Analysis of Variance (Statistics Project Sample)

Analysis of Variance Name Institution Course Professor Date Analysis of Variance Topic 1 The theory called “Wisdom of the Crowd” suggests that the average of a group’s guesses is likely to be more accurate than the individual guesses of the participants (Annenberg Learner, 2019). This means that there is a likelihood of the average value provided in the group to provide a better overall estimation due to the cancelling out of individual errors by members. The clipboards handed to the students differed in terms of weight due to storage compartments for extra paper. It is notable that the students were not aware of the weight differences in the clipboards. In this case, the null hypothesis for the one-way ANOVA was that the means of the population are the same, with the averages of three groups being compared being the same, indicating that the weight of the clipboards does not affect their estimation. The test statistic that results from ANOVA is the F-statistic that determines whether there are any statistically significant differences among three or more sample means. From the F statistic calculated in the ANOVA test the professor was not able to conclude from that there were differences in populations depending on the weight of the clipboard. The p-value obtained from the test was 0.45, which was higher than the usual threshold of significance (Annenberg Learner, 2019). As a result, the null hypothesis could not be rejected leading to the conclusion that there were significant differences between the population means of the groups. In conclusion, the crowd proved to be wiser that the individual students. However, this was only limited due to the extreme variance of the individual guesses in most cases. It is notable that the average of the crowd’s guesses was $129.22, which was far off from the actual amount of $237.52 (Annenberg Learner, 2019). This indicates that the mean of the crowd’s guess was much better than the individual guesses that were mostly farfetched. Topic 2 The boxplot below shows the depression scores for the three quality of sleep groups enabling the identification of any potential differences or patterns in the data.
The one-way ANOVA test was conducted together with the Tukey's HSD to perform pairwise comparisons with the results shown in the tables below (Komaroff, 2023).


From the results, sleep quality was significantly related to depression, F(2,895) = 72.515, p < 0.001. Further post hoc analyses with Tukey’s HSD test revealed that all pairwise comparisons of means were significant. Conclusion Since sleep plays a crucial role in regulating mood and emotional well-being any disruptions can disrupt the body’s hormonal balance heightening risk of developing depressive symptoms. In most cases, individuals with depression experience troubles in their circadian rhythms, leading to irregular cycles. This is because such thoughts make it difficult to fall and stay asleep (Hayashino et al., 2010). Having depression can increase an individual’s anxiety and negative thoughts, making it difficult to relax and fall asleep thus intensify the symptoms of depression, leading to a continued cycle where poor sleep quality and depression affect each other. Creating an experimental design assigning participants to two groups with one experience controlled poor sleep and the other main...