# Why is a paired t-test used

## Paired t-test: application examples

**paired t-test**

There are several study designs in which the t-test for paired samples makes sense. What all designs have in common is that we have two groups and that we want to know whether there is a difference in the means of the dependent variables between these two groups.

### Design # 1: The classic experimental setup

The first design is also the design that is most frequently examined with the t-test. Here we have a group of people that we are examining for the same dependent variable at two different points in time. We were interested in whether there is a difference between measurement time 1 and measurement time 2 or between treatment 1 and treatment 2.

The measurement of the dependent variable does not have to be tied to a point in time. Instead, we could follow the first condition (treatment) with the second immediately. Here, however, the order itself could have an influence on the dependent variable. Therefore a cross-over design would be better for this situation, which is discussed in the next point.

### Design # 2: Cross-Over Design

A very popular design in many studies is this **Cross-over design**. In the first step of cross-over design, test subjects are randomly divided into one of two groups. One group then receives the first treatment, the other the second. In the second step, each group receives the treatment that they have not yet received. Depending on the research question, a break should be taken between the treatments so that **Wash out** (e.g. for medication, where it must be ensured that there are no more residues). The illustration below shows the classic cross-over design.

Cross-over designs are more complex in terms of organization, but at the same time have a higher level of complexity **internal validity**. This is because the **sequence** can also have an effect on the dependent variable (sequence effect). However, by randomizing the order, an attempt is made to control this as much as possible.

### Design # 3: Matched pair comparison

Another possibility is for individuals (or other statistical objects) to do so **match**that they are no longer considered independent. * Matching*can be understood as the search for a statistical twin. In medical studies, the statistical twin is often also a biological one: Identical twins are often not considered independent, but rather one

*matched pair*. In this way one could match other properties. In this way a pair is obtained which is the same with regard to a specific characteristic. Instead of a t-test for independent samples, one can then calculate a paired t-test.

Matching can also take place within a person (or a statistical object). For example, if we wanted to compare the performance of the left and right kidney, we would also use a paired t-test.

*t*-Test should not be averted on data that is relevant for each group

*z*- Have been standardized. The result will always be

*p*= Be 1,000!

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