Quantitative Psychology Assignment: ANOVA and Statistical Analysis

This document presents a solution to a Quantitative Psychology assignment focusing on ANOVA (Analysis of Variance). The assignment involves interpreting the results of two-way ANOVA tables. The student calculates and interprets F-values, degrees of freedom, and mean squares to determine the significance of gender, intervention conditions, and their interactions. The solution also addresses the need for follow-up analyses, such as Tukey or Bonferroni post-hoc tests, to further investigate significant conditions. The document includes calculations, interpretations of statistical significance, and recommendations for additional analyses based on the ANOVA results, demonstrating an understanding of statistical concepts and their application to psychological research. The assignment covers topics like calculating SS, degrees of freedom, MS, and F-statistics for two-way ANOVA, and interpreting the results in the context of a psychological experiment. The student has analyzed the effect of gender and condition on a memory task and the effect of stress manipulation.

Running head: QUANTITATIVE PSCHOLOGY 1
Quantitative Psychology
Name
Institution

QUANTITATIVE PSCHOLOGY 2
Quantitative Psychology
Question 1
The SS for within groups is calculated as follows as the differences between the total
SS and the sum of SS for Rows, Column and interactions (Cramer et al., 2016).
SSWithing Groups = SSTotal - (SSGender + SScondition + SSinteraction) = 12152.26 – (1.72 + 369.85 + 639.4) =
11141.29.
Next, the degrees of freedom are calculated as follows:
DfRows = r – 1, where r = 2. Dfcolumns = c – 1, where c = 3 and Dfinteractions = (r – 1) * (c-1).
Finally, the MS are calculated as follows:
MSGender = SSGender
Table 1: Completed Two-Way ANOVA
Source SS df MS F Fcrit
Rows (Gender) 1.72 1 1.72 0.01 4.00
Columns (Condition) 369.85 2 184.93 1.01 3.15
RXC
interaction 639.4 2 319.70 1.75 3.15
Within Groups 11141.29 61 182.64
Total 12152.26 66
16. is there a significant mean effect of gender why or why not?
There is no significant effect of gender on the thoughts about the stressful event since the
calculated F = 0.01 which is less than Fcrit = 4.00. Thus, fail to reject the null hypothesis of no
significant difference at 95% level of significance.
17. is there a significant mean effect of the intervention (condition) why or why not?
There is no significant effect of the intervention (condition) on the thoughts about the
stressful event since the calculated F = 1.01 which is less than Fcrit = 3.15. Implying, we fail
to reject the null hypothesis of no significant difference at 95% level of significance.

QUANTITATIVE PSCHOLOGY 3
18. is there interaction? Why or why not?
There is not interaction effect since the calculated F-value of 1.75 is less than the critical F-
value of 3.15. Therefore, the null hypothesis of no effect is not rejected at 55 level of
significance.
19. do you need to conduct any further analysis? Why or why not?
There is no need of conducting further analysis since the rows (gender), columns (conditions)
and interactions are all not significant.
Question 2
20. The table below shows Two-way ANOVA completed.
Table 1: Completed Two-Way ANOVA
Source SS df MS F Fcrit
Rows (Gender) 44.93 1 44.93 0.87 3.91
Columns
(Condition) 3539.62 2 1769.81 34.31 3.06
RXC interaction 5.19 2 2.60 0.05 3.06
Within Groups 8562.52 166 51.58
Total 12152.26 171
21. What do the results of this two-way ANOVA tell us about the effect of the stress
manipulation on the memory task?
Gender and interactions are do not have significant effect on the stress manipulation on the
memory task since the calculated F-values of 0.87 and 0.05 are less than tabulated F-values
of 3.91 and 3.06 respectively. However, the conditions are significant since the F-value of
34.31 is greater than 3.06 hence we reject the null hypothesis.
22. do you need to conduct any follow up analysis? If so what analysis?

QUANTITATIVE PSCHOLOGY 4
There is need to perform follow up analysis to identify the significant condition among
control, post stressor, and anticipatory stressors. The analysis to use is either
Tukey or Bonferroni post-hoc tests (Cramer et al., 2016).

QUANTITATIVE PSCHOLOGY 5
References
Cramer, A. O., van Ravenzwaaij, D., Matzke, D., Steingroever, H., Wetzels, R., Grasman, R.
P., ... & Wagenmakers, E. J. (2016). Hidden multiplicity in exploratory multiway
ANOVA: Prevalence and remedies. Psychonomic Bulletin & Review, 23(2), 640-647.