My previous post discussed p-values in SPSS and Stata for probability-weighted data. This post provides more information on weighting in the base module of SPSS. Data in this post are from Craig and Richeson (2014), downloaded from the TESS archives; SPSS commands are from personal communication with Maureen Craig, who kindly and quickly shared her replication code.
Figure 2 in Craig and Richeson's 2014 Personality and Social Psychology Bulletin article depicts point estimates and standard errors for racial feeling thermometer ratings made by white non-Hispanic respondents. The article text confirms what the figure shows: whites in the racial shift condition (who were exposed to a news article titled, "In a Generation, Racial Minorities May Be the U.S. Majority") rated Blacks/African Americans, Latinos/Hispanics, and Asian-Americans lower on the feeling thermometers at a statistically significant level than whites in the control condition (who were exposed to a news article titled, "U.S. Census Bureau Reports Residents Now Move at a Higher Rate").
Craig and Richeson generated a weight variable that retained the original post-stratification weights for non-Hispanic white respondents but changed the weight to 0.001 for respondents who were not non-Hispanic white. Figure 2 results were drawn from the SPSS UNIANOVA command, which "provides regression analysis and analysis of variance for one dependent variable by one or more factors and/or variables," according to the SPSS web entry for the UNIANOVA command.
The SPSS output below represents a weighted analysis in the base SPSS module for the command UNIANOVA therm_bl BY dummyCond WITH cPPAGE cPPEDUCAT cPPGENDER, in which therm_bl, dummyCond, cPPAGE, cPPEDUCAT, and cPPGENDER respectively indicate numeric ratings on a 0-to-100 feeling thermometer scale for blacks, a dummy variable indicating whether the respondent received the control news article or the treatment news article, respondent age, respondent education on a four-level scale, and respondent sex. The 0.027 Sig. value for dummyCond indicates that the mean thermometer rating made by white non-Hispanics in the control condition was different at the 0.027 level of statistical significance from the mean thermometer rating made by white non-Hispanics in the treatment condition.
The image below presents results for the same analysis conducted using probability weights in Stata, with weightCR indicating a weight variable mimicking the post-stratification weight created by Craig and Richeson: the corresponding p-value is 0.182, not 0.027, a difference due to the Stata p-value reflecting a probability-weighted analysis and the SPSS p-value reflecting a frequency-weighted analysis.
So why did SPSS return a p-value of 0.027 for dummyCond?
The image below is drawn from online documentation for the SPSS weight command. The second bullet point indicates that SPSS often rounds fractional weights to the nearest integer. The third bullet point indicates that SPSS statistical procedures ignore cases with a weight of zero, so cases with fractional weights that round to zero will be ignored. The first bullet point indicates that SPSS arithmetically replicates a case according to the weight variable: for instance, SPSS treats a case with a weight of 3 as if that case were 3 independent and identical cases.
Let's see if this is what SPSS did. The command gen weightCRround = round(weightCR) in the Stata output below generates a variable with the values of weightCR rounded to the nearest integer. When the Stata command used the frequency weight option with this rounded weight variable, Stata reported p-values identical to the SPSS p-values.
The Stata output below illustrates what happened in the above frequency-weighted analysis. The expand weightCRround command replicated each dataset case n-1 times, in which n is the number in the weightCRround variable: for example, each case with a weightCRround value of 3 now appears three times in the dataset. Stata retained one instance of each case with a weightCRround value of zero, but SPSS ignores cases with a weight of zero for weighted analyses; therefore, the regression excluded cases with a zero value for weightCRround.
Stata p-values from a non-weighted regression on this adjusted dataset were identical to SPSS p-values reported using the Craig and Richeson commands.
So how much did SPSS alter the dataset? The output below is for the original dataset: the racial shift and control conditions respectively had 233 and 222 white non-Hispanic respondents with full data on therm_bl, cPPAGE, cPPEDUCAT, and cPPGENDER; the difference in mean therm_bl ratings across conditions was 3.13 units.
The output below is for the dataset after executing the round and expand commands: the racial shift and control conditions respectively had 189 and 192 white non-Hispanic respondents with a non-zero weight and full data on therm_bl, cPPAGE, cPPEDUCAT, and cPPGENDER; the difference in mean therm_bl ratings across conditions was 4.67, a 49 percent increase over the original difference of 3.13 units.
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Certain weighted procedures in the SPSS base module report p-values identical to p-values reported in Stata when weights are rounded, cases are expanded by those weights, and cases with a zero weight are ignored; other weighted procedures in the SPSS base module report p-values identical to p-values reported in Stata when the importance weight option is selected or when the analytic weight option is selected and the sum of the weights is 1.
(Stata's analytic weight option treats each weight as an indication of the number of observations represented in a particular case; for instance, an analytic weight of 4 indicates that the values for the corresponding case reflect the mean values for four observations; see here.)
Test analyses that I conducted produced the following relationship between SPSS output and Stata output.
SPSS weighted base module procedures that reported p-values identical to Stata p-values when weights were rounded, cases were expanded by those weights, and cases with a zero weight were ignored:
- UNIANOVA with weights indicated in the WEIGHT BY command
SPSS weighted base module procedures that reported p-values identical to Stata p-values when the importance weight or analytic weight option was selected and the sum of the weights was 1:
- Independent samples t-test
- Linear regression with weights indicated in the WEIGHT BY command
- Linear regression with weights indicated in the REGWT subcommand in the regression menu (weighted least squares analysis)
- UNIANOVA with weights indicated in the REGWT subcommand in the regression menu (weighted least squares analysis)
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SPSS has a procedure that correctly calculates p-values with survey weights, as Jon Peck noted in a comment to the previous post. The next post will describe that procedure.
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UPDATE (June 20, 2015)
Craig and Richeson have issued a corrigendum to the "On the Precipice of a 'Majority-Minority' America" article that had used incorrect survey weights.
