# Does sample size affect the value of median?

I have two groups of A and B. Group A consists of 11 people and group B of 35 people. The results of one behavioral outcome measure is higher for the group B while logically it should be the other way around (considering the group characteristics). Can this be related to the sample size? what factors could affect median?

• Sample size could and should influence the variability of the median, but not its value. If you are surprised by your results, always plot the data too. In fact, your dataset is small enough to post here. Commented Apr 3 at 16:46
• You can find a lot of useful, relevant information about sample medians at stats.stackexchange.com/questions/45124.
– whuber
Commented Apr 3 at 17:09

## 3 Answers

First what you are calling 'logic' almost certainly is not exactly logic. Logic is things like from Aristotle or Gödel or people like that. Statistics plays no role. What you almost certainly have are expectations based on substantive knowledge.

Second No, the median is not affected by sample size. The median is the value that splits the ordered data into two equal (or, in some cases, as close to equal as possible) sets.

What affects the median is the values.

Third: You didn't get the results you expected. You are surprised. There are two sorts of explanations: 1) You coded something wrong, mislabeled the groups, or something like that. 2) Your expectations were wrong.

My favorite professor in grad school often said "If you're not surprised, you haven't learned anything." Assuming you haven't made any kind of error as in 1), what have you learned?

Maybe your sample is odd. Maybe you have an omitted variable. Or maybe the theory that gave rise to your expectations is incorrect.

• I mean the variance of the median (and it's overall efficiency) depends on the sample size... Commented Apr 3 at 16:59
• That is true, but has nothing to do with your question Commented Apr 3 at 19:57
• Re "nothing to do with:" In their answer to the explicit question "what factors could affect median," Anti writes "the deviation of the sample median [relative to] to the median of the whole population of course also depends on your sample size." Moreover, in a trivial technical sense -- but nevertheless worth noting, sample size can affect the sample median profoundly. For instance, in a binary dataset of odd size the median is either $0$ or $1$ but for even sizes the median (according to a convention) can also be $1/2,$ a value impossible for odd-sized samples.
– whuber
Commented Apr 3 at 20:17

I wouldn't say it depends on the sample size, more on the group-intrinsic medians of the parameters/characteristics you're interested in. If you've for instance measure the body height of women (group A) and men (group B), I'd argue that you'll find higher medians in the male group. Are you sure that the grouping can't have any impact on the median itself?

However, the deviation of the sample median to the median of the whole population of course also depends on your sample size. Thus, the higher your sample size, the closer you should be to the true median (on average). Thus, the approximation of the true median should be better in your group B in comparison to your group A. Nevertheless, your sample size is not that big, and thus there can be still some deviations that could have caused an "inaccurate" measure ...

• thanks! that's what I was looking for but couldn't articulate.
– Lily
Commented Apr 3 at 19:20

The median (or for that matter any parameter) is NOT affected by the sample size. But the variance of your statistic (your observed estimate of said parameter) obviously is. The smaller your sample size, the more noise there will be on your estimates. The larger your sample size, the closer to the true population parameter will your estimate be (on average), and the less variable will these estimates be.

So, yes, you could have made an error. Or your expectations could be ill-founded. But it could also be that your estimate of A was quite noisy (11 is NOT a large sample size). So if you expected your smaller sample A, to have a higher value than B, just try to collect more samples for A...

One way to check that is to compute confidence intervals of your measured statistic (mean?) for A and B. If they overlap substantially, then the fact that one is larger than the other means nothing. Your sample size(s) was too small...