## Lesson 5: Paired-Samples *t* Test

#### Objectives

- Conduct a paired-samples
*t*test. - Interpret the output of the paired-samples
*t*test.

#### Overview

The paired-samples or dependent *t* test is used for within-subjects or matched-pairs designs in which observations in the groups are linked. The linkage could be based on repeated measures, natural pairings such as mothers and daughters, or pairings created by the experimenter. In any of these cases, the analysis is the same. The dependency between the two observations is taken into account, and each set of observations serves as its own control, making this a generally more powerful test than the independent-samples *t* test. Because of the dependency, the degrees of freedom for the paired-samples *t* test are based on the number of **pairs** rather than the number of observations.

#### Example

Imagine that you conducted an experiment to test the the effects of the presence of others (independent variable) on problem-solving performance (dependent variable). Assume further that you used a within-subjects design; that is, each participant was tested alone and in the presence of others on different days using comparable tasks. Higher scores indicate better problem-solving performance. The data appear below:

Participant |
Alone |
Others |

1 |
12 |
10 |

2 |
8 |
6 |

3 |
4 |
5 |

4 |
6 |
5 |

5 |
12 |
10 |

6 |
6 |
5 |

7 |
11 |
7 |

8 |
5 |
3 |

9 |
7 |
6 |

10 |
12 |
7 |

11 |
9 |
8 |

12 |
5 |
2 |

The following figure shows the variable view of the structure of the dataset:

Figure 5-1 Dataset variable view

Figure 5-1 Dataset variable view

#### Entering Data for a Within-Subjects Design: Key Point

When you enter data for a within-subjects design, there must be a separate column for each condition. This tells SPSS that the two data points are linked for a given participant. Unlike the independent-samples *t* test where a grouping variable is required, there is no additional grouping variable in the paired-samples *t *test. The properly configured data are shown in the following screenshot of the SPSS Data Editor Data View:

**Figure 5-2 Dataset data view **

#### Performing the Paired-Samples *t* test Step-by-Step

The SPSS data file for this example can be found here. After you have entered or opened the dataset, you should follow these steps in order.

Click on **Analyze**, **Compare Means**, and then **Paired-Samples T test**.

Figure 5-3 Select Paired-Samples T Test

In the resulting dialog box, click on the label for **Alone** and then press <Shift> and click on the label for **Others**. Click on the arrow to move this pair of variables to the Paired Variables window.

Figure 5-4 Identify paired variables

#### Interpreting the Paired-Samples *t* Test Output

Click** OK** and the following output appears in the SPSS Output Viewer Window (see Figure 5-5). Note that the correlation between the two observations is reported along with its *p* level, and that the value of *t*, the degrees of freedom (df), and the *p* level of the calculated *t* are reported as well.

Figure 5-5 Paired-Samples T Test output