### Small Numbers?

#### Posted by BM11 on 31 May 2012 at 04:38 GMT

I'm not a statistician but it seems that with small samples representing age groups (ie only 12) you are likely (15% chance) to get only five smelly specimen in the M group and seven smelly in the O (old) group and that sampling luck played a role in your findings. The population of any age group could be in reality 50% smelly and 50% odorless. So it would be wrong to tell you could recognize old people by their smell when half of them would be odorless.

No competing interests declared.

### RE: Small Numbers?

#### jolen replied to BM11 on 01 Jun 2012 at 07:42 GMT

I am not entirely sure that I understand your numbers. We had 12 donors in the old age group and 16 in the young and middle age, respectively. Each of these donated two pads. These pads where subsequently cut into 4 pieces, each. That renders a total of 128 individual pieces for each age group but the old that had 96. To prevent influence of any one individual, we created so-called "super-donor stimuli" that consisted of four pieces from four separate individuals (from the same age group). Care was taken to avoid repeatedly including the same individuals within the same stimulus. Moreover, in all analyses, any variance that could be explained by the rated intensity was removed (covariates). One could argue that we had a sampling error where a few individuals still managed to influence the outcome. However, if you take a look at the Supplementary Figure 1, you can see the actual ratings of all stimuli. If sampling luck would be a valid concern, clear sporadic “bumps” would be evident. As can be seen in this figure, one such “bump” exists. However, post-hoc tests for statistical outliers did not classify these stimuli (or any other) as statistical outliers. Taken together, I agree that sampling error is, and should always be, a great concern in any study. Nevertheless, we went to a great length to reduce this risk and our post-hoc statistical analyses suggest that our measures were successful in eliminating this risk.

No competing interests declared.

### RE: RE: Small Numbers?

#### BM11 replied to jolen on 01 Jun 2012 at 11:26 GMT

I'm just saying that if the % of smelly people in the population is 50% for the three age groups, by selecting a sample of size 12 for a specific age group there is a 7% chance you get 9 or more smelly people out of 12 for the elderly (20% for 8) and 7% chance you get 3 or less smelly people for the middle aged. If you're unlucky and the elderly have 9 or more smelly people, your study will conclude that they smell more than the others, without being true at the population level. You could have cut by~ half the probability of getting a sample with 75% or more smelly subjects by increasing the sample size from 12 to 16. For cutting the pads in 4, you also introduce dependency among the variables so it's not as good as having a real sample size of 128.

No competing interests declared.