28.3 About sampling distributions and expectations

The sampling distribution describes, approximately, how the sample statistic (such as ˉx) is likely to vary from sample to sample over many repeated samples, when H0 is true: it describes the sampling variation. Under certain circumstances, sampling distributions often have an approximate normal distribution, which is the basis for computing P-values (or approximating P-values using the 68–95–99.7 rule).

When the sampling distribution is described by a normal distribution, the mean of the normal distribution is the parameter value given in the assumption (H0), and the standard deviation of the normal distribution is called the standard error.

In some cases, the sample statistic may not have a normal distribution, but a quantity easily derived from the sample statistic does have a normal distribution (for example, the odds ratio12).

  1. In this case, the logarithm of the odds ratio has an approximate normal distribution.↩︎