# Friedman’s Test

### Your homework problem:

You are interested in the effects of arousal on motor performance. A random sample of subjects perform a complex motor task under 3 conditions: no caffeine (low arousal), a small dose of caffeine (moderate arousal), and a large dose of caffeine (high arousal).

The dependent variable represents performance level: higher scores represent better performance.

This study resulted in the following data:

Subject | Low Difficulty |
Moderate Difficulty |
High Difficulty |

1 | 15 | 17 | 19 |

2 | 2 | 7 | 4 |

3 | 11 | 12 | 6 |

4 | 13 | 15 | 5 |

5 | 12 | 12 | 7 |

6 | 2 | 18 | 11 |

7 | 8 | 12 | 5 |

8 | 9 | 14 | 2 |

Did the perceived level of caffeine significantly affect the participants’ performance (alpha = .05)? If your analysis reveals a significant overall effect, then make sure to explore all possible mean differences with a post-hoc analysis (same alpha).

Note that these are the same data that we worked with when you were working with the one-factor ANOVA for repeated-measures designs. This will allow you to compare and contrast the results of the two procedures.

Enter these data into *Stats Homework’s* data manager and rename the variables. Your screen should look like this:

Make sure to double-check and save your data. To conduct your analysis, pull down the **Analyze** menu, choose **Non-Parametric Tests**, and then choose **Friedman’s Test**. You will be presented with a dialog that asks you to specify your variables:

Add your three variables to the window on the right. When you are ready, click the **Compute** button. *Stats Homework* will produce the following output:

**Rank Data**. This table includes the number of scores for each group, and the sum of the ranks for each group.

**Inferential Statistics**. This table presents the Chi Square approximation to estimating the significance level of Friedman’s test.

- Chi-Square (8.06): This is the value of χ². This procedure does not have the ability to compute the exact significance level of Friedman’s test, so we will use the χ² approximation. (Food for thought: the exact p for this test can now be computed with a permutation test that is now included in
*Stats Homework*). - df (2): This is the
*df*for the χ² statistic (equal to k – 1). - p (.018): This is the significance level of the χ² test.

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