Are Lib Dem supporters more credulous?

I decided to have some fun with statistics today. YouGov have recently completed a survey on public attitudes to various “alternative medicine” practices. Rather than get depressed about the sheer numbers of people who are taken in by these varying degrees of nonsense (66% of people believe acupuncture is possibly or definitely an effective treatment; 47% for reflexology and a staggering 70% for chiropracty, to pull some headline figures out), I looked a little closer into the tables YouGov provide for their survey.

YouGov break down their sample in various ways, including both current and past voting intention. Looking through the figures I noticed that the numbers in the “Lib Dem” column appeared to be slightly higher, for those “effective treatment” responses, than either their Labour or Conservative counterparts. I wondered whether this could be borne out statistically – in other words, are Liberal Democrat supporters more likely to believe in the effectiveness of “alternative medicine?”

Firstly I added together the “definitely” and “possibly an effective treatment” scores for each treatment within each voter ID group, then I averaged between the Conservative and Labour scores to produce two columns: Lib Dem belief in each treatment compared with the average of the other two major parties.

I then performed a paired t-test on these two sets of figures, to determine whether the Lib Dem scores really were higher than for the other parties, or whether this was just a statistical fluke.

Using individuals’ current voting intention, I found that on average, 4.8% more Lib Dems believe a treatment is effective than their Labour or Conservative counterparts, with a standard deviation of 4.0%. This gives a value for t of 3.7, and a p-value of 0.006. In layman’s language, this means that we can be 99.4 per cent certain that Lib Dems are more likely to believe a treatment is effective than Labour supporters or Conservatives. In many applications of statistics (including biology, which I work in), 95% confidence (i.e. a p-value of less than 0.05) is the threshold level beyond which an effect is inferred to be genuine rather than a statistical anomaly.

For voting intention in May 2010, the figures are similar. An average of 5.9% more people who voted Lib Dem at the general election believe each of the treatments is effective, compared to those who voted for one of the other two major parties. The standard deviation here is 3.8, the t value 4.7, and the p-value is 0.002 – so our confidence that people who voted for the Lib Dems are more likely to believe in these quackeries than other voters rises to 99.8 per cent.

Incidentally, there is no significant difference between the likelihood of Labour and Conservative supporters believing in these therapies, which provides some justification for aggregating them as I have done here.

So what does all of this mean? In all likelihood, not a lot. One thing to consider is the size of the effect – only about 5%. While the statistics show that the effect is very likely to be real, it isn’t very big.

Another thing is sample sizes – there are only 189 current Lib Dem supporters in YouGov’s sample, weighted down to 183. There are 542 people who voted Lib Dem last May, weighted down to 518. The margin of error associated with these small sample sizes is likely to be quite large.

That being said, it is still an interesting observation to make. Lib Dem supporters, it would seem, are slightly more likely to believe in the effectiveness of these treatments than supporters of the other two major parties. I wonder if there are any clear reasons for this?

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