, you identify the data set to be
analyzed and specify sample design information. The DATA= option names the input data set to be analyzed. If your
analysis includes a finite population correction factor, you can input either the sampling rate or the population total using
the RATE= or TOTAL= option. If your design is stratified, with different sampling rates or totals for different strata, then
you can input these stratum rates or totals in a SAS data set containing the stratification variables.
In the PROC SURVEYMEANS statement, you also can use statistic-keywords to specify statistics for the procedure to
compute. Available statistics include the population mean and population total, together with their variance estimates
and confidence limits. You can also request data set summary information and sample design information.
You can specify the following options in the PROC SURVEYMEANS statement:
ALPHA=
sets the confidence level for confidence limits. The value of the ALPHA= option must be between 0 and 1, and the
default value is 0.05. A confidence level of produces
% confidence limits. The default of
ALPHA=0.05 produces 95% confidence limits.
DATA=SAS-data-set
specifies the SAS data set to be analyzed by PROC SURVEYMEANS. If you omit the DATA= option, the
procedure uses the most recently created SAS data set.
MISSING
requests that the procedure treat missing values as a valid category for all categorical variables, which include
categorical analysis variables, strata variables, cluster variables, and domain variables.
ORDER=DATA | FORMATTED | INTERNAL
specifies the order in which the values of the categorical variables are to be reported. The following shows how
PROC SURVEYMEANS interprets values of the ORDER= option:
DATA
orders values according to their order in the input data set.
FORMATTED
orders values by their formatted values. This order is operating environment dependent. By default, the order
is ascending.
INTERNAL
orders values by their unformatted values, which yields the same order that the SORT procedure does. This
order is operating environment dependent.
By default, ORDER=FORMATTED.
The ORDER= option applies to all the categorical variables. When the default ORDER=FORMATTED is in effect
for numeric variables for which you have supplied no explicit format, the levels are ordered by their internal values.
RATE=value SAS-data-set
R=value SAS-data-set
specifies the sampling rate as a nonnegative value, or names an input data set that contains the stratum sampling
rates. The procedure uses this information to compute a finite population correction for variance estimation. If your
sample design has multiple stages, you should specify the first-stage sampling rate, which is the ratio of the
number of PSUs selected to the total number of PSUs in the population.
For a nonstratified sample design, or for a stratified sample design with the same sampling rate in all strata, you
should specify a nonnegative value for the RATE= option. If your design is stratified with different sampling rates in
the strata, then you should name a SAS data set that contains the stratification variables and the sampling rates.
See the section "Specification of Population Totals and Sampling Rates" for more details.
The sampling rate value must be a nonnegative number. You can specify value as a number between 0 and 1. Or

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

PROC SURVEYMEANS Statement

Page 2 of 5

you can specify value in percentage form as a number between 1 and 100, and PROC SURVEYMEANS will
convert that number to a proportion. The procedure treats the value 1 as 100%, and not the percentage form 1%.
If you do not specify the TOTAL= option or the RATE= option, then the variance estimation does not include a
finite population correction. You cannot specify both the TOTAL= option and the RATE= option.
STACKING
requests the procedure to produce the output data sets using a stacking table structure, which was the default in
releases prior to Version 9. The new default is to produce a rectangular table structure in the output data sets.
The STACKING option affects the following tables:
Domain
Ratio
Statistics
StrataInfo
When you use the ODS statement to create SAS data sets for these tables in the output, the data set structure can
be either stacking or rectangular. A rectangular structure creates one observation for each analysis variable in the
data set. However, if you use the STACKING option in Version 9, the procedure creates only one observation in
the output data set for all analysis variables. The following example shows these two structures in output data sets.

data new;
input sex$ x;
datalines;
M 12
F 5
M 13
F 23
F 11
;
proc surveymeans data=new mean;
ods output statistics=rectangle;
run;
proc print data=rectangle;
run;
proc surveymeans data=new mean stacking;
ods output statistics=stacking;
run;
proc print data=stacking;
run;

Figure 70.6 shows the rectangular structure of the output data set for the statistics table.

rectangle structure in the output data set

OBS

VarName

VarLevel

Mean

StdErr

12.800000

2.905168

sex

0.600000

0.244949

sex

0.400000

0.244949

Figure 70.6: Rectangular Structure in the Output Data Set
Figure 70.7 shows the stacking structure of the output data set for the statistics table.

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

PROC SURVEYMEANS Statement

Page 3 of 5

stacking structure in the output data set

OBS

x_Mean

x_StdErr

sex_F

sex_F_Mean

sex_F_StdErr

sex_M

sex_M_Mean

sex_M_StdErr

12.800000

2.905168

sex=F

0.600000

0.244949

sex=M

0.400000

0.244949

Figure 70.7: Stacking Structure in the Output Data Set
TOTAL=value SAS-data-set
N=value SAS-data-set
specifies the total number of primary sampling units (PSUs) in the study population as a positive value, or names
an input data set that contains the stratum population totals. The procedure uses this information to compute a
finite population correction for variance estimation.
For a nonstratified sample design, or for a stratified sample design with the same population total in all strata, you
should specify a positive value for the TOTAL= option. If your sample design is stratified with different population
totals in the strata, then you should name a SAS data set that contains the stratification variables and the
population totals. See the section "Specification of Population Totals and Sampling Rates" for more details.
If you do not specify the TOTAL= option or the RATE= option, then the variance estimation does not include a
finite population correction. You cannot specify both the TOTAL= option and the RATE= option.
statistic-keywords
specifies the statistics for the procedure to compute. If you do not specify any statistic-keywords, PROC
SURVEYMEANS computes the NOBS, MEAN, STDERR, and CLM statistics by default.
The statistics produced depend on the type of the analysis variable. If you name a numeric variable in the CLASS
statement, then the procedure analyzes that variable as a categorical variable. The procedure always analyzes
character variables as categorical. See the section "CLASS Statement" for more information.
PROC SURVEYMEANS computes MIN, MAX, and RANGE for numeric variables but not for categorical variables.
For numeric variables, the keyword MEAN produces the mean, but for categorical variables it produces the
proportion in each category or level. Also for categorical variables, the keyword NOBS produces the number of
observations for each variable level, and the keyword NMISS produces the number of missing observations for
each level. If you request the keyword NCLUSTER for a categorical variable, PROC SURVEYMEANS displays for
each level the number of clusters with observations in that level. PROC SURVEYMEANS computes SUMWGT in
the same way for both categorical and numeric variables, as the sum of the weights over all nonmissing
observations.
PROC SURVEYMEANS performs univariate analysis, analyzing each variable separately. Thus the number of
nonmissing and missing observations may not be the same for all analysis variables. See the section "Missing
Values" for more information.
If you use the keyword RATIO without the keyword MEAN, the keyword MEAN is implied.
Other available statistics computed for a ratio are N, NCLU, SUMWGT, RATIO, STDERR, DF, T, PROBT, and
CLM, as listed below. If no statistics are requested, the procedure will compute the ratio and its standard error by
default for a RATIO statement.
The valid statistic-keywords are as follows:
ALL
all statistics listed
CLM
% two-sided confidence limits for the MEAN, where

is determined by the ALPHA= option, and

the default is

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

PROC SURVEYMEANS Statement

Page 4 of 5

CLSUM
% two-sided confidence limits for the SUM, where

is determined by the ALPHA= option, and

the default is
CV
coefficient of variation for MEAN
CVSUM
coefficient of variation for SUM
DF
degrees of freedom for the t test
LCLM
% one-sided lower confidence limit of the MEAN, where

is determined by the ALPHA= option,

and the default is
LCLMSUM
% one-sided lower confidence limit of the SUM, where

is determined by the ALPHA= option,

and the default is
MAX
maximum value
MEAN
mean for a numeric variable, or the proportion in each category for a categorical variable
MIN
minimum value
NCLUSTER
number of clusters
NMISS
number of missing observations
NOBS
number of nonmissing observations
RANGE
range, MAX-MIN
RATIO
ratio of means or proportions
STD
standard deviation of the SUM. When you request SUM, the procedure computes STD by default.
STDERR
standard error of the MEAN or RATIO. When you request MEAN or RATIO, the procedure computes
STDERR by default.
SUM
weighted sum,

, or estimated population total when the appropriate sampling weights are used

SUMWGT
sum of the weights,
T
t-value and its corresponding p-value with DF degrees of freedom for
where

is the population mean or the population ratio

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

PROC SURVEYMEANS Statement

Page 5 of 5

UCLM
% one-sided upper confidence limit of the MEAN, where

is determined by the ALPHA= option,

and the default is
UCLMSUM
% one-sided upper confidence limit of the SUM, where

is determined by the ALPHA= option,

and the default is
VAR
variance of the MEAN or RATIO
VARSUM
variance of the SUM
See the section "Statistical Computations" for details on how PROC SURVEYMEANS computes these statistics.
Previous

| Next | Top of Page

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

CLUSTER Statement

Page 1 of 1

The SURVEYMEANS Procedure

CLUSTER Statement
CLUSTER CLUSTERS variables ;
The CLUSTER statement names variables that identify the clusters in a clustered sample
design. The combinations of categories of CLUSTER variables define the clusters in the
sample. If there is a STRATA statement, clusters are nested within strata.
If your sample design has clustering at multiple stages, you should identify only the firststage clusters, or primary sampling units (PSUs), in the CLUSTER statement. See the
section "Primary Sampling Units (PSUs)" for more information.
The CLUSTER variables are one or more variables in the DATA= input data set. These
variables can be either character or numeric. The formatted values of the CLUSTER
variables determine the CLUSTER variable levels. Thus, you can use formats to group
values into levels. Refer to the discussion of the FORMAT procedure in the SAS
Procedures Guide and to the discussions of the FORMAT statement and SAS formats in
SAS Language Reference: Dictionary.
You can use multiple CLUSTER statements to specify cluster variables. The procedure
uses variables from all CLUSTER statements to create clusters.
Previous | Next | Top of Page

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

STRATA Statement

Page 1 of 1

The SURVEYMEANS Procedure

STRATA Statement
STRATA STRATUM variables < / option > ;

The STRATA statement names variables that form the strata in a stratified sample design.
The combinations of categories of STRATA variables define the strata in the sample.
If your sample design has stratification at multiple stages, you should identify only the firststage strata in the STRATA statement. See the section "Specification of Population Totals
and Sampling Rates" for more information.
The STRATA variables are one or more variables in the DATA= input data set. These
variables can be either character or numeric. The formatted values of the STRATA
variables determine the levels. Thus, you can use formats to group values into levels. See
the discussion of the FORMAT procedure in the SAS Procedures Guide.
You can specify the following option in the STRATA statement after a slash (/):
LIST
displays a "Stratum Information" table, which includes values of the STRATA variables
and sampling rates for each stratum. This table also provides the number of
observations and number of clusters for each stratum and analysis variable. See the
section "Displayed Output" for more details.
Previous | Next | Top of Page

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

WEIGHT Statement

Page 1 of 1

The SURVEYMEANS Procedure

WEIGHT Statement
WEIGHT WGT variable ;
The WEIGHT statement names the variable that contains the sampling weights. This
variable must be numeric. If you do not specify a WEIGHT statement, PROC
SURVEYMEANS assigns all observations a weight of 1. Sampling weights must be positive
numbers. If an observation has a weight that is nonpositive or missing, then the procedure
omits that observation from the analysis. If you specify more than one WEIGHT statement,
the procedure uses only the first WEIGHT statement and ignores the rest.
Previous | Next | Top of Page

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

VAR Statement

Page 1 of 1

The SURVEYMEANS Procedure

VAR Statement
VAR variables ;
The VAR statement names the variables to be analyzed.
If you want a categorical analysis for a numeric variable, you must also name that variable
in the CLASS statement. For categorical variables, PROC SURVEYMEANS estimates the
proportion in each category or level, instead of the overall mean. Character variables are
always analyzed as categorical variables. See the section "CLASS Statement" for more
information.
If you do not specify a VAR statement, then PROC SURVEYMEANS analyzes all variables
in the DATA= input data set, except those named in the BY, CLUSTER, STRATA, and
WEIGHT statements.
Previous | Next | Top of Page

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

Survey Data Analysis

Page 1 of 2

The SURVEYMEANS Procedure

Survey Data Analysis
Specification of Population Totals and Sampling Rates
If your analysis should include a finite population correction (fpc), you can input either the
sampling rate or the population total using the RATE= option or the TOTAL= option. (You
cannot specify both of these options in the same PROC SURVEYMEANS statement.) If you
do not specify one of these options, the procedure does not use the fpc when computing
variance estimates. For fairly small sampling fractions, it is appropriate to ignore this
correction. Refer to Cochran (1977) and Kish (1965).
If your design has multiple stages of selection and you are specifying the RATE= option,
you should input the first-stage sampling rate, which is the ratio of the number of PSUs in
the sample to the total number of PSUs in the study population. If you are specifying the
TOTAL= option for a multistage design, you should input the total number of PSUs in the
study population. See the section "Primary Sampling Units (PSUs)" for more details.
For a nonstratified sample design, or for a stratified sample design with the same sampling
rate or the same population total in all strata, you should use the RATE=value option or the
TOTAL=value option. If your sample design is stratified with different sampling rates or
population totals in the strata, then you can use the RATE= SAS-data-set option or the
TOTAL= SAS-data-set option to name a SAS data set that contains the stratum sampling
rates or totals. This data set is called a secondary data set, as opposed to the primary data
set that you specify with the DATA= option.
The secondary data set must contain all the stratification variables listed in the STRATA
statement and all the variables in the BY statement. If there are formats associated with the
STRATA variables and the BY variables, then the formats must be consistent in the primary
and the secondary data sets. If you specify the TOTAL=SAS-data-set option, the secondary
data set must have a variable named _TOTAL_ that contains the stratum population totals.
Or if you specify the RATE=SAS-data-set option, the secondary data set must have a
variable named _RATE_ that contains the stratum sampling rates. If the secondary data set
contains more than one observation for any one stratum, then the procedure uses the first
value of _TOTAL_ or _RATE_ for that stratum and ignores the rest.
The value in the RATE= option or the values of _RATE_ in the secondary data set must be
nonnegative numbers. You can specify value as a number between 0 and 1. Or you can
specify value in percentage form as a number between 1 and 100, and PROC
SURVEYMEANS will convert that number to a proportion. The procedure treats the value 1
as 100%, and not the percentage form 1%.
If you specify the TOTAL=value option, value must not be less than the sample size. If you
provide stratum population totals in a secondary data set, these values must not be less
than the corresponding stratum sample sizes.

Primary Sampling Units (PSUs)

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

Survey Data Analysis

Page 2 of 2

When you have clusters, or primary sampling units (PSUs), in your sample design, the
procedure estimates variance from the variation among PSUs. See the section "Variance
and Standard Error of the Mean" and the section "Variance and Standard Deviation of the
Total." You can use the CLUSTER statement to identify the first stage clusters in your
design. PROC SURVEYMEANS assumes that each cluster represents a PSU in the sample
and that each observation is an element of a PSU. If you do not specify a CLUSTER
statement, the procedure treats each observation as a PSU.

Domain Analysis
It is common practice to compute statistics for subpopulations, or domains, in addition to
computing statistics for the entire study population. Analysis for domains using the entire
sample is called domain analysis (subgroup analysis, subpopulation analysis, subdomain
analysis). The formation of these subpopulations of interest may be unrelated to the sample
design. Therefore, the sample sizes for the subpopulations may actually be random
variables.
In order to incorporate this variability into the variance estimation, you should use a
DOMAIN statement. Note that using a BY statement provides completely separate analyses
of the BY groups. It does not provide a statistically valid subpopulation or domain analysis,
where the total number of units in the subpopulation is not known with certainty. For more
detailed information about domain analysis, refer to Kish (1965).
Previous | Next | Top of Page

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp... 1/12/2009

Statistical Computations

Page 1 of 11

The SURVEYMEANS Procedure

Statistical Computations
The SURVEYMEANS procedure uses the Taylor expansion method to estimate sampling
errors of estimators based on complex sample designs. This method obtains a linear
approximation for the estimator and then uses the variance estimate for this approximation
to estimate the variance of the estimate itself (Woodruff 1971, Fuller 1975). When there are
clusters, or PSUs, in the sample design, the procedure estimates variance from the
variation among PSUs. When the design is stratified, the procedure pools stratum variance
estimates to compute the overall variance estimate. For t tests of the estimates, the degrees
of freedom equals the number of clusters minus the number of strata in the sample design.
For a multistage sample design, the variance estimation method depends only on the first
stage of the sample design. So, the required input includes only first-stage cluster (PSU)
and first-stage stratum identification. You do not need to input design information about any
additional stages of sampling. This variance estimation method assumes that the first-stage
sampling fraction is small, or the first-stage sample is drawn with replacement, as it often is
in practice.
Quite often in complex surveys, respondents have unequal weights, which reflect unequal
selection probabilities and adjustments for nonresponse. In such surveys, the appropriate
sampling weights must be used to obtain valid estimates for the study population.
For more information on the analysis of sample survey data, refer to Lee, Forthoffer, and
Lorimor (1989), Cochran (1977), Kish (1965), and Hansen, Hurwitz, and Madow (1953).

Definition and Notation
For a stratified clustered sample design, together with the sampling weights, the sample can
be represented by an n ×(P+1) matrix

where

h = 1, 2, ... , H
i = 1, 2, ... , nh
j = 1, 2, ... , mhi
p = 1, 2, ... , P

is the stratum number, with a total of H strata
is the cluster number within stratum h, with a total of nh clusters
is the unit number within cluster i of stratum h, with a total of mhi units
is the analysis variable number, with a total of P variables
is the total number of observations in the sample

whij denotes the sampling weight for observation j in cluster i of stratum h
yhij = ( yhij(1), yhij(2), ... , yhij(P)) are the observed values of the analysis variables for
observation j in cluster i of stratum h, including both the values of numerical variables
and the values of indicator variables for levels of categorical variables.

For a categorical variable C, let l denote the number of levels of C, and denote the level

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

Statistical Computations

Page 2 of 11

values as c1, c2, ... , cl. Then there are l indicator variables associated with these levels.
contains the values of the
That is, for level C=ck (k = 1, 2, ... , l), a y(q)
indicator variable for the category C=ck, with the value of observation j in cluster i of stratum
h:

Therefore, the total number of analysis variables, P, is the total number of numerical
variables plus the total number of levels of all categorical variables.
Also, fh denotes the sampling rate for stratum h. You can use the TOTAL= option or the
RATE= option to input population totals or sampling rates. See the section "Specification of
Population Totals and Sampling Rates" for details. If you input stratum totals, PROC
SURVEYMEANS computes fh as the ratio of the stratum sample size to the stratum total. If
you input stratum sampling rates, PROC SURVEYMEANS uses these values directly for fh.
If you do not specify the TOTAL= option or the RATE= option, then the procedure assumes
that the stratum sampling rates fh are negligible, and a finite population correction is not
used when computing variances.
This notation is also applicable to other sample designs. For example, for a sample design
without stratification, you can let H=1; for a sample design without clusters, you can let
mhi=1 for every h and i.

Mean
When you specify the keyword MEAN, the procedure computes the estimate of the mean
(mean per element) from the survey data. Also, the procedure computes the mean by
default if you do not specify any statistic-keywords in the PROC SURVEYMEANS
statement.
PROC SURVEYMEANS computes the estimate of the mean as

where

is the sum of the weights over all observations in the sample.

Variance and Standard Error of the Mean

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

Statistical Computations

Page 3 of 11

When you specify the keyword STDERR, the procedure computes the standard error of the
mean. Also, the procedure computes the standard error by default if you specify the
keyword MEAN, or if you do not specify any statistic-keywords in the PROC
SURVEYMEANS statement. The keyword VAR requests the variance of the mean.
PROC SURVEYMEANS uses the Taylor series expansion theory to estimate the variance
of the mean

. The procedure computes the estimated variance as

where if nh>1,

and if nh=1,

The standard error of the mean is the square root of the estimated variance.

Ratio
When you use a RATIO statement, the procedure produces statistics requested by the
statistics-keywords in the PROC SURVEYMEANS statement.
Suppose that you want to calculate the ratio of variable Y over variable X. Let xhij be the
value of variable X for the jth member in cluster i in the hth stratum.
The ratio of Y over X is

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

Statistical Computations

Page 4 of 11

PROC SURVEYMEANS uses the Taylor series expansion method to estimate the variance
of the ratio as

where if nh>1,

and if nh=1,

The standard error of the ratio is the square root of the estimated variance.

t Test for the Mean
If you specify the keyword T, PROC SURVEYMEANS computes the t-value for testing that
the population mean equals zero,
. The test statistic equals

The two-sided p-value for this test is

where T is a random variable with the t distribution with df degrees of freedom.

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

Statistical Computations

Page 5 of 11

PROC SURVEYMEANS calculates the degrees of freedom for the t test as the number of
clusters minus the number of strata. If there are no clusters, then df equals the number of
observations minus the number of strata. If the design is not stratified, then df equals the
number of clusters minus one. The procedure displays df for the t test if you specify the
keyword DF in the PROC SURVEYMEANS statement.
If missing values or missing weights are present in your data, the number of strata, the
number of observations, and the number of clusters are counted based on the observations
in non-empty strata. See the section "Missing Values" for details. For degrees of freedom in
domain analysis, see the section "Domain Statistics."

Confidence Limits for the Mean
If you specify the keyword CLM, the procedure computes two-sided confidence limits for the
mean. Also, the procedure includes the confidence limits by default if you do not specify any
statistic-keywords in the PROC SURVEYMEANS statement.
The confidence coefficient is determined by the value of the ALPHA= option, which by
default equals 0.05 and produces 95% confidence limits. The confidence limits are
computed as

where

is the estimate of the mean,
is the

is the standard error of the mean, and

percentile of the t distribution with df calculated as described

in the section " t Test for the Mean."
If you specify the keyword UCLM, the procedure computes the one-sided upper
confidence limit for the mean:

If you specify the keyword LCLM, the procedure computes the one-sided lower
confidence limit for the mean:

Coefficient of Variation
If you specify the keyword CV, PROC SURVEYMEANS computes the coefficient of
variation, which is the ratio of the standard error of the mean to the estimated mean.

If you specify the keyword CVSUM, PROC SURVEYMEANS computes the coefficient of
variation for the estimated total, which is the ratio of the standard deviation of the sum to the
estimated total.

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

Statistical Computations

Page 6 of 11

Proportions
If you specify the keyword MEAN for a categorical variable, PROC SURVEYMEANS
estimates the proportion, or relative frequency, for each level of the categorical variable. If
you do not specify any statistic-keywords in the PROC SURVEYMEANS statement, the
procedure estimates the proportions for levels of the categorical variables, together with
their standard errors and confidence limits.
The procedure estimates the proportion in level ck for variable C as

where yhij(q) is the value of the indicator function for level C=ck, defined in the section
"Definition and Notation," and yhij(q) equals 1 if the observed value of variable C equals ck,
and yhij(q) equals 0 otherwise. Since the proportion estimator is actually an estimator of the
mean for an indicator variable, the procedure computes its variance and standard error
according to the method outlined in the section "Variance and Standard Error of the Mean."
Similarly, the procedure computes confidence limits for proportions as described in the
section "Confidence Limits for the Mean."

Total
If you specify the keyword SUM, the procedure computes the estimate of the population
total from the survey data. The estimate of the total is the weighted sum over the sample.

For a categorical variable level,

estimates its total frequency in the population.

Variance and Standard Deviation of the Total
When you specify the keyword STD or the keyword SUM, the procedure estimates the
standard deviation of the total. The keyword VARSUM requests the variance of the total.
PROC SURVEYMEANS estimates the variance of the total as

where if nh>1,

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

Statistical Computations

Page 7 of 11

and if nh=1,

The standard deviation of the total equals

Confidence Limits of a Total
If you specify the keyword CLSUM, the procedure computes confidence limits for the total.
The confidence coefficient is determined by the value of the ALPHA= option, which by
default equals 0.05 and produces 95% confidence limits. The confidence limits are
computed as

where

is the estimate of the total,
is the

is the estimated standard deviation, and

percentile of the t distribution with df calculated as described

in the section " t Test for the Mean."
If you specify the keyword UCLSUM, the procedure computes the one-sided upper
confidence limit for the sum:

If you specify the keyword LCLSUM, the procedure computes the one-sided lower
confidence limit for the sum:

Domain Statistics

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

Statistical Computations

Page 8 of 11

When you use a DOMAIN statement to request a domain analysis, the procedure computes
the requested statistics for each domain.
For a domain D, let ID be the corresponding indicator variable:

Let

The requested statistics for variable y in domain D are computed based on the values of z.
Domain Mean The estimated mean of y in the domain D is

where

The variance of

is estimated by

where if nh>1,

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

Statistical Computations

Page 9 of 11

and if nh=1,

Domain Total The estimated total in domain D is

and its estimated variance is

where if nh>1,

and if nh=1,

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

Statistical Computations

Page 10 of 11

Degrees of Freedom For domain analysis, PROC SURVEYMEANS computes the degrees
of freedom for t tests as the number of clusters in the non-empty strata minus the number of
non-empty strata. When the sample design has no clusters, the degrees of freedom equals
the number of observations in non-empty strata minus the number of non-empty strata. As
discussed in the section "Missing Values," missing values and missing weights can result in
empty strata. In domain analysis, an empty stratum can also occur when the stratum
contains no observations in the specified domain. If no observations in a whole stratum
belong to a domain, then this stratum is called an empty stratum for that domain.
For example,
data new;
input str clu y w d;
datalines;
1 1 . 40 9
1 2 2 . 9
1 3 . 25 9
2 4 5 20 9
2 5 8 15 9
3 6 5 30 7
3 7 9 89 7
3 8 6 23 7
;
proc surveymeans df nobs nclu nmiss;
strata str;
cluster clu;
var y;
weight w;
domain d;
run;

Table 70.2: Calculations of df for Y

Non Empty Strata

Domain D=7

Domain D=9

STR=3

STR=2

Clusters Used in the Analysis CLU=6, CLU=7, and CLU=8 CLU=4 and CLU=5
df

3-1=2

2-1=1

Although there are three strata in the data set, STR=1 is an empty stratum for variable Y
because of missing values and missing weights. In addition, no observations in stratum
STR=3 belong to domain D=9. Therefore, STR=3 becomes an empty stratum as well for
variable Y in domain D=9. As a result, the total number of non-empty strata for domain D=9
is one. The non-empty stratum for domain D=9 and variable Y is stratum STR=2. The total
number of clusters for domain D=9 is two, which belong to stratum STR=2. Thus, for
variable Y in domain D=9, the degrees of freedom for the t tests of the domain mean is
df=2-1=1. Similarly, for domain D=7, strata STR=1 and STR=2 are both empty strata, so the
total number of strata is one (STR=3), and the total number of clusters is three ( CLU=6,
CLU=7, and CLU=8). Table 70.2 illustrates how domains affect the total number of clusters
and total number of strata in the df calculation. Figure 70.8 shows the df computed by the
procedure.

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

Statistical Computations

Page 11 of 11

The SURVEYMEANS Procedure

Domain Analysis: d
d

Variable

N Miss

Clusters

Figure 70.8: Degrees of Freedoms in Domain Analysis
Previous | Next | Top of Page

mk:@MSITStore:C:\Program%20Files\SAS\SAS%209.1\core\help\statug.chm::/statug.hlp/...

1/5/2009

File Type	application/pdf
File Title	Overview
Author	sgabbard
File Modified	2009-01-12
File Created	2009-01-12