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APPENDIX D: NON-RESPONSE BIAS ANALYSIS PLAN

(previously approved, OMB# 1850-0075 v.14)

Outline of the PISA 2015 Non-response Bias Analyses

The PISA 2015 contractor, Westat, is planning to conduct two nonresponse bias analyses (NRBA). A preliminary 

NRBA will be conducted in the early spring, prior to the data adjudication by the International Consortium in April, 

2016. These analyses are a subset of the full analysis and are outline after the full analysis below. The full (final) 

NRBA will be conducted for schools. Currently, it is assumed that the student response rate for PISA 2015 is above 

85 percent, as it has been in prior rounds of PISA, and thus no NRBA at the student level will be required.

Final PISA School Nonresponse Bias Analysis Outline

If school response rates are below NCES statistical standards, the final NRBA will be conducted in the summer of 

2016 before the release of the PISA 2015 national report in December of 2016. A summary of the NRBA findings 

will be included in the technical appendix of the U.S. national report. The full NRBA will be included in the U.S. 

technical report.

1. INTRODUCTION

2. METHODOLOGY

The analysis will be conducted in three parts:

 First, the distribution of the participating original school sample will be compared with that of the total 

eligible original school sample. The original sample is the sample before substitution. In each sample, 

schools will be weighted by their school base weights, excluding any nonresponse adjustment factor.

 Second, the distribution of the participating sample, which includes the participating replacements for 

schools from the original sample that did not participate, will be compared to the total eligible final 

sample. The final sample is the sample after substitution. Again, school base weights will be used for both 

the eligible sample and the participating schools.

 Third, the same sets of schools will be compared as in the second analysis but, this time, when analyzing 

the participating schools alone, school nonresponse adjustments will be applied to the weights.

The following categorical variables will be available for all schools:

 School type—public or private;

 Locality—urban-centric locale code, i.e., city, suburb, town, rural;

 Census region; and

 Poverty level—for public schools, a high poverty school is defined as one in which 50 percent or more of 

the students are eligible for participation in the National School Lunch Program (NSLP), and a low poverty 

school is defined as one in which less than 50 percent are eligible; all private schools are treated as low 

poverty schools.

The following continuous variables will be available for all schools:

 Number of age-eligible students enrolled;

 Total number of students;

 Mean percentage of students by race/ethnicity (White, non-Hispanic, Black, non-Hispanic, Hispanic, Asian 

or Pacific Islander, American Indian or Alaska Native, and two or more races).

An additional continuous variable, the percentage of students eligible to participate in the NSLP, was available 

only for public schools.

Two forms of analysis will be undertaken:

 A test of the independence of each school characteristic and participation status, and

 A logistic regression in which the conditional independence of these school characteristics as predictors of 

participation will be examined.
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For categorical variables, the distribution of frame characteristics for participants will be compared with the 

distribution for all eligible schools. The hypothesis of independence between the characteristic and participation 

status will be tested using a Rao-Scott modified Chi-square statistic at the 5 percent level (Rao and Thomas 2003). 

For continuous variables, summary means will be calculated and the difference between means will be tested 

using a t test. In addition to these tests, logistic regression models (including all characteristics) will be used to 

provide a multivariate analysis in which the conditional independence of these school characteristics as predictors 

of participation will be examined.

3. RESULTS

For each categorical or continuous variable, a table will be shown giving the percentage (or mean) for the 

participating and eligible populations along with the bias, relative bias, and the p-value of the test. Text 

summaries of the results will also be provided. The logistic regression results will be shown giving the parameter 

estimate, standard error, t test and p-value. The results will be given for each analysis.

3.1 Original Respondent Sample

Categorical Variables

Continuous Variables 

Logistic Regression Model 

3.2 Respondent Sample with Replacements (Final Sample)

Categorical Variables

Continuous Variables

Logistic Regression Model

3.3 Final Sample, With Nonresponse Adjustments Applied

Categorical Variables

Continuous Variables

Logistic Regression Model

4. CONCLUSIONS

A summary of the results will be presented along with a conclusion on the effect of substitutes and the 

nonresponse weighting adjustment.

Preliminary PISA School Nonresponse Bias Analysis Outline

If school response rates are below NCES standards, this NRBA will be conducted in the first quarter of the 2016 to 

be available to the International Consortium by April.

1. INTRODUCTION

A preliminary analysis will be conducted just on the original respondent sample. The analysis will be identical to 

the final analysis except that the base weights and school statuses may not be final.

2. METHODOLOGY

3. RESULTS

Original Respondent Sample

Categorical Variables

Continuous Variables 

Logistic Regression Model 

4. CONCLUSIONS