A More Appropriate Statistical Test

The student in this scenario wants to investigate whether there is a difference in how likable women find two different descriptions of a potential romantic partner. They have collected data from the same group of women, who rated both descriptions on a scale of 1 to 10 for likability. The student plans to use an independent samples t-test to analyze this data. However, a more appropriate statistical test would be the Wilcoxon test.

Here are two reasons why the Wilcoxon test is more appropriate for this study:

1. Repeated Measures Design

The study uses a repeated measures design (also known as a within-subjects design). This means that each woman in the study participates in both conditions - judging the likability of both descriptions. An independent samples t-test is designed for comparing two independent groups, not for analyzing data from the same individuals across different conditions. The Wilcoxon test, on the other hand, is specifically designed to handle data from repeated measures designs.

2. Ordinal Data

The data collected in this study are ordinal. While the likability scale uses numbers from 1 to 10, these numbers represent subjective opinions about the descriptions. The intervals between each number on the scale are not necessarily equal. For example, the difference in likability between a 4 and a 5 might not be the same as the difference between a 7 and an 8. The Wilcoxon test is a non-parametric test, making it suitable for analyzing ordinal data. It does not assume that the data have a normal distribution, unlike the independent samples t-test.

Alternative Tests and Justifications

While the Wilcoxon test is the most appropriate choice, other acceptable alternatives exist depending on how the data is treated:

* Sign Test: If the focus is simply on whether one description is liked more than the other (treating the liking scale as "like" or "dislike"), the data could be categorized and analyzed using a Sign Test. This test is also suitable for repeated measures designs and does not assume a normal distribution. * Related t-test: While the data is technically ordinal, some argue that a related t-test can be used due to its robustness. With a scale of 1 to 10, the intervals between points are arguably interpretable as roughly equal, allowing the data to be treated as interval data. However, using the Wilcoxon test avoids this assumption and is a more conservative choice.