**[StATS]:** **Relationship between sample size and
p-values (February 14, 2005)**

I got a rather basic inquiry about p-values, but it is worth mentioning. Someone had a data set with 9,000 observations and was unhappy with the p-value that he got in a logistic regression model. So just as an experiment, he decided to replicate the data set (copy the entire matrix and paste it immediately below). This gave him a sample size of 18,000 observations. He noted that the odds ratio stayed the same but the p-value got smaller. Actually, in his example, it was cut exactly in half, but that was just a fluke.

I told him about the time when I only had $900 in charitable contributions at tax time, so I decided to xerox all my checks and then claim $1800 on my tax return. But in all seriousness, I did this when I first learned about Statistics, just to see what would happen. It turns out that when you increase your sample size, the p-value always goes down. There are a few exceptions for one-sided hypotheses, but this is a general rule that almost always works.

There is an obvious lesson here, but it wasn’t obvious to me the first time I did it. If two data sets show the same estimated odds ratio (or mean difference, or hazard ratio, or whatever) and are otherwise identical except for the sample size, it will be the larger of the two data sets that provides more precision, and therefore more evidence against the null hypothesis.

You can also browse for pages similar to this one at Category: Pvalues.

You can find an earlier version of this page on my website.