That is such a small sample size that the results could be masking underlying probabilities world wide. This study certainly has no meaning to places like Saudi Arabia where it is illegal to touch a dropped wallet unless you are the security staff of the building, the police, or an agent of the owner. Imagine if they did the exact same experiment there.
If half of all wallets get returned, then the variance of the number returned is on the order of 40 * 1/2 * (1-1/2) = 10, which means a standard deviation on the order of 3 wallets returned, or ~ 8% return rate. So the "puppy" and "family" figures might be out by about that much.
The cute-baby category had a measured return rate of 88%, which means a variance of something like 40 * 0.88 * 0.12~=4.2, for a standard deviation of ~ 2 wallets or about 5% in the return rate.
So if these results are unlucky to the tune of two 2-sigma errors pointing in the "right" direction, the puppy category might really be as good as 69%, and the baby category might really be as bad as 78%.
So, at least as far as simple sampling error goes, the "baby beats puppies" result seems pretty robust.
(No need to tell me about all the oversimplifications in the above. I know.)
Certainly they can't use the science of statistics to determine the sample size, since a good statistical study would require using a good sample size.
"In the study, 40 wallets were sent out in each photograph category as well as 40 containing a card suggesting that the owner had recently made a contribution to charity. A control batch contained no additional item.
All of the wallets were stuffed with the same set of everyday items, including raffle tickets, discount vouchers, and membership cards. None of them contained money, however."
(Added italics mine.)