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Explain two reasons why it was appropriate to use a Wilcoxon test in this situation. Refer to the description of the study in your answer.

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Wilcoxon Test: Appropriateness in a Repeated Measures Design Examining Happiness Ratings

The Wilcoxon signed-rank test is a non-parametric statistical test used to investigate differences between two related samples. It is particularly useful when dealing with ordinal data or when the assumptions of parametric tests, such as the t-test, are not met. In the context of this study, where a psychologist aims to examine the difference in happiness ratings between participants when alone and with a friend, the Wilcoxon test proves to be an appropriate statistical tool for two key reasons: the study's repeated measures design and the ordinal nature of the data.

Reason 1: Repeated Measures Design

The study utilizes a repeated measures design, also known as a within-subjects design. This means that each participant is tested under both conditions: alone and in the presence of a friend. This related-samples design directly violates one of the key assumptions of many parametric tests, including the independent samples t-test, which requires data from independent groups. The Wilcoxon test, however, is specifically designed to handle related samples by analyzing the differences in scores between the two conditions for each participant. This approach effectively controls for individual differences in baseline happiness levels, making the test more sensitive to the specific effect of the friend's presence.

Reason 2: Ordinal Data

The study utilizes a ratings scale to measure participants' happiness, which is considered ordinal data. Ordinal data allows for ranking (e.g., happier, less happy) but does not have equal intervals between each point on the scale. This means that the difference in happiness between a rating of "1" and "2" might not be the same as the difference between "3" and "4". Parametric tests, on the other hand, assume that the data is interval or ratio, where intervals are equal. The Wilcoxon test circumvents this issue by ranking the differences in happiness scores between the two conditions and analyzing the distribution of these ranks. This approach avoids making assumptions about the intervals between points on the happiness rating scale, making it a more appropriate choice for analyzing ordinal data.

Conclusion

In conclusion, the Wilcoxon test is a suitable statistical analysis for this study because it effectively addresses the two key characteristics of the data: the repeated measures design, with participants tested in both conditions, and the ordinal nature of the happiness ratings. By accounting for these factors, the Wilcoxon test allows the psychologist to draw more robust and accurate conclusions about the impact of a friend's presence on happiness levels.

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