A Response Propensity Based Evaluation of the Treatment of 

Unit Nonresponse for Selected Business Surveys 

Katherine Jenny Thompson and Katrina T. Washington1 

U.S. Census Bureau 

4600 Silver Hill Road, Washington DC 20233 

Katherine.J.Thompson@census.gov / Katrina.T.Washington@census.gov 

Introduction 

In the world of survey design, methodologists select a “representative” sample that achieves targeted reliability from 

a complete frame. In the world of survey collection, not all sample units respond (complete non-response), and 

those that do will not always provide data on every questioned characteristic (partial non-response). Business 

surveys publish totals. Consequently, complete-case analyses – analyses based solely on unadjusted respondent data 

– are biased, so the survey practitioner assumes a model for the nonresponse and develops adjustments to their 

survey estimates accordingly. Under an ignorable response mechanism, adjustment can be accomplished via weight 

adjustment or imputation. The choice of adjustment method and model(s) should be determined by the survey 

publication objectives and supported by analysis of the survey response set. 

In this paper, we examine the unit nonresponse adjustment procedure used in the Services Annual Survey (SAS). 

Our analysis is considerably simplified from the production procedures outlined in Nelson (2011). These ongoing 

programs impute complete records for unit nonresponse using a hierarchy that imputes items in a pre-specified 

sequence determined by the expected reliability of available imputation models. Each item has its own imputation 

model hierarchy that maximizes the use of logical edits and direct substitution before attempting model imputation. 

Our analysis focuses entirely on the ratio model imputation used by these programs. The ratio imputation model 

utilizes a prediction model between the missing (dependent) variable and the auxiliary (independent) variable. 

Auxiliary variables differ by item. This approach allows for maximum flexibility in modeling and preserves the 

expected cell totals, but does not preserve multivariate relationships between items and creates variance estimation 

challenges. Generally, there is an abundance of reliable auxiliary data that are used to formulate the imputation 

models for the key totals, such as revenue and expenses. However, these programs also request detailed 

“breakdowns” of each total, and there is often little auxiliary information on the detail items. 

An alternative approach is to develop a single unit nonresponse weight adjustment procedure. We consider two 

adjustment-to-sample weighting approaches, both described in Kalton and Flores-Cervantes (2003): one that adjusts 

the respondent units’ final weights by the weighted inverse response rate, i.e. the so-called “quasi-randomization 

estimator” or “count estimator”(Oh and Scheuren, 1983 ); and an alternative that adjusts the respondent units’ final 

weights by an unweighted inverse response rate, i.e. the InfoP estimator described in Särndal and Lundström (2005, 

Chapter 7.3) and endorsed by Little and Vartivarian (2005). We also examine the simplified version of the 

currently-used ratio imputation procedure, which can be rewritten as the InfoS ratio estimator described in Särndal 

and Lundström (2005, Chapter 7.5). 

We use six years of historical data to empirically examine the ignorable response assumptions and the prediction 

models for each considered adjustment method. First, we describe our analysis approach. We follow with 

background information on the studied programs, including information on survey design, content, and data 

limitations. After this, we present and discuss our results, concluding with broad observations. 

Developing Adjustment Procedures for Unit Nonresponse 

Several factors must be considered before developing a treatment for unit nonresponse. First is the availability of 

“useful” auxiliary data for each sampled or population element, in the sense that the auxiliary data is related to 

nonresponse or is predictive of survey outcome. As mentioned above, survey totals that use only unadjusted 

1

 This paper is released to inform interested parties of research and to encourage discussion. The views expressed are 

those of the authors and not necessarily those of the U.S. Census Bureau. 

1 
 

 

 

 

 

 

 

 

respondent data are biased. When implementing an adjustment procedure to reduce the magnitude of this bias, care 

must be taken to avoid large increases in variance as a consequence. Little and Vartivarian (2005) summarize the 

effects of adjustments on bias and variance of a mean or total by strength of association of the adjustment cell 

variables with nonresponse and outcome by Figure 1, with the optimal adjustment procedure being indicated by the 

(shaded) Cell 4. 

Association with Outcome (Prediction) 

Low High 

Association with 

Low 

Cell One 

Bias: --

Variance: --

Cell Two 

Bias: --

Variance: 

Response (Propensity) 

High 

Cell Three 

Bias: --

Variance: 

Cell Four 

Bias: 

Variance: 

Figure 1: Effects of Adjustments on Bias and Variance With Respect to Auxiliary Variables 

 Little and Vartivarian (2005) 

How is this balance achieved in practice? First, the population must be partitioned into P disjoint subpopulations 

(nonresponse adjustment cells) using xp, a vector of auxiliary categorical variables available for all units in the 

population. This partitioning process assumes that xp is related to response propensity, and that the respondents 

comprise a random subsample within the nonresponse adjustment cells. After establishing the nonresponse 

adjustment cells, the unit nonresponse adjustment procedures can be evaluated. 

Throughout the remainder of this document, we use the following notation. Each sample S has been partitioned into 

P disjoint subpopulations (indexed by p = 1, 2,..., P), each containing np units. Within each subpopulation p, sp,r = 

the respondent portion of the sample containing rp units and sp,nr = the nonrespondent portion of the sample 

containing mp units. Each unit j within subpopulation p has a design weight wj. Auxiliary data x are available for all 

sampled units, and elements in x may be either continuous (indicated by xpj) or categorical (indicated by xp). 

Characteristic data y are collected in the survey, and values in y may or may not be reported. Each unit j has a 

response indicator Ipj whose value is assigned after data collection; each Ipj has a probability of response φpj. 

Evaluation Procedures 

Response Propensity Analysis 

Under the “quasi-randomization model” (Oh and Scheuren, 1983; Särndal and Lundström , 2005, Chapter 6.1), unit 

nonresponse is treated as the second phase of a two phase sample, where each sampled unit j has an unknown 

probability of responding(φpj). Thus, rp is a random variable with expected value npφj

. 

We consider two different ignorable response mechanisms: covariate-dependent and missing-at-random (MAR). 

The covariate-dependent response mechanism assumes that in each subpopulation p, P(Ipj=1| ypj, xpj) = P(Ipj=1|xpj) > 

0, E( y pj | xpj )  xpj , and V (y ) 

2

pj | xpj  p

xpj . Thus, the probability of unit j in subpopulation cell p is related 

to the observed auxiliary value, not the characteristic of interest, and the expectation and variance of the 

characteristic of interest are likewise statistically related to the auxiliary variable. For example, xpj could be the 

frame measure of size (MOS) for unit j. Because business populations tend to be positively highly skewed, the 

MOS is often highly correlated with probability of response i.e., the larger units are more likely to provide response 

data. Moreover, survey designers take great care to develop MOS variables that are highly correlated with 

characteristics of interest. In the applications presented below, the MOS is generally highly correlated with the 

collected totals items, less so with the detail items. Under this response mechanism, it can be shown that the best 

linear unbiased estimator (B.L.U.E.) for each y is the ratio estimator presented later in equation (4). 

The MAR response mechanism assumes that in each subpopulation p, P(Ipj=1| ypj, xpj) = P(Ipj=1|xpj) = φp > 0, i.e., φp 

is constant within sub-population p. Thus, the MAR unit nonresponse adjustment uses an “inverse response rate” 

adjustment to the design weights to produce an “unbiased” total estimate. Under this model, the literature (Kalton 

2 
 

 

 

 

 

 

 

and Flores-Cervantes, 2003) has repeatedly shown that the minimum requirements for developing weighting cells 

for unit nonresponse adjustment are that: 

i. The probability of response (φpj) for unit j in cell p is the same for all sampled units j (j = 1, 2, ..., np) in 

cell p (φpj= φp) or E(yp) = μp for all units j in cell p; and 

ii. The probability of response in cell p differs from that of cell p

⁄

for all p ≠ p

⁄

or the cell mean for variable y 

differs by weighting cell. 

We examine whether a given set of adjustment cells satisfies these two conditions via logistic regression analysis 

and via comparisons of unit response rates (URR). Response propensity modeling (Little and Rubin, 2002) uses 

logistic regression analysis to determine sets of explanatory covariates that result in adjustment cells with differing 

response propensities. Our response propensity model estimates 

ˆ with the model   f ( ), where p p p 

v  log[ f ( ) /{1 f ( )}]  x ( ), where xp is the vector of categorical values defined earlier, and β is a p p p p 

vector of unknown parameters estimated via maximum likelihood estimation with the appropriate “sandwich” 

estimator variance estimates. We fitted the logistic regression models with the SAS SURVEYLOGISTIC 

procedure, which incorporates the complex survey adaptations outlined in Roberts, Rao, and Kumar (1987). 

Certainty units are excluded from these analyses to facilitate appropriate complex survey adjustments to the test 

statistics (the SAS procedure excludes certainty units from the sandwich variance estimation computations). 

For each fitted logistic regression model, we test the goodness-of-fit hypothesis (H0: β=0). If we fail to reject the 

null hypothesis, we examine the marginal test results for each individual cell. With these analyses, rejecting the null 

hypothesis provides evidence that the variables used to construct adjustment cells are related to response propensity. 

We can add a continuous covariate to xp such as the MOS to assess whether the size of the unit is a predictor of unit 

nonresponse. 

The logistic regression analysis can indicate that the covariates used for the adjustment cells are predictors of 

response propensity. Alone, however, the model analysis does not provide empirical evidence of condition (ii), i.e. 

different response propensities by adjustment cell. For this, we compute unit response rates (URRs) within 

adjustment cells (see Särndal and Lundström , 2005, Chapter 3.3). 

Unit Nonresponse Adjustment Procedures 

The imputed estimator of the population total for characteristic y is given by 

 

Yˆ    wpj y pj  wpj y 

* 

pj   Yˆ 

R  Yˆ M (1) I 

p   js j p ,r p s 

,nr 

* where y is the imputed value obtained for nonrespondent unit j in adjustment cell p. We present three imputation pj 

models, both of which are re-expressed as adjustment weighting models. We use the variance estimation procedure 

from Shao and Thompson (2009) to obtain reweighted estimate variances. 

The first two models assume a MAR response mechanism, with the true unknown response probabilities estimated 

by the weighted and unweighted unit response rates, respectively. 

wpj y pjI pj 

 js Y Weighted Mean (Count): Imputed value y pj   wpjI pj 

js 

This imputed estimate can be re-expressed as the reweighted count estimate 

ˆ p   ˆ C N  c (2) Y  

ˆ P wj y pj  wpj y pj 

js NR  js pr pr 

p 

R 

p 

R 

Nˆ 

ˆ 

3 
 

 

 

 

 

 

 

 

 

 

 

 

 

* Unweighted Mean (Count_u): Imputed value y pj 

r 

y pjI pj 

j s 

This imputed estimate can be re-expressed as the reweighted count _u estimate 







p 

p 







w yj pj 

n

ˆ C _ U

Y 

j s 

 j s 

c u w y pj (3) 

_ 

pj  r

pr pr 

Both adjustments are designed to reduce or eliminate the bias caused by unit nonresponse and require that the 

adjustment cells satisfy conditions (i) and (ii). Besides the bias reduction properties, these adjustment methods have 

the advantage of computational simplicity. However, the additional stage of weighting will cause the variance to 

increase, especially when the adjustment factors are quite variable (Kish, 1992; Kalton and Flores-Cervantez, 2003; 

Little and Vartivarian, 2005). Indeed, when the categorical variables used to define the weighting adjustment cells 

are associated only with response propensity and are not predictive of characteristic outcome, then the bias 

amelioration of the reweighted estimates is minimal but carries a cost of increased variance. 

Ratio imputation models are designed to reduce the nonresponse bias and increase the estimate precision of a given 

characteristic y. These models require a strictly positive auxiliary variable x. 

  n 

p 



p 





1 



1 

This imputed estimate can be re-expressed as the reweighted ratio estimate 

wjy pjI  pj 

















* j

Ratio Model (Ratio): Imputed value y x pj pj  n 

w x I j pj pj 

j 

ˆ p X 







j s j s 

Under the covariate-dependent response mechanism, this ratio estimator is the B.LU.E of β, and the resultant ratio 

estimate will have increased precision over the count or count_u adjusted estimate. If the prediction model is not 

valid or if the strength of association between x and y is weak, then the bias induced by the ratio estimator increases 

the MSE over the corresponding count or count_u estimates. This situation can occur with the ancillary survey 

values -- such as detail items -- that are not primary characteristics of interest. 

Our studied business programs utilize two ratio imputation models: 





(4) ˆ R

Y   R  w y w y j pj pj pj ˆ P

 X  pr R  pr 

j

2 Trend y y y     , ~ (0, ) tj 



1, j tj 1, 

~ (0, 

2

) 

t t tj

Auxiliary y x x    ,

tj tj tj tj tj 

where t indexes the statistical period. Within imputation cell, the imputation base used to estimate β is restricted to 

complete respondent data2

 after outlier detection and treatment. This imputation procedure is referred to in-house as 

the “ratio-of-identicals” procedure. We assess the goodness-of-fit of these models to our survey data using the SAS 

SURVEYREG procedure within the six-digit industry cells, again excluding certainty cases. 

2The trend model parameters use reported or imputed data from respondents. 

4 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Random Subsample Analysis 

For each considered set of adjustment cells, we used a contingency table analysis to determine whether respondents 

comprise a random subsample within adjustment cell p. For nonresponse adjustment cells that are not equivalent to 

sampling strata (e.g., industry cells), we constructed the 3 x 2 contingency table shown in Figure 2 within each 

imputation cell. For these analyses, the design weight (wj) is the analysis variable, and P33 and P66 represent the 33rd 

and 66th percentiles, respectively, of the imputation cell’s distribution of wj. We chose these percentile values to 

ensure that each cell in the contingency table contains at least five noncertainty units; we did not perform any type 

of “optimality” analysis. 

The null hypothesis of interest is that response status is independent of unit size. Failing to reject the null hypothesis 

provides evidence of a random subsample within imputation cell. To perform the chi-squared tests for independence 

with the Rao-Scott adjustment procedure to account for complex survey sampling (Rao and Scott, 1992), we used 

the SAS SURVEYFREQ procedure. As with the logistic regression analyses presented above, certainty units are 

excluded from this analysis. 

Respondent Nonrespondent 

0 <= wj

 < P33 n11 n21 n1

P33 <= wj < P66 n12 n22 n2

P66 <= wj n13 n23 n3

n1

 n2 n

Figure 2: Contingency Table for Tests of Independence 

When using sampling strata as adjustment cell, we performed a similar analysis using a 1 x 2 contingency table 

because the noncertainty units in the same stratum generally have the same design weight. 

Survey Background 

The Service Annual Survey (SAS) is a mandatory scientifically designed sample survey of approximately 75,000 

employer businesses having one or more locations that provide services to individuals, businesses, and governments. 

The SAS surveys companies in NAICS sectors 22, 48-49, 51, 52, 53, 54, 56, 61, 62, 71, and 81. The SAS collects 

aggregate and detailed revenues and expenses, e-commerce, exports and inventories data from a sample of business 

firms with paid employees. Additionally, North American Product Classification System (NAPCS) data are 

collected in selected industries. SAS uses a stratified random sample design with one certainty stratum and multiple 

non-certainty strata assigned for each industry. In the initial sampling, companies are stratified by their major kind 

of business (determined by the industry containing the largest portion of total receipts for the company), and then 

sub-stratified by estimated annual receipts or revenue. All companies with total receipts above applicable size 

cutoffs for each kind of business are included in the survey as part of the certainty stratum and are asked to report 

for all their service industry locations. For companies with receipts below the applicable size cutoff, the Employer 

Identification Numbers (EINs) of these companies are then stratified by major kind of business and sub-stratified by 

total annual receipts or revenue. Within each noncertainty size stratum, a simple random sample without 

replacement of (EINs) is selected. Thus, the sampling units are either companies or EINs. Each sampling unit 

represents one or more establishments/locations owned or controlled by the same firm. The initial sample is updated 

quarterly to reflect births and deaths, adding new employer businesses identified in the Business and Professional 

Classification Survey and dropping firms and EINs that are no longer active. 

The SAS collects total revenue, total and detailed expenses, and e-commerce for all industries, both taxable and taxexempt; sources of revenue and expenses by type, as well as export and inventory data for selected industries; 

operating expenses for tax-exempt firms; and other selected industry-specific items. The key items collected by SAS 

are total revenue and total expenses. For both revenue and expenses, there are many detail revenue and expense 

items collected that sum up to their respective totals. Collected detail revenue items vary across industries within 

NAICS sectors. Expense detail items are primarily the same for all sectors, with an occasional additional expense 

detail or two collected for select industries. Appendix One presents item relationships in SAS. 

5 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Data collection and nonresponse adjustment for total revenue and total expenses are much less problematic than for 

the detail items. Companies are usually able to proportion out their “bottom line” revenue or expenses in a number 

of ways. However, methods of bookkeeping, limited staffing, company structure, and smaller company size may 

make it difficult for some respondents to calculate or even estimate values for a number of requested detailed 

revenue or expense items. For example, companies may do all their accounting by region, as opposed to by types of 

industries in which they do business. Similarly, a company’s line item in its bookkeeping may hold their expenses 

for all computer needs -- both hardware and software -- together. However, the SAS collects hardware and software 

expenses separately. For nonrespondents, missing values are replaced by predicted values obtained using 

appropriate imputation models for nonresponse. Imputation methodology is used to account for both unit and item 

nonresponse in the SAS. The imputation models use auxiliary survey and administrative records data as input. 

Survey and administrative records data for the detailed receipts and expenses are often very sparse or nonexistent. 

Thus, the imputation models for these variables are not as reliable nor predictive as desired. The research outlined 

in this paper was conducted to determine if weight adjustment could be used as an alternative nonresponse 

adjustment methodology for SAS. 

For processing purposes, the SAS is divided into five subsurveys, each covering one or more NAICS service sectors. 

This research is focused on the SAS subsurveys covering the transportation and health industries (SAS-T and SASH, respectively). These subsurveys cover NAICS sectors 48-49 and 62. 

Results 

All of the presented analyses use six years of historical data. In the two studied data sets, the six-digit industry code 

(NAICS), tax-exempt status (all units in SAS-T are in taxable industries), certainty status, weights, and sampling 

stratum are available for all sampled units, and frame measure of size (MOS) is available for most units. 

Response Propensity Analysis (Logistic Regression Analysis) 

The first step of our evaluation was to determine candidate sets of auxiliary variables that could be used to form 

adjustment cells. Currently, SAS-T uses six-digit industry to define adjustment cells; SAS-H uses six-digit industry 

and tax-status (taxable or tax-exempt) to define adjustment cells. Certainty and noncertainty units are not considered 

separately and are jointly used to develop ratio imputation parameters. For these analyses, we fit four separate 

logistic regression models using noncertainty cases: 

Model 1: xp = Current procedure adjustment cells 

Model 2: xp = Current adjustment cells and frame unit MOS (a continuous variable) 

Model 3: xp = frame unit MOS nested within current adjustment cells 

Model 4: xp = sampling strata (noncertainty) 

Model 1 evaluates the current adjustment cells. Model 2 addresses whether the existing adjustment cells need to be 

further refined to incorporate unit size by testing whether MOS contributes to response propensity, given the 

existing covariates. In all cases, the MOS was significant, and consequently, Model 3 addresses whether unit size 

within adjustment cell yields an improved propensity model. Lastly, Model 4 uses sampling strata, which 

incorporates both primary industry and unit size in the cell definitions [Note: sample sizes within a stratum can be 

quiet small due to fine stratification and limited numbers of “large” units in the population.] 

Appendix Two provides counts of significant logistic regression goodness-of–fit tests and individual parameter tests 

for the six years of historical data for SAS-H and SAS-T for Models 1, 3, and 4; the MOS covariate in Model 2 was 

always significant (6 of 6 years), and the other parameter tests are – as expected -- identical. Each tallied count 

represents the results from one statistical period, with a maximum of six possible tests. Recall that significant tests 

results provide evidence that β ≠ 0, i.e. that the auxiliary vector is a predictor of response propensity. 

For both SAS-H and SAS-T, the logistic regression analysis provides evidence that industry classification is not 

strongly related to response propensity (Model 1 results), but the unit size (MOS) and MOS nested within industry 

are (Models 2 and 3). It also provides evidence that stratum classification is related to response propensity. Given 

these results, we decided to evaluate two alternative sets of adjustment cells in addition to the currently-used six 

digit industry cells: 

6 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

     

1. Six-digit industry with four separate unit size class adjustment cells defined within industry (one certainty 

industry and the other three defined using the design weight classification parameters defined for the 

contingency table analyses presented in 4.1.2) 

2. Sampling stratum with two separate adjustment cells defined by certainty and noncertainty status whenever the 

within-cell sample size was five or greater; some form of collapsed stratum meeting the sample size and 

common sector criteria otherwise. This collapsing was necessary because several strata comprised two or fewer 

certainty units. 

Appendix Three presents average unit response rates (URR) for each considered set of adjustment cells for SAS-H 

and SAS-T. With each set of adjustment cells, unit response rates appear to be quite different, providing some 

indication that response propensities do differ by imputation cell. However, no statistical tests were performed to 

validate this observation. 

Prediction Model Analysis 

Ratio estimation improves estimate precision if and only if the auxiliary (independent) variable is highly positively 

correlated with the (imputed) dependent characteristic. Appendix Four summarizes the regression analysis results 

for SAS-H and SAS-T. We present two separate diagnostics: the results of the goodness-of-fit test (H0: β=0) and 

average R2

. Note that some results are missing. For both programs, trend model evaluations cannot be performed 

with the 2005 data sets. With SAS-T, there was insufficient data from noncertainty units to fit some detail 

regression models in the 2006 data sets. With SAS-H, the complete set of collected detail items differs sometimes 

by statistical period. 

Figure 2 summarizes the predictive model analysis by plotting average model-R2 values obtained from fitting the 

weighted list squares auxiliary ratio-of-imputation models for SAS-H; trend models are not considered. Blue 

diamonds indicate where null hypothesis (β=0) was rejected in 80-percent or more of the tests. The blue vertical 

asymptote separates the total items (182100/Total Payroll and 190000/Total Expenses) from the details. The grey 

horizontal asymptote is located at R2

 = 0.75. We define any observation that falls above this horizontal asymptote as 

a “highly predictive” model. Notice that the regression models used for the total items are significant and highly 

predictive, whereas the majority of the detail item models are not significant. The two apparently predictive “notsignificant” models for detail items 4061A00 and 189900 are attributed to random sampling error. 

0

0.75

182100190000174100174200179800

4001A004002A004003A004004A004005A004006A004007A004008A004009A004061A004062A004063A004064A004071A004072A00

182200182300182400182500182600182700182800182900183000183100183200180900401000401100

R

2

Significant Models Not Significant Models

Figure 2: Prediction Model Analysis for SAS-H 

Figure 3 summarizes the predictive model analysis by plotting average model-R2 values obtained from fitting the 

weighted list squares auxiliary ratio-of-imputation models for SAS-T. 

7 
 

 

 

 

 

 

 

 

 

 

 

 

 

     

0

0.75

180000182100182100190000506100506500509000509300509600179900182200182300182400182500182600182700182800182900183000183100183200189900509700509800509900508800508900509100509200509400509500

R

2

Significant Models Not Significant Models

Figure 3: Prediction Model Analysis for SAS-T 

As with the SAS-H models, the prediction model results are quite strong for the total items (180000/Total Payroll, 

182100 and 190000), providing some validation of the ratio adjustment procedure. For the subtotals, (506100, 

506500, 509000, 509300, and 509600), this strong relationship between independent variable and prediction 

variable holds for two of the five items. For the detail items, however, the majority of the models items do very 

little to explain the overall variance in the dependent variable, even though the regression parameters are significant. 

Random Subsample Analysis 

Appendix Five summarizes the results of the chi-squared tests for independence. These tests evaluate whether 

response is independent of size for the industry cells (Current Adjustment Cells columns) and whether the response 

is a random subsample within stratum (Strata Adjustment Cells columns). Consequently, rejecting the null 

hypothesis provides evidence against a random subsample. 

Recall that the Pearson chi-squared test for independence requires a minimum of five units per cell. The Rao-Scott 

modification for sample survey data requires that each cell contain an effective sample size3

 of five and generally 

sets a minimum value of five sampled units per cell in addition. These sample size constraints limited our analysis. 

For SAS-H, 11 of the 74 industry by tax status imputation cells were excluded from the 3x2 contingency cell 

analysis; 44 of the 63 remaining cells had “good fits,” providing evidence that the currently used adjustment cells 

could be “improved” by adding within-cell size categories. In SAS-H, each primary stratum is further classified by 

size category. Sixteen of the 79 primary strata were excluded from the analysis due to sample size limitations; 

another 20 were excluded due to small within-size-class counts. Thirty-five of the remaining 43 strata had good fits, 

however. 

For SAS-T, only four of the 12 industry imputation cells had good fits, providing evidence that subdividing industry 

by size does not result in more representative samples This result is not unexpected, as the sampling weights for 

non-certainty SAS-T units are not very variable, especially when compared to SAS-H. Ten of the 22 SAS-T strata 

were excluded from the analysis due small sample size, but the remaining 12 strata had good fits. Thus, for SAS-T, 

the test results provide evidence against a random subsample of units within industry cells, but provide evidence of a 

random subsample within noncertainty strata. 

3

 Actual sample size divided by the design effect 

8 
 

 

 

 

 

 

 

 

 

 

 

 

 

For both SAS-H and SAS-T, a visual inspection of the within-industry or within-industry/tax status contingency 

tables provided further indication that larger units (i.e., units with smaller design weights) are more likely to 

respond. 

Overall, the response propensity and prediction model results reinforce the concerns about the currently-used ratio 

imputation procedures for unit nonresponse. The logistic regression analysis provides little evidence for 

nonresponse bias reduction, given the current set of industry adjustment cells. The prediction models appear to be 

valid, but the SAS-H and SAS-T respondent samples consist of the larger sampled units and are not representative 

subsamples. Thus, the ratio imputation procedure tends to create units that resemble the larger sampled units. 

Estimate and Variance Estimate Effects 

In this section, we examine the effects of the alternative adjustment methods on estimates and variance estimates. 

For this, we computed three sets of estimates per set of adjustment cells and item: a ratio estimate that uses the 

currently used ratio-of-identicals model for each applicable item (equation 5); the count estimate that uses the 

weighted inverse response rate within adjustment cell as adjustment factor (equation 3); and the count_u estimate 

that uses the unweighted inverse response rate within adjustment cell as adjustment factor (equation 4). The 

auxiliary variables for ratio estimation differ by item; the same inverse response rate adjustment is applied to each 

unit within adjustment cell for the count and count_u procedures. The Taylor linearization estimates of sampling 

variance were obtained using the SAS SURVEYMEANS procedure. 

All of our comparisons are presented with respect to the ratio estimates. These comparisons give indications of 

estimation and variance estimation effects caused entirely by changes in adjustment cell and/or adjustment 

methodology. They do not provide any indication of the effects of these changes on the production totals, which 

use ratio imputation for unit nonresponse as a last resort in all cases. Moreover, our variance estimation results 

cannot be extrapolated to the production estimates. SAS uses the method of random groups for variance estimation; 

the variance estimator does not account for unit nonresponse or imputation effects on variances. Shao and Steel 

(1999) derives the appropriate variance estimator for a survey that uses composite imputation such as SAS, but is 

very difficult and expensive to implement; the Shao and Thompson method (2009) is easy to implement for either 

version of the count estimator, but is only accurate for reweighted estimators or imputed estimators that use one 

mean or ratio imputation model and requires that the auxiliary variable used in the ratio estimator be available for all 

sampled units. 

Appendix Six presents average ratios of estimates and sampling variances computed with each adjustment procedure 

(count, count_u, and ratio) within the same set of adjustment cells for SAS-H and SAS-T. These statistics examine 

the effects on estimation and variance estimation due to a change in adjustment procedure. From these results, we 

see that changing the adjustment model from a ratio model to an inverse response rate (count or count_u) tends to 

increase the estimates and the associated sampling variances. The estimation results are completely in-line with the 

earlier analyses, since the majority of the responding units are large and using the ratio-of-identicals models force 

the imputed values to look like "large values" whose ratios tend to be more stable and are often smaller than those 

obtained from smaller units. With the sampling variance calculations, using the inverse response rates increase the 

2

variance by a multiplicative factor 1/ . The sampling variances are, however, underestimates. p 

To gauge whether these large increases in variance are “reasonable,” we computed the variance inflation factor 

(VIF) proposed in Kish (1992, equation 4.2), which provides a rough estimate of the increased variance in the 

sample mean obtained using the count or count_u reweighting procedure. The VIF’s obtained for the q = c (count) 

and q=c_u (count_u) adjusted estimates for a given set of adjustment cells are given as 

q 2 q q 2 q 



2 

VIF  1 cv (wpj )  nwpj  /



wpj 

 (5) 

j  j 

Appendix Seven presents the average, minimum, and maximum VIFs for these two procedures by adjustment cell 

for SAS-H and SAS-T. These factors tend to be quite large, with approximately a 13-percent increase for SAS-H 

and a 27-percent increase for SAS-T in expected variance regardless of adjustment cells. This provides supporting 

evidence of the large variance increases with the count or count_u procedures over the ratio models that have strong 

predictive power (e.g., totals, subtotals). 

9 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Lastly, Appendix Eight presents average ratios of estimates and sampling variances by adjustment procedure (count, 

count_u, and ratio) between sets of adjustment cells. These tables examine the effects on estimation and variance 

estimation due to a change in adjustment cell, given the same adjustment procedure. Surprisingly, the change in 

adjustment cell doesn't appear to have much of an effect with the ratio estimators, but does come into play with the 

two inverse response rate adjustments (count and count_u). Adding a unit size classification within industry greatly 

increases the count and count_u total estimates generally, while reducing the sampling variance by quite a bit. 

Discussion 

This research was motivated by the need to validate the currently-used procedures implemented by several ongoing 

business programs at the U.S. Census Bureau. Survey sampling literature discusses methods of weight adjustment 

to account for unit nonresponse; the studied programs impute a complete record instead. If properly implemented, 

weight adjustment can reduce nonresponse bias and well as estimate variance while preserving multivariate 

relationships. 

So, why impute? Ultimately, the implemented procedures are designed to fulfill survey objectives to publish timely 

and accurate estimates of key survey data items. With the SAS data, it is often possible to build excellent unit level 

imputation models for the totals items, by logically deriving a replacing value from other reported items, by using 

historic data from the same unit, or by using administrative or even census data. For these programs, ratio 

imputation is a last resort. Unfortunately, the same wealth of auxiliary data is not available for many detail items, 

and the individual item response rates tend to be fairly low. Especially for these items, there is little evidence that 

the respondent values are “representative,” and it is difficult to develop strong predictive models. 

Our analysis of the SAS-H and SAS-T ratio models provides some validation of the ratio imputation procedure for 

totals, but does draw some “red flags.” The adjustment cells do not appear to be predictive of unit nonresponse, so 

there are bias concerns. The respondent sample is comprised mostly of larger sample units. Certainty and 

noncertainty units are used jointly to develop imputation parameters, even though their response propensities appear 

to differ substantially within industry imputation cell. It appears that nonresponse bias effects could be ameliorated 

using the same ratio imputation models, but modifying the adjustment cells, perhaps subdividing industry cells by 

unit size categories or by using some combination of sampling strata as adjustment cell. 

In contrast, we have presented evidence of estimation benefits for detail items by using reweighting instead of 

imputation. It should be noted, however, that the item-level response rates for many of the detail items are quite low 

and tend to be reported by the larger units. Consequently, the reweighted detail items will still suffer from some 

model bias, and the extent of this bias cannot be determined without additional data collection/non-response followup. However, the reweighting does preserve multivariate relationships between items. An alternative approach – 

not discussed in the paper – would be to publish unadjusted detail items along with a “not specified by kind” 

remainder.4 

In general, this analysis highlights several of the major challenges that business surveys encounter in addressing unit 

nonresponse. Respondents often do not comprise a random subsample, as larger units are more likely to provide 

data than smaller units. This phenomenon is an artifact of several factors, including the perceived benefits of the 

survey by the business community and the existing analyst nonresponse follow-up procedure, which focus on 

obtaining the most accurate estimated totals. Developing a more representative set of adjustment cells that contain 

sufficient respondents is equally challenging, as there are considerably fewer “large” units in the population than 

small units. Finally, there are data challenges, as several of the detail items that the survey would like to collect may 

not be available from the majority of the sampled units. Again, the respondent sample size issues for the detail 

items are compounded by collecting different sets of detail items by industry or sector. 

Acknowledgements 

4

 This procedure aggregates the weighted residual difference between the summed reported data values and the 

corresponding total. 

10 
 

 

 

 

 

 

The authors thank William Davie Jr., Xijian Liu, Philip Steel, and Julianne Zamora for their useful comments on 

earlier versions of this manuscript. 

References 

Kalton, G. and Flores-Cervantes, I. (2003). Weighting Methods. JOS, 19, pp. 81-97. 

Kish, L. (1992). Weighting for unequal Pi .JOS, 8, 183-200. 

Little, R.J.A. and Rubin, D.R. (2002). Statistical Analysis with Missing Data. New York: John Wiley and Sons. 

Little., R.J.A. and Vartivarian, S. (2005). Does Weighting for Nonresponse Increase the Variance of Survey Means? 

Survey Methodology, 31, pp. 161-168. 

Nelson, M. (2011). StEPS Imputation Specifications for the Transportation Portion of the 2010 Service Annual 

Survey (SAS-T). U.S. Census Bureau internal memorandum, EDMS #38537, available upon request. 

Oh, H.L. and Scheuren, F.J. (1983). Weighting Adjustment of Unit Nonresponse. Incomplete Data in Sample 

Surveys (Vol.20). New York: Academic Press, 143-184. 

Rao, J.N.K. and Scott, A.J. (1992). A Simple Method of the Analysis of Clustered Binary Data. Biometrika, 74, pp. 

577-585. 

Roberts, G., Rao, J.N.K., and Kumar, S. (1987). Logistic Regression Analysis of Sample Survey Data. Biometrika, 

74, pp. 1 - 12. 

Särndal, C.E. and Lundström, S. (2005). Estimation in Surveys with Nonresponse. New York: John Wiley & Sons, 

Inc. 

Shao, J. and Steel, P. (1999). Variance Estimation For Survey Data With Composite Imputation and Non-negligible 

Sampling Fractions. Journal of the American Statistical Association, 93, pp. 254-265. 

Shao, J. and Thompson, K.J. (2009). Variance Estimation In The Presence Of Nonrespondents and Certainty Strata. 

Survey Methodology, 35, pp. 215-225. 

11 
 

 

 

 

 

 

 

 

Appendix One 

Definition of Item Relationships in SAS-H and SAS-T 

Total Details: For Sector/subsectors: 

190000 (Total Expenses) 

182100, 182200, 182300, 182400, 182500, 

182600, 182700, 182800, 182900, 183000, 

183100, 183200, 189900 

49, 62 (2008 onward) 

182100, 182200, 182300, 182400, 182500, 

182600, 182700, 182800, 509700, 182900, 

509800, 183000, 509900, 183100, 183200, 

189900 

48 

1800000 (Total Revenue) 

174100, 174200, 179800 624 

4001A00, 4002A00, 4003A00, 4004A00, 

4005A00, 4006A00, 4007A00, 4009A00, 

4061A00, 4062A00, 4063A00, 4064A00 

6215 

4001A00, 4002A00, 4003A00, 4004A00, 

4005A00, 4006A00, 4008A00, 4071A00, 

4072A00, 174100, 174200, 180900, 

Tax-exempt 623 

4001A00, 4002A00, 4003A00, 4004A00, 

4005A00, 4006A00, 4008A00, 4071A00, 

4072A00, 180900, 

Taxable 623 

4001A00, 4002A00, 4003A00, 4004A00, 

4005A00, 4006A00, 4007A00, 4008A00, 

4009A00 

621, excluding six-digit 

industries that begin with 

‘6214,’ ‘6215,’ ‘6216,’ and 

‘6219’ 

4001A00, 4002A00, 4003A00, 4004A00, 

4005A00, 4006A00, 4007A00, 4008A00, 

174100 (selected industries), 174200 

(selected industries), 180900 

Tax-exempt 622 and six-digit 

industries that begin with 

‘6214,’ ‘6216,’ and ‘6219’ 

506100, 179900 484 

509000 (Truck Inventory) 508800, 508900 484 

509300 (Truck-tractor Inventory) 509100, 509200 484 

509600 (Trailer Inventory) 509400, 509500 484 
 

 

 

Appendix Two 

 Counts of Significant Propensity Analyses (Full Model and Individual Parameters) -- χ

2 Test 

SAS-H 

Model 1 Model 3 Model 4 

Industry by Tax Status Adjustment Cells Sampling Strata Adjustment Cells 

Full Sample 6 6 6 

Marginal 

Models 

180900χ

2 

only 

Cell Count Cell Count Cell Count Cell Count Cell Count Cell Count 

621111T0 1 622218E0 4 621111T0 6 622218E0 5 H11A 6 H23P 4 

621112T0 0 622219E0 1 621112T0 0 622219E0 3 H12A 5 H31A 6 

621210T0 6 622219T0 2 621210T0 1 622219T0 1 H13A 6 H31Z 3 

621310T0 2 622318E0 2 621310T0 2 622318E0 4 H13B 5 H32A 4 

621320T0 4 622319E0 0 621320T0 0 622319E0 0 H13C 6 H32B 5 

621330T0 5 622319T0 6 621330T0 1 622319T0 2 H13D 6 H32Y 4 

621340T0 1 623110E0 6 621340T0 0 623110E0 6 H13E 6 H32Z 1 

621391T0 3 623110T0 1 621391T0 4 623110T0 3 H13F 6 H33A 5 

621399T0 6 623210E0 6 621399T0 5 623210E0 5 H14A 5 H33B 6 

621410E0 1 623210T0 0 621410E0 5 623210T0 0 H14B 6 H33Y 5 

621410T0 0 623220E0 0 621410T0 0 623220E0 0 H14C 6 H33Z 3 

621420E0 1 623220T0 5 621420E0 5 623220T0 0 H14D 6 H39A 6 

621420T0 0 623311E0 6 621420T0 1 623311E0 6 H14E 6 H39Z 5 

621491E0 1 623311T0 0 621491E0 1 623311T0 0 H14F 6 H41A 6 

621491T0 3 623312E0 3 621491T0 2 623312E0 0 H14U 4 H41B 6 

621492E0 0 623312T0 3 621492E0 1 623312T0 1 H14V 4 H41C 6 

621492T0 1 623990E0 1 621492T0 0 623990E0 0 H14W 3 H41X 3 

621493E0 1 623990T0 6 621493E0 0 623990T0 4 H14X 3 H41Y 0 

621493T0 1 624110E0 4 621493T0 2 624110E0 0 H14Y 5 H41Z 1 

621498E0 1 624110T0 3 621498E0 4 624110T0 0 H14Z 1 H42A 5 

621498T0 4 624120E0 6 621498T0 2 624120E0 6 H15A 6 H42B 6 

621511T0 5 624120T0 6 621511T0 0 624120T0 1 H15B 6 H42C 6 

621512T0 5 624190E0 3 621512T0 1 624190E0 0 H16A 6 H42X 2 

621610E0 2 624190T0 0 621610E0 6 624190T0 1 H16Z 3 H42Y 2 

621610T0 2 624210E0 4 621610T0 2 624210E0 6 H19A 6 H42Z 2 

621910E0 3 624210T0 4 621910E0 3 624210T0 0 H19B 6 H43A 6 

621910T0 5 624221E0 6 621910T0 0 624221E0 2 H19Y 3 H43Z 1 

621991E0 6 624221T0 3 621991E0 2 624221T0 6 H19Z 3 H44A 6 

621991T0 1 624229E0 6 621991T0 2 624229E0 1 H21A 6 H44Z 5 

621999E0 1 624229T0 6 621999E0 0 624229T0 1 H21G 5 O33Z 2 

621999T0 4 624230E0 2 621999T0 1 624230E0 3 H21P 0 Y150 6 

622118E0 3 624230T0 6 622118E0 6 624230T0 0 H22A 6 

622119E0 6 624310E0 5 622119E0 6 624310E0 0 H22G 6 

622119T0 0 624310T0 1 622119T0 5 624310T0 0 H22P 5 

624410E0 0 624410E0 5 H23A 6 
 

 

Appendix Two 

SAS-T 

Model 1 Model 3 Model 4 

Industry Adjustment Cells Sampling Strata Adjustment Cells 

Full Sample 3 6 6 

Marginal 

Models 

χ

2

 only 

Cell Count Count Cell Count Cell Count 

484110 4 6 E14C 6 T42B 6 

484121 1 6 L11B 6 T42C 5 

484122 0 5 L31A 6 T85A 6 

484210 1 5 P16A 6 U12A 6 

484220 1 6 T11A 6 W21A 5 

484230 2 4 T11B 5 W22A 6 

492110 0 3 T12A 5 W31A 5 

492210 0 0 T411 5 W31B 4 

493110 0 0 T41A 6 W31C 4 

493120 1 2 T41B 6 W31D 6 

493130 1 6 T41C 3 W31C 4 

493190 3 1 T42A 5 W31D 6 
 

 

 

 

 

 

 

Appendix Three 

Average Unit Response Rates (URR) Using Current Adjustment Cells Subdivided by Certainty Status for SAS-H 

Imputation Cell/ 

Certainty Status URR 

Imputation Cell/ 

Certainty Status URR 

Imputation Cell/ 

Certainty Status URR 

Imputation Cell/ 

Certainty Status URR 

621111T0 C 60.50 621493E0 C 57.95 622218E0 C 74.51 624110E0 C 46.60 

621111T0 N 76.62 621493E0 N 52.94 622218E0 N 67.66 624110E0 N 81.62 

621112T0 C 38.59 621493T0 C 69.01 622219E0 C 60.92 624110T0 C 59.14 

621112T0 N 72.82 621493T0 N 74.57 622219E0 N 67.74 624110T0 N 62.93 

621210T0 C 79.44 621498E0 C 35.50 622219T0 C 59.05 624120E0 C 45.69 

621210T0 N 80.52 621498E0 N 86.08 622219T0 N 61.30 624120E0 N 87.41 

621310T0 C 64.68 621498T0 C 58.18 622319E0 C 53.29 624120T0 C 64.16 

621310T0 N 67.04 621498T0 N 61.03 622319E0 N 77.84 624120T0 N 64.03 

621320T0 C 67.31 621511T0 C 49.59 622319T0 C 58.66 624190E0 C 41.04 

621320T0 N 73.69 621511T0 N 66.82 622319T0 N 55.57 624190E0 N 82.72 

621330T0 C 62.35 621512T0 C 48.57 623110E0 C 62.60 624190T0 C 65.83 

621330T0 N 73.16 621512T0 N 66.18 623110E0 N 85.41 624190T0 N 66.35 

621340T0 C 49.83 621610E0 C 61.45 623110T0 C 62.63 624210E0 C 64.51 

621340T0 N 70.48 621610E0 N 85.24 623110T0 N 74.45 624210E0 N 82.25 

621391T0 C 79.87 621610T0 C 60.56 623210E0 C 59.53 624210T0 C 63.48 

621391T0 N 73.12 621610T0 N 67.42 623210E0 N 88.33 624210T0 N 48.56 

621399T0 C 58.46 621910E0 C 79.75 623210T0 C 48.72 624221E0 C 42.86 

621399T0 N 56.31 621910E0 N 80.48 623210T0 N 72.89 624221E0 N 87.00 

621410E0 C 61.79 621910T0 C 62.96 623220E0 C 52.63 624221T0 C 48.27 

621410E0 N 81.80 621910T0 N 64.11 623220E0 N 77.92 624221T0 N 55.86 

621410T0 C 70.68 621991E0 C 88.51 623220T0 C 52.80 624229E0 C 46.07 

621410T0 N 70.92 621991E0 N 87.30 623220T0 N 62.11 624229E0 N 81.62 

621420E0 C 52.71 621991T0 C 54.31 623311E0 C 53.21 624229T0 C 52.51 

621420E0 N 84.20 621991T0 N 53.04 623311E0 N 94.11 624229T0 N 41.24 

621420T0 C 58.38 621999E0 C 35.54 623311T0 C 39.25 624230E0 C 67.49 

621420T0 N 68.91 621999E0 N 76.77 623311T0 N 69.80 624230E0 N 81.14 

621491E0 C 43.06 621999T0 C 36.01 623312E0 C 52.23 624230T0 C 66.45 

621491E0 N 77.78 621999T0 N 53.75 623312E0 N 68.57 624230T0 N 39.51 

621491T0 C 45.99 622118E0 C 90.94 623312T0 C 47.69 624310E0 C 52.83 

621491T0 N 43.13 622118E0 N 74.83 623312T0 N 66.15 624310E0 N 86.13 

621492E0 C 29.41 622119E0 C 77.78 623990E0 C 46.15 624310T0 C 54.43 

621492E0 N 90.24 622119E0 N 87.27 623990E0 N 76.64 624310T0 N 62.82 

621492T0 C 35.31 622119T0 C 73.77 623990T0 C 57.90 624410E0 C 44.35 

621492T0 N 65.70 622119T0 N 70.50 623990T0 N 47.50 624410E0 N 79.18 

624410T0 C 55.20 

624410T0 N 61.10 
 

 

Appendix Three 

Average Unit Response Rates (URR) Using Current Adjustment Cells Subdivided by Size Category for SAS-H 

Imputation 

Cell 

Size 

Class URR Imputation 

Cell 

Size 

Class URR Imputation 

Cell 

Size 

Class URR Imputation 

Cell Size Class URR 

621111T0 C 60.50 621410E0 C 61.79 621498T0 C 58.18 621999T0 C 36.01 

621111T0 N1 82.62 621410E0 N1 90.15 621498T0 N1 64.40 621999T0 N1 57.32 

621111T0 N2 80.17 621410E0 N2 75.14 621498T0 N2 60.70 621999T0 N2 55.29 

621111T0 N3 68.13 621410E0 N3 75.62 621498T0 N3 58.53 621999T0 N3 49.09 

621112T0 C 38.59 621410T0 C 70.68 621511T0 C 49.59 622118E0 C 90.94 

621112T0 N1 78.83 621410T0 N1 81.48 621511T0 N1 72.40 622118E0 N1 82.10 

621112T0 N2 69.14 621410T0 N2 67.15 621511T0 N2 73.65 622118E0 N2 69.08 

621112T0 N3 70.12 621410T0 N3 62.86 621511T0 N3 57.27 622118E0 N3 71.97 

621210T0 C 79.44 621420E0 C 52.71 621512T0 C 48.57 622119E0 C 77.78 

621210T0 N1 82.05 621420E0 N1 88.45 621512T0 N1 72.50 622119E0 N1 87.43 

621210T0 N2 82.79 621420E0 N2 84.27 621512T0 N2 73.05 622119E0 N2 87.58 

621210T0 N3 77.82 621420E0 N3 80.62 621512T0 N3 56.22 622119E0 N3 86.93 

621310T0 C 64.68 621420T0 C 58.38 621610E0 C 61.45 622119T0 C 73.77 

621310T0 N1 65.96 621420T0 N1 69.29 621610E0 N1 90.67 622119T0 N1 72.43 

621310T0 N2 68.64 621420T0 N2 64.61 621610E0 N2 84.32 622119T0 N3 67.71 

621310T0 N3 67.19 621420T0 N3 71.58 621610E0 N3 81.02 622218E0 C 74.51 

621320T0 C 67.31 621491E0 C 43.06 621610T0 C 60.56 622218E0 N1 79.70 

621320T0 N1 70.52 621491E0 N3 77.78 621610T0 N1 70.73 622218E0 N2 75.00 

621320T0 N2 77.05 621491T0 C 45.99 621610T0 N2 67.53 622218E0 N3 54.94 

621320T0 N3 73.68 621491T0 N3 43.13 621610T0 N3 64.56 622219E0 C 60.92 

621330T0 C 62.35 621492E0 C 29.41 621910E0 C 79.75 622219E0 N1 81.57 

621330T0 N1 74.33 621492E0 N1 94.44 621910E0 N1 84.45 622219E0 N2 50.00 

621330T0 N2 68.84 621492E0 N3 88.19 621910E0 N2 80.27 622219E0 N3 59.84 

621330T0 N3 75.24 621492T0 C 35.31 621910E0 N3 76.52 622219T0 C 59.05 

621340T0 C 49.83 621492T0 N1 66.95 621910T0 C 62.96 622219T0 N1 77.84 

621340T0 N1 75.94 621492T0 N2 86.48 621910T0 N1 68.59 622219T0 N2 70.24 

621340T0 N2 67.80 621492T0 N3 49.25 621910T0 N2 65.99 622219T0 N3 38.85 

621340T0 N3 67.82 621493E0 C 57.95 621910T0 N3 58.90 622319E0 C 53.29 

621391T0 C 79.87 621493E0 N1 62.50 621991E0 C 88.51 622319E0 N1 97.62 

621391T0 N1 76.37 621493E0 N2 75.00 621991E0 N1 88.20 622319E0 N2 100.00 

621391T0 N2 72.28 621493E0 N3 45.55 621991E0 N3 86.18 622319E0 N3 61.27 

621391T0 N3 70.94 621493T0 C 69.01 621991T0 C 54.31 622319T0 C 58.66 

621399T0 C 58.46 621493T0 N1 82.15 621991T0 N1 43.33 622319T0 N1 76.17 

621399T0 N1 58.29 621493T0 N2 78.27 621991T0 N2 100.00 622319T0 N2 60.04 

621399T0 N2 55.38 621493T0 N3 67.36 621991T0 N3 38.61 622319T0 N3 38.45 

621399T0 N3 55.33 621498E0 C 35.50 621999E0 C 35.54 623110E0 C 62.60 

621498E0 N1 89.12 621999E0 N1 95.83 623110E0 N1 84.36 

621498E0 N2 85.88 621999E0 N3 57.22 623110E0 N2 85.84 

621498E0 N3 83.42 623110E0 N3 86.19 
 

 

Appendix Three 

Average Unit Response Rates (URR) Using Current Adjustment Cells Subdivided by Size Category for SAS-H 

(Continued) 

Imputation 

Cell 

Size 

Class URR Imputation 

Cell 

Size 

Class URR Imputation 

Cell 

Size 

Class URR Imputation 

Cell Size Class URR 

623110T0 C 62.63 623990E0 C 46.15 624210T0 C 63.48 624410E0 C 44.35 

623110T0 N1 71.09 623990E0 N1 78.57 624210T0 N1 69.52 624410E0 N1 83.48 

623110T0 N2 86.04 623990E0 N2 84.66 624210T0 N2 37.14 624410E0 N2 83.83 

623110T0 N3 68.95 623990E0 N3 67.90 624210T0 N3 41.15 624410E0 N3 71.65 

623210E0 C 59.53 623990T0 C 57.90 624221E0 C 42.86 624410T0 C 55.20 

623210E0 N1 87.05 623990T0 N1 56.48 624221E0 N1 87.32 624410T0 N1 67.86 

623210E0 N2 88.94 623990T0 N2 53.45 624221E0 N2 89.78 624410T0 N2 60.23 

623210E0 N3 89.10 623990T0 N3 37.43 624221E0 N3 85.43 624410T0 N3 55.41 

623210T0 C 48.72 624110E0 C 46.60 624221T0 C 48.27 

623210T0 N1 82.73 624110E0 N1 79.26 624221T0 N1 66.67 

623210T0 N2 75.10 624110E0 N2 83.79 624221T0 N3 51.82 

623210T0 N3 64.91 624110E0 N3 82.27 624229E0 C 46.07 

623220E0 C 52.63 624110T0 C 59.14 624229E0 N1 83.02 

623220E0 N1 77.66 624110T0 N1 77.97 624229E0 N2 80.75 

623220E0 N2 75.00 624110T0 N2 53.64 624229E0 N3 81.14 

623220E0 N3 79.22 624110T0 N3 57.53 624229T0 C 52.51 

623220T0 C 52.80 624120E0 C 45.69 624229T0 N1 55.09 

623220T0 N1 72.87 624120E0 N1 85.50 624229T0 N2 19.64 

623220T0 N2 75.78 624120E0 N2 89.45 624229T0 N3 35.83 

623220T0 N3 48.66 624120E0 N3 87.58 624230E0 C 67.49 

623311E0 C 53.21 624120T0 C 64.16 624230E0 N1 85.27 

623311E0 N1 96.20 624120T0 N1 76.41 624230E0 N2 77.69 

623311E0 N2 93.50 624120T0 N2 66.09 624230E0 N3 80.07 

623311E0 N3 92.52 624120T0 N3 51.31 624230T0 C 66.45 

623311T0 C 39.25 624190E0 C 41.04 624230T0 N1 34.08 

623311T0 N1 78.23 624190E0 N1 82.38 624230T0 N2 54.96 

623311T0 N2 71.28 624190E0 N2 88.79 624230T0 N3 32.49 

623311T0 N3 60.65 624190E0 N3 79.41 624310E0 C 52.83 

623312E0 C 52.23 624190T0 C 65.83 624310E0 N1 89.00 

623312E0 N1 82.33 624190T0 N1 69.22 624310E0 N2 87.71 

623312E0 N2 75.04 624190T0 N2 66.13 624310E0 N3 82.90 

623312E0 N3 50.10 624190T0 N3 64.23 624310T0 C 54.43 

623312T0 C 47.69 624210E0 C 64.51 624310T0 N1 61.02 

623312T0 N1 72.52 624210E0 N1 84.04 624310T0 N2 68.99 

623312T0 N2 65.92 624210E0 N2 78.73 624310T0 N3 60.23 

623312T0 N3 60.26 624210E0 N3 82.12 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix Three 

Average Unit Response Rates (URR) Using Pseudo-Stratum for SAS-H 

Pseudo-strata URR Pseudo-strata URR Pseudo-strata URR Pseudo-strata URR 

62 0.00 H14V N 55.33 H3 63.12 H42A N 49.45 

A1 34.79 H14X C 16.67 H31A C 55.42 H42B C 16.67 

A12A C 1.67 H14Y C 55.16 H31A N 75.69 H42B N 48.66 

C39W C 19.87 H14Y N 85.64 H31Z C 66.67 H42C C 100.00 

E16Z C 30.56 H14Z C 66.67 H31Z N 85.09 H42C N 40.64 

F11A C 22.22 H14Z N 84.02 H32A C 46.30 H42X C 63.76 

F41B C 50.13 H15A C 69.95 H32A N 71.75 H42X N 82.30 

H1 67.15 H15A N 66.84 H32B C 50.00 H42Y C 55.38 

H11A C 100.00 H15B C 83.33 H32B N 59.99 H42Y N 84.31 

H11A N 76.51 H15B N 66.21 H32Y C 34.88 H42Z C 66.67 

H12A C 83.33 H16A C 66.67 H32Y N 79.78 H42Z N 81.46 

H12A N 80.62 H16A N 66.91 H32Z C 33.33 H43A C 67.82 

H13A C 66.67 H16Z C 74.02 H32Z N 88.36 H43A N 64.34 

H13A N 66.59 H16Z N 87.09 H33A C 50.21 H43Z C 33.33 

H13B C 16.67 H19A C 16.67 H33A N 73.30 H43Z N 85.45 

H13B N 73.69 H19A N 64.14 H33B C 51.12 H44A C 57.03 

H13C C 83.33 H19B C 51.54 H33B N 67.28 H44A N 60.80 

H13C N 73.17 H19B N 54.47 H33Y C 74.12 H44Z C 44.06 

H13D C 50.00 H19Y C 78.33 H33Y N 71.10 H44Z N 79.52 

H13D N 70.45 H19Y N 90.10 H33Z C 59.12 L11A C 52.69 

H13E C 100.00 H19Z C 100.00 H33Z N 93.61 L22D C 48.57 

H13E N 73.28 H19Z N 80.95 H39A C 0.00 O1 41.68 

H13F C 100.00 H2 50.15 H39A N 48.54 O32Z C 31.46 

H13F N 57.40 H21A C 50.15 H39Z C 83.33 O33Z C 25.45 

H14A C 78.47 H21A N 71.57 H39Z N 77.41 O34Z C 39.29 

H14A N 73.24 H21G C 83.68 H4 61.93 P17A C 30.95 

H14B C 61.65 H21G N 75.61 H41A C 60.96 X160 C 91.11 

H14B N 69.43 H21P C 0.00 H41A N 63.01 XP10 C 43.19 

H14C C 83.33 H21P N 87.55 H41B C 83.33 XY 50.21 

H14C N 53.31 H22A C 56.63 H41B N 63.96 

H14D C 100.00 H22A N 61.43 H41C C 83.33 

H14D N 63.29 H22G C 86.43 H41C N 66.24 

H14E C 83.33 H22G N 79.19 H41X C 0.00 

H14E N 74.73 H22P C 83.33 H41X N 83.51 

H14F C 0.00 H22P N 78.19 H41Y C 56.25 

H14F N 61.12 H23A C 55.58 H41Y N 88.16 

H14U C 57.83 H23A N 55.58 H41Z C 51.80 

H14U N 86.62 H23P C 41.94 H41Z N 81.97 

H14V C 66.02 H23P N 97.62 H42A C 100.00 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix Three 

Average Unit Response Rates (URR) By Candidate Sets of Adjustment Cells for SAS-T 

Industry by 

Certainty Industry by Unit Size Stratum or Collapsed Stratum 

Industry/ 

Certainty URR Industry Size 

Category URR Industry Size 

Category URR Strata/ 

Certainty URR Strata/ 

Certainty URR 

484110 C 65.59 

484110 

C 65.59 

492110 

C 13.81 484B 19.10 W31B C 78.92 

484110 N 56.38 N1 67.43 N1 80.20 492B 12.31 W31B N 73.16 

484121 C 49.05 N2 56.78 N2 67.88 493B 19.68 W31C C 69.96 

484121 N 58.14 N3 45.22 N3 64.42 T31A C 2.78 W31C N 60.68 

484122 C 40.72 

484121 

C 49.05 

492210 

C 67.51 T32A C 12.50 W31D C 70.83 

484122 N 64.13 N1 71.22 N1 66.68 T41A C 68.09 W31D N 60.89 

484210 C 72.72 N2 61.26 N2 56.36 T41A N 56.33 

484210 N 58.91 N3 44.77 N3 55.27 T41B C 57.80 

484220 C 67.17 

484122 

C 40.72 

493110 

C 34.88 T41B N 58.14 

484220 N 56.28 N1 74.31 N1 70.54 T41C C 68.82 

484230 C 55.13 N2 69.44 N2 78.23 T41C N 64.13 

484230 N 58.34 N3 50.75 N3 48.76 T42A C 64.80 

492110 C 13.81 

484210 

C 72.72 

493120 

C 53.13 T42A N 58.91 

492110 N 70.75 N1 70.39 N1 76.71 T42B C 67.97 

492210 C 67.51 N2 59.16 N2 82.14 T42B N 56.31 

492210 N 59.03 N3 47.91 N3 68.03 T42C C 58.65 

493110 C 34.88 

484220 

C 67.17 

493130 

C 75.61 T42C N 58.40 

493110 N 64.26 N1 65.53 N1 65.63 T85A C 37.14 

493120 C 53.13 N2 53.38 N2&3 56.51 W21A C 48.41 

493120 N 73.94 N3 48.97 

493190 

C 39.04 W21A N 71.47 

493130 C 75.61 

484230 

C 55.13 N1 68.65 W22A C 66.77 

493130 N 60.68 N1 60.97 N2 66.14 W22A N 59.03 

493190 C 39.04 N2 66.43 N3 51.00 W31A C 54.44 

493190 N 60.38 N3 50.04 W31A N 65.31 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix Four 

Regression Analysis Results for SAS-H with Industry by Tax Status Adjustment Cells 

Numerator Denominator 

Imputation 

Model 

Number of 

Imputation Cells 

Average Percentage 

of Significant Cells 

Mean R2 

2005 2006 2007 2008 2009 2010 

TOTAL 

182100 182101 Trend 70 99.43 0.93 0.97 0.97 0.98 0.96 

180000 180001 Trend 70 99.71 0.94 0.96 0.96 0.98 0.97 

182100 190000 Auxiliary 70 89.52 0.83 0.88 0.88 0.88 0.88 0.88 

190000 180000 Auxiliary 70 90.95 0.95 0.96 0.95 0.96 0.96 0.96 

SUBTOTAL 185600 190000 Auxiliary 32 81.25 0.44 

DETAIL 

174100 180000 Auxiliary 32 82.29 0.43 0.36 0.45 0.46 0.46 0.43 

174200 180000 Auxiliary 33 77.78 0.35 0.34 0.34 0.32 0.28 0.29 

179800 180000 Auxiliary 32 36.98 0.81 0.59 0.48 0.48 0.46 0.45 

4001A00 180000 Auxiliary 52 86.22 0.69 0.69 0.71 0.73 0.72 0.71 

4002A00 180000 Auxiliary 52 84.29 0.65 0.63 0.62 0.64 0.62 0.62 

4003A00 180000 Auxiliary 52 79.17 0.48 0.45 0.46 0.43 0.46 0.44 

4004A00 180000 Auxiliary 52 62.82 0.70 0.42 0.44 0.48 0.46 0.42 

4005A00 180000 Auxiliary 52 83.65 0.58 0.70 0.68 0.68 0.69 0.67 

4006A00 180000 Auxiliary 49 55.44 0.64 0.39 0.45 0.42 0.39 0.41 

4007A00 180000 Auxiliary 41 83.33 0.58 0.56 0.60 0.56 0.56 0.56 

4008A00 180000 Auxiliary 50 78.67 0.55 0.49 0.46 0.43 0.44 0.44 

4009A00 180000 Auxiliary 54 32.72 0.47 0.41 0.38 0.30 0.19 0.16 

4061A00 180000 Auxiliary 26 7.69 0.87 0.83 0.83 0.87 0.84 

4062A00 180000 Auxiliary 26 7.69 0.66 0.66 0.66 0.65 0.64 

4063A00 180000 Auxiliary 26 6.92 0.11 0.16 0.19 0.33 0.32 

4064A00 180000 Auxiliary 26 7.69 0.52 0.63 0.64 0.68 0.71 

4071A00 180000 Auxiliary 12 88.89 0.47 0.54 0.60 0.61 0.60 0.60 

4072A00 180000 Auxiliary 12 77.78 0.41 0.53 0.49 0.51 0.44 0.49 

182200 190000 Auxiliary 70 60.00 0.81 0.83 0.37 0.84 

182300 190000 Auxiliary 70 76.43 0.34 0.39 0.37 0.36 0.34 0.33 

182400 190000 Auxiliary 70 82.62 0.42 0.43 0.45 0.47 0.42 0.47 

182500 190000 Auxiliary 70 82.38 0.47 0.52 0.52 0.52 0.51 0.52 

182600 190000 Auxiliary 70 75.95 0.36 0.41 0.39 0.42 0.44 0.44 

182700 190000 Auxiliary 70 79.05 0.66 0.66 0.68 

182800 190000 Auxiliary 70 57.86 0.52 0.59 0.85 0.62 

182900 190000 Auxiliary 70 56.07 0.58 0.58 0.18 0.60 
 

 

 

 

 

 

Appendix Four 

Numerator Denominator 

Imputation 

Model 

Number of 

Imputation Cells 

Average Percentage 

of Significant Cells 

Mean R2 

2005 2006 2007 2008 2009 2010 

183000 190000 Auxiliary 70 80.48 0.36 0.42 0.44 0.45 0.45 0.43 

183100 190000 Auxiliary 70 87.62 0.68 0.67 0.65 0.69 0.68 0.67 

183200 190000 Auxiliary 70 79.76 0.34 0.45 0.44 0.43 0.43 0.44 

180900 190000 Auxiliary 70 61.79 0.77 0.76 0.82 0.77 

401000 190000 Auxiliary 53 84.28 0.64 0.64 0.64 0.66 0.65 0.64 

401100 190000 Auxiliary 52 81.09 0.61 0.62 0.59 0.65 0.65 0.64 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix Four 

Regression Analysis Results for SAS-T with Industry Adjustment Cells 

Item Type 

Dependent 

Variable 

Independent 

Variable 

Imputation 

Model 

Number of 

Imputation Cells 

Average Percentage 

of Significant Cells

 Average R2 

2005 2006 2007 2008 2009 2010 

TOTAL 

180000 180001 Trend 12 100.00 0.95 0.96 0.98 0.97 0.95 

190000 180000 Auxiliary 12 100.00 0.96 0.98 0.98 0.98 0.98 0.89 

506500 506100 Auxiliary 6 100.00 0.87 0.88 0.88 0.86 0.86 0.84 

SUBTOTAL 

506100 180000 Auxiliary 6 100.00 0.99 0.99 0.98 0.99 0.98 0.99 

509000 506100 Auxiliary 6 63.89 0.27 0.21 0.17 0.17 0.20 0.14 

509300 506100 Auxiliary 6 83.33 0.71 0.73 0.70 0.71 0.72 0.57 

509600 506100 Auxiliary 6 100.00 0.71 0.71 0.71 0.67 0.72 0.68 

DETAIL 

179900 180000 Auxiliary 6 100.00 0.28 0.44 0.42 0.41 0.39 0.38 

182100 182101 Trend 12 100.00 0.89 0.97 0.98 0.98 0.89 

182100 190000 Auxiliary 12 98.61 0.81 0.83 0.84 0.82 0.81 0.78 

182200 190000 Auxiliary 12 98.33 0.68 0.74 0.75 0.72 0.69 

182300 190000 Auxiliary 12 75.00 0.31 0.26 0.26 0.27 0.31 0.34 

182400 190000 Auxiliary 12 84.72 0.28 0.29 0.25 0.25 0.21 0.19 

182500 190000 Auxiliary 12 87.50 0.50 0.44 0.46 0.49 0.47 0.43 

182600 190000 Auxiliary 12 75.00 0.28 0.26 0.45 0.34 0.37 0.30 

182700 190000 Auxiliary 12 91.67 0.54 0.56 0.52 0.48 0.61 

182800 190000 Auxiliary 12 90.00 0.43 0.45 0.45 0.46 0.51 

182900 190000 Auxiliary 12 91.67 0.50 0.62 0.60 0.56 0.57 

183000 190000 Auxiliary 12 93.06 0.41 0.51 0.51 0.41 0.38 0.40 

183100 190000 Auxiliary 12 97.22 0.64 0.64 0.64 0.63 0.66 0.68 

183200 190000 Auxiliary 12 88.89 0.58 0.57 0.63 0.58 0.55 0.47 

189900 190000 Auxiliary 12 100.00 0.66 0.70 0.67 0.71 0.77 

509700 190000 Auxiliary 6 88.89 0.56 0.58 0.50 0.63 0.64 0.62 

509800 190000 Auxiliary 6 91.67 0.71 0.65 0.68 0.78 0.70 0.60 

509900 190000 Auxiliary 6 94.44 0.71 0.71 0.71 0.67 0.70 0.62 

508800 509000 Auxiliary 6 100.00 0.87 0.82 0.82 0.87 0.83 0.79 

508900 509000 Auxiliary 6 58.33 0.25 0.40 0.26 0.27 0.22 0.27 

509100 509300 Auxiliary 6 97.22 0.86 0.86 0.83 0.84 0.81 0.83 

509200 509300 Auxiliary 6 83.33 0.30 0.31 0.28 0.33 0.37 0.30 

509400 509600 Auxiliary 6 100.00 0.82 0.81 0.78 0.79 0.77 0.80 

509500 509600 Auxiliary 6 75.00 0.26 0.31 0.32 0.33 0.38 0.32 
 

Appendix Five 

Random Subsample Assessment for Considered SAS-H Adjustment Cells: Current Cells (3 x 2 Contingency Table) 

Industry / 

Tax Status 

Number of 

Statistical 

Periods 

Number of 

Significant 

Tests 

Percentage of 

Statistical Periods with 

Significant Tests 

Industry/ 

Tax Status 

Number of 

Statistical 

Periods 

Number of 

Significant 

Tests 

Percentage of 

Statistical Periods with 

Significant Tests 

621111T0 6 6 100.00 622219T0 6 4 66.67 

621112T0 6 0 0.00 622319T0 6 4 66.67 

621210T0 6 6 100.00 623110E0 6 0 0.00 

621310T0 6 2 33.33 623110T0 6 6 100.00 

621320T0 6 0 0.00 623210E0 6 0 0.00 

621330T0 6 1 16.67 623210T0 6 0 0.00 

621340T0 6 2 33.33 623220E0 6 0 0.00 

621391T0 6 0 0.00 623220T0 6 4 66.67 

621399T0 6 3 50.00 623311E0 5 2 40.00 

621410E0 5 0 0.00 623311T0 6 1 16.67 

621410T0 6 1 16.67 623312E0 6 5 83.33 

621420E0 6 4 66.67 623312T0 6 2 33.33 

621420T0 6 0 0.00 623990E0 6 5 83.33 

621492T0 6 5 83.33 623990T0 6 5 83.33 

621493E0 4 0 0.00 624110E0 6 0 0.00 

621493T0 6 5 83.33 624110T0 6 0 0.00 

621498E0 6 2 33.33 624120E0 6 1 16.67 

621498T0 6 1 16.67 624120T0 6 5 83.33 

621511T0 6 6 100.00 624190E0 6 3 50.00 

621512T0 6 6 100.00 624190T0 6 0 0.00 

621610E0 6 3 50.00 624210E0 6 1 16.67 

621610T0 6 3 50.00 624210T0 6 4 66.67 

621910E0 6 0 0.00 624221E0 6 0 0.00 

621910T0 6 4 66.67 624229E0 6 0 0.00 

621991E0 2 0 0.00 624229T0 6 2 33.33 

621991T0 2 0 0.00 624230E0 6 0 0.00 

621999T0 6 2 33.33 624230T0 6 1 16.67 

622118E0 6 0 0.00 624310E0 6 3 50.00 

622119E0 6 0 0.00 624310T0 6 1 16.67 

622119T0 6 0 0.00 624410E0 6 4 66.67 

622218E0 6 6 100.00 624410T0 6 3 50.00 

622219E0 5 2 40.00 

Random Subsample Assessment for Considered SAS-H Adjustment Cells: Current Cells (2 x1 Contingency Table) 

Industry Number of 

Statistical 

Periods 

Number of 

Significant 

Tests 

Percentage of 

Statistical Periods with 

Significant Tests 

Industry Number of 

Statistical 

Periods 

Number of 

Significant 

Tests 

Percentage of 

Statistical Periods with 

Significant Tests 

621410E0 1 1 100.00 621999E0 5 0 0.00 

621491T0 5 1 20.00 622219E0 1 0 0.00 

621492E0 4 3 75.00 622319E0 6 3 50.00 

621493E0 2 0 0.00 623311E0 1 1 100.00 

621991E0 4 4 100.00 624221T0 5 4 80.00 

621991T0 4 0 0.00 
 

Appendix Five 

Random Subsample Assessment for Considered SAS-H Adjustment: Sampling Stratum (3 x 2 Contingency Table) 

Strata Number of 

Statistical 

Periods 

Number of 

Significant 

Tests 

Percentage of 

Statistical Periods with 

Significant Tests 

Strata Number of 

Statistical 

Periods 

Number of 

Significant 

Tests 

Percentage of 

Statistical Periods with 

Significant Tests 

H12A 6 6 100.00 H14U 1 0 0.00 

H13A 6 6 100.00 H14V 6 1 16.67 

H13B 3 1 33.33 H15A 6 3 50.00 

H13C 5 3 60.00 H16A 2 1 50.00 

H13D 3 2 66.67 H19A 6 2 33.33 

H13E 3 0 0.00 H19B 3 0 0.00 

H13F 6 1 16.67 H19Y 2 0 0.00 

H14A 5 2 40.00 H19Z 2 0 0.00 

H14B 6 4 66.67 H21A 1 0 0.00 

H14E 1 0 0.00 H21G 1 0 0.00 

H14F 3 1 33.33 H22A 4 1 25.00 

H14U 1 0 0.00 H22P 1 0 0.00 

H14V 6 1 16.67 H23A 6 2 33.33 

H15A 6 3 50.00 H31A 4 3 75.00 

H16A 2 1 50.00 H32A 2 1 50.00 

H19A 6 2 33.33 H33A 2 0 0.00 

H19B 3 0 0.00 H33B 6 4 66.67 

H19Y 2 0 0.00 H33Y 1 1 100.00 

H19Z 2 0 0.00 H39A 1 0 0.00 

H21A 1 0 0.00 H41A 5 0 0.00 

H21G 1 0 0.00 H41B 1 0 0.00 

H12A 6 6 100.00 H41C 3 1 33.33 

H13A 6 6 100.00 H41Y 2 1 50.00 

H13B 3 1 33.33 H41Z 3 0 0.00 

H13C 5 3 60.00 H42A 2 1 50.00 

H13D 3 2 66.67 H42B 4 0 0.00 

H13E 3 0 0.00 H42C 4 1 25.00 

H13F 6 1 16.67 H42Y 5 0 0.00 

H14A 5 2 40.00 H43A 4 0 0.00 

H14B 6 4 66.67 H43Z 1 0 0.00 

H14E 1 0 0.00 H44A 6 1 16.67 

H14F 3 1 33.33 H44Z 6 3 50.00 
 

 

Appendix Five 

Random Subsample Assessment for Considered SAS-T Adjustment Cells 

Current Adjustment Cells Strata Adjustment Cells 

Industry 

Number of 

Statistical 

Periods 

Number of 

Significant 

Tests 

Percentage of 

Statistical 

Periods with 

Significant 

Tests 

Strata** 

Number of 

Statistical 

Periods 

Number of 

Significant 

Tests 

Percentage of 

Statistical 

Periods with 

Significant 

Tests 

484110 6 6 100.00 T41A 6 3 50.00 

484121 6 5 83.33 T41B 6 1 16.67 

484122 6 1 16.67 T41C 6 0 0.00 

484210 6 5 83.33 T42A 6 0 0.00 

484220 6 3 50.00 T42B 6 1 16.67 

484230 6 6 100.00 T42C 6 1 16.67 

492110 6 1 16.67 W21A 6 1 16.67 

492210 6 1 16.67 W22A 6 3 50.00 

493110 6 5 83.33 W31A 6 0 0.00 

493120 6 1 16.67 W31B 6 1 16.67 

493130 6 3 50.00 W31C 6 1 16.67 

493190* 6 3 60.00 W31D 6 0 0.00 

* There was insufficient sample to use the 3 x 2 contingency table test in this adjustment cell with the 2006 data. 

The p-value for the1x 2 contingency table analysis was 0.1026. 

** There were several strata that were excluded from this analysis due to prohibitively small samples of 

nonrespondents within adjustment cell. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix Six 

Effect of Unit Nonresponse Adjustment by Type of Adjustment cell (Average Ratios): SAS-H 

Item Type 

TOTAL 

DETAIL 

Item Estimates

C/R C_U/R 

182100 1.00 0.96 

190000 1.00 0.97 

174100 0.99 0.98 

174200 1.00 1.00 

179800 1.00 1.00 

4001A00 1.00 0.98 

4002A00 1.00 0.98 

4003A00 1.02 0.97 

4004A00 0.99 0.94 

4005A00 1.00 0.98 

4006A00 1.00 0.94 

4007A00 0.98 0.95 

4008A00 1.01 0.95 

4009A00 1.01 0.93 

4061A00 1.00 0.90 

4062A00 1.00 0.93 

4063A00 1.02 0.97 

4064A00 1.03 0.95 

4071A00 1.00 0.97 

4072A00 1.00 0.98 

182300 1.01 0.96 

182400 0.98 0.95 

182500 0.99 0.96 

182600 1.00 0.97 

183000 1.00 0.94 

183100 1.00 0.98 

183200 0.99 0.94 

401000 1.00 0.97 

401100 1.00 0.99 

Industry 

 Sampling Variances 

C/R C_U/R 

0.90 0.99 

0.93 1.02 

0.98 0.95 

1.04 0.99 

0.91 0.87 

0.86 0.94 

0.98 0.98 

1.11 1.12 

0.80 0.80 

0.87 0.93 

0.95 0.89 

0.95 0.98 

0.94 0.95 

0.88 0.90 

0.90 0.79 

0.93 0.72 

1.05 0.79 

1.16 0.50 

0.78 0.78 

0.95 0.74 

0.90 0.88 

0.92 0.89 

0.90 0.90 

0.98 0.99 

0.85 0.87 

0.85 0.97 

0.89 0.88 

0.96 0.99 

0.87 0.99 

Industry by Size 

Estimates Sampling Variances 

C/R C_U/R C/R C_U/R 

0.99 1.12 0.89 0.93 

1.00 1.13 0.91 0.92 

1.08 1.10 0.91 0.88 

1.04 1.23 0.96 0.88 

1.10 1.13 0.87 0.86 

1.00 1.17 0.83 0.95 

1.00 1.12 0.92 0.89 

0.96 0.99 1.03 0.90 

0.96 1.10 0.82 0.96 

0.99 1.18 0.83 0.96 

0.98 1.09 0.93 0.95 

0.98 1.08 0.93 0.96 

1.01 1.10 0.89 0.95 

0.98 1.08 0.80 0.96 

1.05 0.89 0.67 0.78 

1.06 0.91 0.71 0.70 

0.93 0.98 0.83 0.77 

1.03 0.92 0.83 0.47 

1.03 1.04 0.78 0.88 

1.00 1.05 0.92 0.76 

1.00 1.11 0.90 0.95 

0.99 1.07 0.94 0.96 

1.03 1.11 0.91 0.94 

0.99 1.11 0.94 0.96 

0.98 1.07 0.80 0.96 

1.01 1.20 0.83 0.93 

0.99 1.08 0.91 0.97 

0.99 1.13 0.91 0.97 

1.00 1.20 0.83 0.95 

Pseudo-Strata 

Estimates Sampling Variances 

C/R C_U/R C/R C_U/R 

1.00 1.10 0.94 0.95 

1.00 1.12 0.98 0.98 

0.96 0.97 0.80 0.76 

1.00 1.16 0.93 0.86 

0.96 0.98 0.66 0.60 

1.02 1.17 0.82 0.89 

1.00 1.10 0.92 0.87 

0.99 1.02 1.21 1.09 

0.99 1.08 0.83 0.84 

1.01 1.17 0.82 0.87 

1.00 1.07 0.96 0.88 

1.00 1.07 1.01 0.97 

1.02 1.10 0.91 0.90 

1.01 1.06 0.90 0.92 

1.14 0.91 0.78 0.71 

1.15 0.95 0.81 0.63 

0.99 0.94 0.95 0.70 

1.11 0.91 0.94 0.42 

1.03 1.00 0.71 0.71 

0.98 1.00 0.86 0.67 

1.01 1.09 0.91 0.87 

1.00 1.05 0.98 0.94 

1.02 1.08 0.88 0.86 

1.00 1.09 0.98 0.94 

0.99 1.05 0.85 0.87 

1.01 1.18 0.83 0.93 

1.01 1.07 0.91 0.88 

1.01 1.12 0.99 0.96 

1.01 1.19 0.87 0.95 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix Six 

Effect of Unit Nonresponse Adjustment by Type of Adjustment cell (Average Ratios): SAS-T 

Item Type Item 

Industry Industry by Size Pseudo-Strata 

Estimates Sampling 

Variances Estimates Sampling 

Variances Estimates Sampling 

Variances 

C/R C_U/R C/R C_U/R C/R C_U/R C/R C_U/R C/R C_U/R C/R C_U/R 

TOTAL 190000 1.36 1.25 1.76 1.27 2.04 2.03 1.36 1.34 1.37 1.27 2.25 1.43 

SUBTOTAL 

506100 1.36 1.14 1.78 1.26 1.19 1.17 1.41 1.36 1.25 1.12 2.37 1.45 

506500 1.12 1.16 1.88 1.44 1.14 1.19 1.46 1.40 1.16 1.16 2.40 1.52 

509000 1.30 1.05 1.80 1.23 1.18 1.13 1.47 1.42 1.33 1.11 2.36 1.48 

509300 1.32 1.12 1.63 1.14 1.21 1.18 1.51 1.42 1.30 1.15 2.09 1.38 

509600 1.36 1.34 1.66 1.26 1.21 1.16 1.48 1.42 1.31 1.33 2.12 1.46 

DETAIL 

179900 1.39 1.11 1.92 1.38 1.10 1.08 1.32 1.28 1.07 0.96 2.25 1.40 

182100 1.41 1.32 1.93 1.55 2.20 2.19 1.58 1.51 1.39 1.30 2.52 1.60 

182200 1.39 1.38 1.88 1.51 2.44 2.43 1.49 1.46 1.48 1.41 2.50 1.60 

182300 1.35 1.27 1.65 1.53 1.91 1.89 1.77 1.61 1.39 1.27 2.35 1.46 

182400 1.40 1.31 1.77 1.27 2.40 2.38 1.58 1.54 1.51 1.35 2.41 1.53 

182500 1.39 1.42 1.71 1.28 3.40 3.38 1.55 1.49 1.58 1.49 2.23 1.48 

182600 1.39 1.37 1.80 1.32 2.52 2.50 1.65 1.45 1.54 1.44 2.11 1.61 

182700 1.39 1.37 1.77 1.31 1.92 1.91 1.62 1.45 1.47 1.37 2.41 1.97 

182800 1.39 1.31 1.87 1.43 1.81 1.80 1.34 1.37 1.34 1.20 2.48 1.65 

182900 1.34 1.22 1.90 1.35 2.01 1.99 1.59 1.53 1.51 1.40 2.55 1.57 

183000 1.43 1.37 1.91 1.29 2.74 2.72 1.54 1.40 1.51 1.41 2.40 1.72 

183100 1.40 1.28 1.86 1.29 2.06 2.04 1.47 1.41 1.49 1.39 2.56 1.61 

183200 1.41 1.27 1.89 1.46 1.68 1.66 1.49 1.44 1.48 1.36 2.47 1.64 

180900 1.48 1.47 2.03 1.67 2.59 2.56 1.46 1.40 1.62 1.45 2.26 1.60 

509700 1.41 1.17 1.93 1.33 1.15 1.14 1.49 1.44 1.20 1.10 2.55 1.59 

509800 1.39 1.16 1.87 1.31 1.22 1.20 1.56 1.53 1.36 1.19 2.64 1.61 

509900 1.39 1.16 1.86 1.33 1.22 1.20 1.59 1.54 1.37 1.19 2.47 1.59 

508800 1.27 1.02 1.66 1.19 1.14 1.09 2.12 1.97 1.31 1.09 2.32 1.60 

508900 1.28 1.02 1.58 1.11 1.02 0.99 2.05 1.85 0.85 0.73 2.19 1.49 

509100 1.44 1.22 1.70 1.23 1.29 1.27 1.52 1.47 1.41 1.24 2.38 1.51 

509200 1.29 1.06 1.60 1.10 1.08 1.06 1.67 1.57 0.94 0.83 2.31 1.47 

509400 1.33 1.14 1.85 1.41 1.19 1.18 1.23 1.19 1.26 1.12 2.47 1.53 

509500 1.29 1.06 1.64 1.11 1.08 1.06 1.59 1.50 0.93 0.83 2.18 1.41 

C/R = Count adjusted estimate/Ratio estimate 

C_U/R = Count_u adjusted estimate/Ratio estimate 
 

 

 

 

 

 

Appendix Seven 

Variance Inflation Factors for Reweighted Estimates Using Inverse Response Rates: 

SAS-T 

Adjustment Cell Weighted Inverse Response Rate (count) Unweighted Inverse Response Rate (count_u) 

Average Minimum Maximum Average Minimum Maximum 

Industry/Tax Status 12.92 12.32 14.36 12.74 12.01 13.99 

Industry/Tax Status by Unit Size 13.70 12.87 15.48 13.59 12.81 15.37 

Pseudo-Strata 12.98 12.36 14.38 12.60 11.84 13.82 

SAS-H 

Adjustment Cell Weighted Inverse Response Rate (count) Unweighted Inverse Response Rate (count_u) 

Average Minimum Maximum Average Minimum Maximum 

Industry 25.87 22.25 35.80 26.24 22.84 36.06 

Industry by Unit Size 28.12 24.04 39.11 28.34 25.06 38.92 

Pseudo-Strata 25.91 22.28 35.88 25.22 21.88 34.61 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix Eight 

Effect of Adjustment Cells by Type of Estimator (Average Ratios): SAS-H

Item Type Item 

Estimates Sampling Variances 

Ratio Count Count_u Ratio Count Count_u 

IS/I PS/I IS/I PS/I IS/I PS/I IS/I PS/I IS/I PS/I IS/I PS/I 

TOTAL 182100 1.00 0.96 0.99 1.12 1.00 1.10 0.90 0.99 0.89 0.93 0.94 0.95 

190000 1.00 0.97 1.00 1.13 1.00 1.12 0.93 1.02 0.91 0.92 0.98 0.98 

DETAIL 

174100 0.99 0.98 1.08 1.10 0.96 0.97 0.98 0.95 0.91 0.88 0.80 0.76 

174200 1.00 1.00 1.04 1.23 1.00 1.16 1.04 0.99 0.96 0.88 0.93 0.86 

179800 1.00 1.00 1.10 1.13 0.96 0.98 0.91 0.87 0.87 0.86 0.66 0.60 

4001A00 1.00 0.98 1.00 1.17 1.02 1.17 0.86 0.94 0.83 0.95 0.82 0.89 

4002A00 1.00 0.98 1.00 1.12 1.00 1.10 0.98 0.98 0.92 0.89 0.92 0.87 

4003A00 1.02 0.97 0.96 0.99 0.99 1.02 1.11 1.12 1.03 0.90 1.21 1.09 

4004A00 0.99 0.94 0.96 1.10 0.99 1.08 0.80 0.80 0.82 0.96 0.83 0.84 

4005A00 1.00 0.98 0.99 1.18 1.01 1.17 0.87 0.93 0.83 0.96 0.82 0.87 

4006A00 1.00 0.94 0.98 1.09 1.00 1.07 0.95 0.89 0.93 0.95 0.96 0.88 

4007A00 0.98 0.95 0.98 1.08 1.00 1.07 0.95 0.98 0.93 0.96 1.01 0.97 

4008A00 1.01 0.95 1.01 1.10 1.02 1.10 0.94 0.95 0.89 0.95 0.91 0.90 

4009A00 1.01 0.93 0.98 1.08 1.01 1.06 0.88 0.90 0.80 0.96 0.90 0.92 

4061A00 1.00 0.90 1.05 0.89 1.14 0.91 0.90 0.79 0.67 0.78 0.78 0.71 

4062A00 1.00 0.93 1.06 0.91 1.15 0.95 0.93 0.72 0.71 0.70 0.81 0.63 

4063A00 1.02 0.97 0.93 0.98 0.99 0.94 1.05 0.79 0.83 0.77 0.95 0.70 

4064A00 1.03 0.95 1.03 0.92 1.11 0.91 1.16 0.50 0.83 0.47 0.94 0.42 

4071A00 1.00 0.97 1.03 1.04 1.03 1.00 0.78 0.78 0.78 0.88 0.71 0.71 

4072A00 1.00 0.98 1.00 1.05 0.98 1.00 0.95 0.74 0.92 0.76 0.86 0.67 

182300 1.01 0.96 1.00 1.11 1.01 1.09 0.90 0.88 0.90 0.95 0.91 0.87 

182400 0.98 0.95 0.99 1.07 1.00 1.05 0.92 0.89 0.94 0.96 0.98 0.94 

182500 0.99 0.96 1.03 1.11 1.02 1.08 0.90 0.90 0.91 0.94 0.88 0.86 

182600 1.00 0.97 0.99 1.11 1.00 1.09 0.98 0.99 0.94 0.96 0.98 0.94 

183000 1.00 0.94 0.98 1.07 0.99 1.05 0.85 0.87 0.80 0.96 0.85 0.87 

183100 1.00 0.98 1.01 1.20 1.01 1.18 0.85 0.97 0.83 0.93 0.83 0.93 

183200 0.99 0.94 0.99 1.08 1.01 1.07 0.89 0.88 0.91 0.97 0.91 0.88 

401000 1.00 0.97 0.99 1.13 1.01 1.12 0.96 0.99 0.91 0.97 0.99 0.96 

401100 1.00 0.99 1.00 1.20 1.01 1.19 0.87 0.99 0.83 0.95 0.87 0.95 

IS/I = Unit Size within Industry/Tax-Status Adjustment Cells/Industry/Tax Status Adjustment Cells 

PS/I = Pseudo-Strata Within Industry/Tax Status Adjustment Cells 
 

 

 

 

Appendix Eight 

Effect of Adjustment Cells by Type of Estimator (Average Ratios): SAS-T

Item Type Item 

Estimates Sampling Variances 

Ratio Count Count_u Ratio Count Count_u 

IS/I PS/I IS/I PS/I IS/I PS/I IS/I PS/I IS/I PS/I IS/I PS/I 

TOTAL 190000 1.00 1.00 1.50 1.01 1.62 1.02 0.71 0.75 0.66 1.01 0.93 0.91 

SUBTOTAL 

506100 1.00 0.99 0.87 0.91 1.03 0.96 0.70 0.76 0.57 1.00 0.76 0.89 

506500 0.99 0.92 0.85 0.91 1.01 0.96 0.72 0.74 0.61 1.00 0.82 0.89 

509000 0.98 0.95 0.88 0.97 1.06 1.00 0.90 0.79 0.82 1.00 1.12 0.96 

509300 0.98 0.95 0.89 0.93 1.03 0.97 0.79 0.80 0.72 1.00 0.95 0.93 

509600 1.00 0.93 0.89 0.89 1.03 0.94 0.72 0.78 0.57 1.00 0.71 0.83 

DETAIL 

179900 0.99 1.19 0.79 0.92 0.97 1.04 0.81 0.85 0.59 1.00 0.80 0.90 

182100 1.01 1.03 1.58 1.02 1.67 1.01 0.73 0.77 0.59 1.00 0.73 0.82 

182200 1.07 0.96 1.82 1.02 1.81 0.97 0.66 0.76 0.53 1.00 0.65 0.83 

182300 0.98 1.02 1.39 1.05 1.45 1.02 0.75 0.72 0.84 1.00 0.96 0.79 

182400 0.99 0.95 1.71 1.02 1.78 0.98 1.00 0.75 0.85 1.00 1.14 0.90 

182500 1.00 0.95 2.43 1.08 2.39 1.00 0.76 0.76 0.74 1.00 0.90 0.86 

182600 0.96 0.99 1.76 1.10 1.71 1.04 0.67 0.77 0.66 1.02 0.75 0.93 

182700 1.02 0.99 1.41 1.05 1.45 1.01 1.05 0.91 0.92 1.31 1.10 1.51 

182800 1.00 1.07 1.30 1.03 1.40 0.99 0.76 0.71 0.56 1.00 0.76 0.85 

182900 1.05 0.88 1.49 1.00 1.60 1.01 0.82 0.75 0.69 1.00 0.93 0.91 

183000 1.01 1.02 1.94 1.08 2.01 1.05 1.02 1.42 0.78 1.43 1.01 1.95 

183100 1.01 0.94 1.48 1.00 1.60 1.02 0.83 0.72 0.69 1.00 0.92 0.89 

183200 1.01 0.93 1.20 0.97 1.32 1.00 0.80 0.77 0.61 1.01 0.78 0.87 

180900 0.99 0.98 1.76 1.07 1.78 0.98 0.72 0.81 0.73 1.02 0.98 0.91 

509700 1.02 1.06 0.83 0.90 1.00 1.00 0.65 0.75 0.53 1.00 0.72 0.89 

509800 0.99 0.95 0.87 0.93 1.02 0.97 0.75 0.72 0.64 1.00 0.86 0.89 

509900 0.99 0.94 0.87 0.93 1.03 0.97 0.83 0.75 0.71 1.00 0.95 0.90 

508800 0.99 0.94 0.89 0.97 1.06 1.00 0.65 0.72 0.82 1.00 1.11 0.96 

508900 1.05 1.47 0.84 0.97 1.03 1.04 0.69 0.71 0.84 1.00 1.18 0.97 

509100 1.01 0.94 0.90 0.92 1.04 0.96 0.74 0.76 0.69 1.00 0.90 0.91 

509200 0.97 1.35 0.81 0.98 0.97 1.05 0.65 0.71 0.68 1.00 0.91 0.93 

509400 1.00 0.94 0.90 0.89 1.04 0.92 0.80 0.77 0.56 1.00 0.70 0.82 

509500 0.98 1.30 0.82 0.93 0.98 1.01 0.67 0.75 0.64 1.00 0.86 0.92 

IS/I = Unit Size within Industry Adjustment Cells/Industry Adjustment Cells 

PS/I = Pseudo-Strata Within Industry Adjustment Cells/Industry Adjustment Cells