In statistics, if your treatment effect is small, do you need a large sample size to reach significance?

Question

In statistics, if your treatment effect is small, do you need a large sample size to reach significance?

Answer 1

as the sample size increases the standard deviation of the test statistic decreases and the smaller and small effect is statistically significant.

I had to deal with this when working on my master's thesis.  there was a statistically significant difference between pre and post tests.  this difference was not practically significant as it was only one more correct answer on one test out of seven students on the post than the pre test.

Answer 2

Depending how small the effect is you may never be able to get a statistically significant result.

But, on average, yes the smaller the effect the larger the sample size you would want.  The reverse also applies although there is of course a limit to small of a sample size you can use to be considered significant.  The larger the effect the smaller the sample size required.