The mean score on the "I believe" scale was 41 in the Thinker group. The standard deviation was 31 (76% of the mean). The mean in the Discobolus group was 62 with an SD of 36 (58% of the mean). There's a lot of overlap between the two groups. I could go on here about what's wrong with their "statistical analysis." Doesn't look like they proved anything to me.

Well, analytic thinking is not always so easy... OF COURSE there is an overlap between the two groups. Think again. How could it be otherwise? The standard deviation measures the variation in people's religious views. The participants have different religious views going in to the experiment, and obviously you are not going to change that by having some look at one picture and one looking at another. You are causing a shift between two normal distributions that supposedly were overlapping, and had large standard deviations, before the experiment started.

If there was no overlap at all, that would mean that all those who looked at picture A would consider God more likely than all those who looked at the other picture. That is not going to happen, of course. But even a shift of one or two standard deviations is a big change.

The important thing is that there was a statistically significant difference between the two groups, as measured by the t-test.