# 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 $A^{&prime;}_{i}$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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