Because it never turns out the way I want it, that confounded thing!

Seriously, the p value is literally a confounded index because it reflects both the size of the underlying effect and the size of the sample. Hence any information included in the p value is ambiguous (Lang et al. 1998).

Statistical significance = Effect size x Sample size

Now let’s hold the effect size constant for a moment and consider what happens to statistical significance when we fiddle with the sample size (N). Basically, as N goes up, p will go down automatically. It has to. It has absolutely no choice. This is not a question of careful measurement or anything like that. It’s a basic mathematical equation. The bigger the sample, the more likely the result will be statistically significant, regardless of other factors.

Conversely, as N goes down, p must go up. The smaller the sample, the less likely the result will be statistically significant.

So if you happen to get a statistically significant result (a low p value), it could mean that (a) you have found something, or (b) you found nothing but your test was super-powerful because you had a large sample.

This entry was posted on Sunday, May 30th, 2010 at 11:43 pm and is filed under p values, statistical significance, substantive significance. You can follow any responses to this entry through the RSS 2.0 feed.
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“The primary product of a research inquiry is one or more measures of effect size, not p values.”
~ Jacob Cohen

“Statistical significance is the least interesting thing about the results. You should describe the results in terms of measures of magnitude – not just, does a treatment affect people, but how much does it affect them.”
~ Gene Glass