Question

Grade point average, fraternities, sororities, and two-way between-groups ANOVA: A sample of students from our statistics classes reported their GPAs, indicated their genders, and stated whether they were in the university’s Greek system (i.e., in a fraternity or sorority). Following are the GPAs for the different groups of students: Men in a fraternity: 2.6, 2.4, 2.9, 3.0 Men not in a fraternity: 3.0, 2.9, 3.4, 3.7, 3.0 Women in a sorority: 3.1, 3.0, 3.2, 2.9 Women not in a sorority: 3.4, 3.0, 3.1, 3.1 What are the independent variables and their levels? What is the dependent variable? Draw a table that lists the cells of the study design. Include the cell means. Conduct all six steps of hypothesis testing.

Answer 1

data

	yes	not
men	2.6	3
	2.4	2.9
	2.9	3.4
	3	3.7
women	3.1	3.4
	3	3
	3.2	3.1
	2.9	3.1

ANova two way result

Anova: Two-Factor With Replication
SUMMARY	yes	not	Total
men
Count	4	4	8
Sum	10.9	13	23.9
Average	2.725	3.25	2.9875
Variance	0.075833333	0.136667	0.169821429
women
Count	4	4	8
Sum	12.2	12.6	24.8
Average	3.05	3.15	3.1
Variance	0.016666667	0.03	0.022857143
Total
Count	8	8
Sum	23.1	25.6
Average	2.8875	3.2
Variance	0.069821429	0.074286
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	0.050625	1	0.050625	0.781350482	0.394093819	4.747225347
Columns	0.390625	1	0.390625	6.028938907	0.030292996	4.747225347
Interaction	0.180625	1	0.180625	2.78778135	0.120843154	4.747225347
Within	0.7775	12	0.064791667
Total	1.399375	15

independent variable

1) Gender

levels - male or female

2) whether in fraternity/soronity

dependent variable

GPA

study design - Anova two way

p-value of columns or fraternity is less than 0.05

hence this factor is significant

Gender(Row) and interaction are not significant as their p-values > 0.05