In 2000, a random sample of adults in a particular population finds that 20% answer “yes” to the question, “Have you ever done X”.

In 2003, doing X is made illegal.

In 2012, another random sample finds that only 10% answer “yes” to the question “Have you ever done X”.

The immediate problem I see with this pair of statistics is that everyone who has “ever” done X as of 2000, by definition has also “ever” done X as of 2012. Which means that theoretically, the 2012 figure would have to be at least as high as the 2000 figure.

Now obviously in a random sample you aren’t going to be asking the *exact* same people, so there’s some room for discrepancy. And 12 years is enough time for at least some of the older population in your 2000 sample to die and be replaced by younger people. But still, a 50% drop in 12 years seems to me to be a little too big to be explained by a natural population turnover.

So basically what I’m wondering is, looking at those two sets of figures, would it be a viable interpretation that behaviour has actually changed from 2000-2012, or would you have to assume that something else is going on (e.g. that in 2012 people are lying because they don’t want to admit to criminal activity). Assume for the sake of argument that the basic methodologies of the two surveys are sound and identical and that the sample sizes are large enough to be taken as representative.

Hope I’ve made this all clear. I have no training in statistical evaluation and I want to be sure that I’m not missing something.