Question

Edward wanted to know whether students’ attitudes towards the extra-curricular activities sponsored by EKU differed as a function of class year and gender. So Edward randomly surveyed 12 freshman, 12 sophomores, 12 juniors, and 12 seniors, with each class year sample having equal numbers of male and female participants. Each student was asked to rate their attitude of EKU’s extra-curricular activities on a 1 – 10 scale with 1 being totally negative and 10 being totally positive.

This is a 2-way ANOVA.  Write out null and alternative hypotheses, complete the table, and provide English translations of significant or nonsignificant findings in sentence form.  Use a 0.05 level of significance (Alpha), nondirectional hypothesis (2-tailed). You do not need to calculate effect size nor Tukey's HSD for this problem.

	SS	df	MS	F	Fcritical	p-value
Between groups	26.0
Class Year (A)	8.0	3	_____	_____	_____	_____
Gender (B)	5.0	1	_____	_____	_____	_____
A x B	_____	3	_____	_____	_____	_____
Within groups	_____	40	_____
Total	98.2	_____

Answer 1

(a) Ho: There is no significant difference between the classes

Ha: There is a significant difference between the classes

Ha: There is no significant difference between the genders

Ha: There is a significant difference between the genders

Ho: There is no interaction between class and gender

Ha:There is interaction between class and gender

(b) ANOVA table:

	SS	df	MS	F	Fcritical	p-value
Between groups	26
Class Year (A)	8	3	8/3 = 2.667	2.667/1.805 = 1.4776	2.8387	0.2352
Gender (B)	5	1	5/1 = 5.000	5/1.805 = 2.7701	4.0847	0.1039
A x B	26 - (8 + 5) = 13	3	13/3 = 4.333	4.333/1.805 = 2.4006	2.8387	0.0820
Within groups	98.2 - 26 = 72.2	40	72.2/40 = 1.805
Total	98.2	47

Conclusion:

Since all the three p- values are greater than 0.05, we fail to reject all the three null hypotheses. So,

There is no sufficient evidence of a significant difference between classes. All the classes seem to have the same attitude towards extra-curricular activities.

There is no sufficient evidence of a significant difference between genders. Both males and females seem to have the same attitude towards extra-curricular activities.

There is no sufficient evidence of a significant interaction between class and gender.