Title: Exploring relationships in samples
Course: UGQuants (SSPS) > Section: Inference

Exploring relationships in samples

Imagine that we are interested in whether men or women are more likely to vote, and that we want to be 99% certain of our results. It might be, for example, that political parties want to target their campaigns to specific groups to mobilise people who don’t usually vote.

First let us formulate our null hypothesis. This is that there is no difference between the proportion of voters who are men and women in the population of Britain. We would reject this hypothesis and provisionally accept our alternative hypothesis that a different proportion of women than men vote in national elections only if there is a less than 1% chance that the results in our sample are consistent with this null hypothesis (that is, if there is a less than 1% chance of getting the strength of relationship we observe in our sample if this relationship did not exist in the population form which the sample has been drawn).

Next, let us produce a contingency table of gender by vote_bin to compare the proportions of voters by sex.

Table 1: voting behaviour by gender

Source: ESS5 (UK) unweighted data

It is the case that slightly more women than men in our sample are voters: 72.6% as compared to 71.3%. But what are the chances of this being the case in the population from which our sample was taken?

Statistical software will calculate the confidence intervals for us if not voting has the value 0 and voting has the value 1. Don’t forget to select a confidence interval of 99%.

Table 2: Confidence of proportion of voters by gender at 99% significance level

Source: ESS5 (UK) unweighted data

Source: ESS5 (UK) unweighted data

Note how confidence intervals widen considerably for a 99% Confidence Intervals comparing the two genders as against a 95% CI for all adults. This is for two reasons. We have tightened our criteria: we want to be 99% rather than 95% certain of our results. We have also reduced our sample sizes. Instead of 2,321 adults we are looking separately at 1,016 men and 1,305 women. Can we be 99% certain - using the estimates from our sample - women were more likely to vote than men during the last national elections? Think about this before you move on...