Example: Assessing Bias in a French Pre-Election Survey with surveybias

 
. use onefrenchsurvey, replace

. surveybias vote, popvalues(28.6 27.18 17.9 9.13 11.1 2.31 1.15 1.79 0.8) 
------------------------------------------------------------------------------
   vote |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
A'           |
    Hollande |  -.0757639   .0697397    -1.09   0.277    -.2124512    .0609233
     Sarkozy |   .0477294   .0689193     0.69   0.489    -.0873499    .1828087
       LePen |  -.0559812   .0823209    -0.68   0.496    -.2173271    .1053648
      Bayrou |   .3057213   .0953504     3.21   0.001     .1188379    .4926047
   Melenchon |  -.0058251   .0988715    -0.06   0.953    -.1996096    .1879594
   Joly |  -.0913924   .2154899    -0.42   0.671    -.5137449      .33096
      Poutou |  -.8802476   .4482915    -1.96   0.050    -1.758883   -.0016125
 DupontAigna |  -.5349338   .3031171    -1.76   0.078    -1.129032    .0591648
       other |   .1841789   .3177577     0.58   0.562    -.4386147    .8069724
-------------+----------------------------------------------------------------
B            |
      B |   .2424193          .        .       .            .           .
    B_w |   .0965423          .        .       .            .           .
------------------------------------------------------------------------------

    Ho: no bias
    Degrees of freedom: 8
    Chi-square (Pearson) = 18.695468
    Pr (Pearson) = .01657592
    Chi-square (LR) = 19.540804
    Pr (LR) = .01222022

Ten candidates stood in the first round of the French presidential election in 2012, but only two of them would progress to the run-off. While surveybias can handle variables with many categories, requesting estimates for very small parties increases the computational burden, may lead to numerically unstable estimates and is often of little substantive interest. In onefrenchsurvey.dta – a poll taken a couple of weeks before the actual election – support for the two-lowest ranking candidates has therefore been recoded to a generic ‘other’ category. The first-round results, which serve as a yardstick for the accuracy of the poll, are submitted in popvalues.

The top panel lists the A^{\prime}_{i} for the first eight candidates plus the ‘other’ category alongside their standard errors, z- and p-values, and confidence intervals. By conventional standards, only two of these values are significantly different from zero: Support for Bayrou was overestimated while support for Poutou was underestimated.

Poutou was the little known candidate for the tiny ‘New Anticapitalist Party’. While the odds of his support were underestimated by a considerable margin, the case of Bayrou is more interesting. Bayrou, a centre-right candidate, stood in the previous 2007 election and came third with a very respectable result of almost 19 per cent, taking many political observers by surprise. In 2012, when he stood for a new party that he had founded immediately after the 2007 election, his vote effectively halved. But this is not fully reflected in the poll. This could be due to (misguided) bandwagon effects, sampling bias, or political weighting of the poll by the company.

The lower panel of the output lists B and B_{w}. B, the unweighed average of the $A^{′}_{i}$s absolute values, is much higher than B_{w}. This is because the estimates for all the major candidates with the exception of Bayrou were reasonably good. While support for Poutou and also for Dupont-Aignan was underestimated by large factors, B_{w} heavily discounts these differences, because they are of little practical relevance unless one is interested specifically in splinter parties.

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