This video describes the concept of inferential statistics when we wish to compare two groups - in particular hypothesis testing in the cases where we wish to compare either two population means, or the mean difference of two populations.

We use a sample from each population to determine whether or not there appears to be differences between the two populations.

Specific observations in one population may either be related to, or *not* related to, specific observations in the second population under consideration. When they aren’t related we consider an independent samples test, whereas when related we consider a paired samples test.

The method of analysis differs slightly depending on the situation.

An example of two independent samples being compared:

- testing whether the response time to a medication (how quickly a painkiller takes effect) differs between males and females. Hence we have two groups: males and females. We would consider two variables: one categorical (Sex: male or female) and one continuous (Time to take effect). The result for any particular male isn’t related to the result for any particular female.

An example of a paired samples test:

- to test the size of the reduction in pain due to a painkiller, we consider a measure of pain (continuous variable), and a measure indicating at what point in time (
*before*or*after*taking painkiller) the measure was taken (categorical variable). This is equivalent to considering pain score*before*taking the painkiller, and comparing this with the measure of pain*after*taking the painkiller, and repeating this on a number of people. - We wouldn’t be interested in comparing Person 1’s measure
*before*taking the painkiller, with Person 2’s measure*after*taking it.

We want to compare Person *1*’s measure *before*, with Person *1*’s measure *after*, and so on for each person.

In this case we have a natural pairing of measures (before and after taking the painkiller) so we consider the paired samples test.

NOTE: although the test refers to samples, the inference is made about the populations from which these samples come.

It is recommended that you are familiar with the content of the StatsTuneUp videos on Random Variables, Visual Displays – One Variable and Visual Displays - Two Variables, and Hypothesis Tests - Single Group before viewing this video.