Two samples are independent when the subjects selected for the first sample do not determine the subjects in the second sample. Two samples are dependent when the subjects in the first sample determine the subjects in the second sample. The data from dependent samples are called matched-pair or paired samples. The key concept in this section is that we consider the differences of matched-pair data as a single sample and perform inference on this sample of differences.
The paired-sample test for the population mean of the differences can be used either when the population is normally distributed or the sample size is large ().
The test may be performed using either the critical-value method or the -value method.
A confidence interval for , which is the population mean of the differences, is given by , where and represent the sample mean and sample standard deviation of the differences, respectively, of the set of paired differences, , , , …, , and where is based on degrees of freedom.
This confidence interval may be used to conduct two-tailed hypothesis tests for .