Factorial ANOVA Analysis and Interpretation of Two Datasets

This assignment presents a detailed analysis of two datasets using two-way factorial ANOVA. The first dataset explores the effects of different approaches (casual conversation, humor, pick-up line) and the attractiveness of the male student (attractive, unattractive) on the length of a conversation. The analysis includes Levene's test for variance, F-tests for main and interaction effects, and interpretation of a profile plot, concluding that humor is the most successful approach. The second dataset investigates the influence of therapy type (SSRI, placebo, Zinc) and medication on the weight change of participants. The analysis includes Levene's test, F-tests, and interpretation of a profile plot, concluding that medication type is a significant factor. Both analyses provide statistical results, including F-values, p-values, and effect sizes, along with relevant references.

Factorial ANOVA
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Data Set1
1. Levene’s test implied that treatment conditions group significantly differ (L = 5.26, p
< 0.05) in variance. Hence the null hypothesis about equality of variances should be
rejected.
2. F-value = 8.47 corresponding to “attract * approach” interaction. The p-value =
0.002 < 0.05 implies that the F-value is statistically significant at 5% level of
significance. Based on the p-value we will reject the null hypothesis.
3. F-value = 10.14 corresponding to “attract” variable. The p-value = 0.004 < 0.05
implies that the F-value is statistically significant at 5% level of significance. Based
on the p-value we will reject the null hypothesis.
4. F-value = 107.66 corresponding to “attract” variable. The p-value = 0.000 < 0.05
implies that the F-value is statistically significant at 5% level of significance. Based
on the p-value we will reject the null hypothesis.
5. Profile plot reflects a significant interaction between humour and casual conversation
since lines are not parallel.
Figure 1: Profile plot of estimated marginal means
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6. Humour was the most successful approach for both types of males (attractive and
unattractive).
7. Casual conversation was the most successful approach depending on type of males
(attractive and unattractive). It is highly successful for attractive males compared to
that of the unattractive ones (Cohen, 2002).
8. The interaction (“attract * approach”) effect was significant, F (2, 24) = 8.47, P <
0.001.
Data Set 2:
9. Levene’s test implied that treatment conditions group do not significantly differ (L =
0.31, p = 0.96) in variance. Hence the null hypothesis about equality of variances
failed to get rejected.
10. F-value = 0.57 corresponding to “Therapy Type * Medication” interaction. The p-
value = 0.69 implies that the F-value is not statistically significant at 5% level of
significance. Based on the p-value we fail to reject the null hypothesis.
11. F-value = 1.00 corresponding to “Therapy Type” variable. The p-value = 0.37
implies that the F-value is not statistically significant at 5% level of significance.
Based on the p-value we fail to reject the null hypothesis.
12. F-value = 33.57 corresponding to “Medication” variable. The p-value = 0.000 < 0.05
implies that the F-value is statistically significant at 5% level of significance. Based
on the p-value we will reject the null hypothesis.
13. Profile plot reflects a significant interaction between SSRI and Placebo since both
lines almost intersects.
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Figure 2: Profile plot of estimated marginal means of weight change
14. Based on the plot and descriptive summary, the treatment of Zinc with Exposure and
Response Prevention has the highest mean of 6.39.
15. For Placebo medication, Cognitive-Behavioural therapy was the most effective one.
16. Medication is the best factor for post hoc analysis since there seems to be difference
in means for the therapies used.
17. Effect size is R squared = 0.37 for the present study.
18. A three way ANOVA was conducted on the influence of Therapy type (3 levels) and
Medication (3 levels) on the Weight Change of participants. The main effect for
Medication type yielded an F ration of F(2, 121) = 33.57, P < 0.01, indicating a
significant difference between effect of Placebo, SSRI, and Zinc.
The main impact variables and their interaction were able to explain more than 37%
of variation in weight change of the participants (Wang, & DeVogel, 2019).
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References
Wang, T., & DeVogel, N. (2019). A revisit to two-way factorial ANOVA with mixed effects
and interactions. Communications in Statistics-Theory and Methods, 1-18.
Cohen, B. H. (2002). Calculating a factorial ANOVA from means and standard deviations.
Understanding Statistics: Statistical Issues in Psychology, Education, and the Social
Sciences, 1(3), 191-203.
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