# Example: Assessing Bias in Educational Attainment with surveybias Using the Survey Estimator

Normally, more educated voters are more likely to participate in opinion surveys and are therefore overrepresented in survey. But this pattern is not reflected in the pre-election wave of the German Longitudinal Election Study (GLES).

. use gles-preelection, replace . surveybias educ, popvalues(4 36.1 30.5 29) ------------------------------------------------------------------------------ educ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- A' | noqualifica | -.5113485 .1461372 -3.50 0.000 -.7977721 -.2249249 upto9yrs | .0115364 .0469027 0.25 0.806 -.0803912 .103464 10yrs | .308362 .0466371 6.61 0.000 .2169549 .3997691 12yrs+ | -.290088 .0532528 -5.45 0.000 -.3944617 -.1857144 -------------+---------------------------------------------------------------- B | B | .2803337 . . . . . B_w | .203609 . . . . . ------------------------------------------------------------------------------ Ho: no bias Degrees of freedom: 3 Chi-square (Pearson) = 63.802082 Pr (Pearson) = 9.048e-14 Chi-square (LR) = 65.206022 Pr (LR) = 4.532e-14

On the contrary, respondents with twelve or more years of schooling are clearly underrepresented, while there is no appreciable bias for respondents with nine years of schooling, and respondents with ten years of schooling are actually overrepresented. Only the misrepresentation of the small group of school dropouts is in line with expectations.

There are some possible reasons for this unusual type of bias. One is the generational gap in educational attainment. Younger voters are much more likely to hold Abitur qualifications and also more mobile and less likely to have a landline connection, hence more difficult to contact for interviewers.

But another plausible and perhaps more interesting reason is the complex design of the GLES: The GLES is a multi-stage survey that deliberately oversamples respondents from the former East Germany (GDR) to account for persistent attitudinal, social, and economic differences between Germany’s Eastern and Western regions. In the GDR, the Communists phased out the Hauptschulabschluss and instead promoted a ten-year-curriculum. At the same time, they limited access to the Abitur. As a consequence, the distribution of school-leaving qualifications in the former East Germany still differs markedly from the West.

**surveybias** supports Stata’s survey estimator, so it is possible to make use of the weights supplied by the GLES team as well as of the information on PSUs and stratification to see if this reduces the apparent bias.

. qui svyset vnvpoint [pweight=w_ipfges_1] , strata(distost) . surveybias educ, popvalues(4 36.1 30.5 29) svy Using survey characteristics of your data Warning: This requires switching to numerical methods ------------------------------------------------------------------------------ educ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- A' | noqualifica | -.2203508 .2777376 -0.79 0.428 -.7647065 .3240049 upto9yrs | .0665091 .0780089 0.85 0.394 -.0863856 .2194038 10yrs | .0202821 .0657158 0.31 0.758 -.1085185 .1490827 12yrs+ | -.0596029 .0943501 -0.63 0.528 -.2445258 .12532 -------------+---------------------------------------------------------------- B | B | .0916863 . . . . . B_w | .0565208 . . . . . ------------------------------------------------------------------------------ Ho: no bias Degrees of freedom: 3 Chi-square (Wald) = 1.3289546 Pr (Wald) = .72226926

Incorporating the information on the design of the survey massively reduces the estimates for bias. The for the three major groups are now very small while the is roughly halved, and none of them differs significantly from zero. , the estimate for the overall bias, drops to one third of the original figure of 0.28, while its weighted version, , is reduced even further from 0.20 to 0.06, because it takes the size of the ‘no qualification’’ group into account.

With complex variance estimators, simple goodness-of-fit tests are not appropriate. They are replaced by the equivalent Wald-test of the null hypothesis that all (and, by implication, the overall measures and ) jointly equal zero. At three degrees of freedom, this hypothesis cannot be rejected.