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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 stu dent 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 l evel will be required. **Final PISA School Nonresponse Bias Analysis Outline**  If school response rates are below NCES statistical standards, t he 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 we ights, 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
— u rban -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 va riable, 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.2

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, su mmary 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 i ndependence 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, t his 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 o riginal respondent sample . The analysis will be identical to the fin al 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