Question

Students completed a high school senior level standardized algebra exam. Major for students was also recorded. Data in terms of percent correct is recorded below for 32 students. We are interested to see if there is any difference between students' high-school algebra test scores and subsequent declared college major.

These students have now also just completed the same college-level calculus class and received a grade. We are therefore now also interested to see if there is any relationship between the students' algebra test scores and their calculus course grades: On average, did students who tended to score higher on the high-school algebra test also finish the course with higher grades? Conveniently, only one student of each major received the same grade (see table - for example, there is only one Education major who received a grad of A).

Use the Microsoft Excel "Anova Single-Factor" Data Analysis tool to conduct a 2-way ANOVA test for the data in the following table:

Declared College Major
Grade	Education	Business/Management	Behavioral/Social Science	Fine Arts
A	62	89	68	87
A-	81	88	71	57
B+	75	82	52	62
B	58	69	50	64
B-	67	59	22	28
C+	48	73	31	29
C	16	40	42	30
C-	26	45	16	15

1. If there is a significant difference between the college majors, where specifically are the differences?
2. If there is a significant difference between grade received, where specifically are the differences?

Answer 1

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	8	433	54.125	526.125
Column 2	8	545	68.125	350.9821
Column 3	8	352	44	406.5714
Column 4	8	372	46.5	601.4286
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	2825.125	3	941.7083	1.998206	0.137095	2.946685
Within Groups	13195.75	28	471.2768
Total	16020.88	31

Here Pvalue is greater than 0.05 therefor null hypothisis is accepted

So, there is no significant difference between the college majors

and   there is no significant difference between grade received