Question

Please solve the following problems in their entirety. That means you will calculate a) all appropriate sums of squares, b) all appropriate mean squares, c) F statistics, d) critical value, and e) η². Additionally, you are going to f) explain what happens to the null(s), g) relate the conclusion back to the problem, and h) perform any required post hoc tests with explanations

1. There is a study where the dependent variable is movie ratings. One independent variable is sex (male, female) and genre (drama, comedy).  α =0.5

                              Male                Female

Drama                 1, 2, 9             4, 3, 8

Comedy         15, 9, 12          10, 13, 4

Answer 1

Descriptive statistics for each factor level is as shown below

SUMMARY	male	Female	Total
Drama
Count	3	3	6
Sum	12	15	27
Average	4	5	4.5
Variance	19	7	10.7
Comedy
Count	3	3	6
Sum	36	27	63
Average	12	9	10.5
Variance	9	21	14.7
Total
Count	6	6
Sum	48	42
Average	8	7
Variance	30.4	16

Hypothesis:

for Factor Sex                               

H₀ : All means are equal

H₁ : All means are not equal

for Factor Genere

H₀ : All means are equal

H₁ : All means are not equal

For Combined effect

H₀ : combinedly both genere and sex does not effect response variable

H₁ :combinedly both genere and sex effect response variable

ANOVA table

ANOVA
Source of Variation	Sum of Squares	df	Mean Square	F- statistic	P-value	F critical
Genere	108	1	108	7.714286	0.024019	5.317655
Sex	3	1	3	0.214286	0.65576	5.317655
Interaction	12	1	12	0.857143	0.38162	5.317655
Error	112	8	14
Total	235	11

f) α =0.5

p-value for Genere is 0.02 which is less than α hence we reject null hypothesis and we conclude that there is significant effect of genere on the response variable.

p-value for Sex and Interaction are 0.655 and 0.381 respectively and are greater than α hence we fail to reject null hypothesis and we conclude that there is no significant effect of Sex and Interaction on the response variable.

g) post hoc test can only be done for genere factor since it is only effecting response variable

multiple comparison using Tukey's procedure

Tukey Pairwise Comparisons: Genere

Grouping Information Using the Tukey Method and 95% Confidence

Genere	N	Mean	Grouping
2	6	10.5	A
1	6	4.5		B

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference of Genere Levels	Difference of Means	SE of Difference	Simultaneous 95% CI	T-Value	Adjusted P-Value
2 - 1	6.00	2.16	(1.02, 10.98)	2.78	0.024

Individual confidence level = 95.00%