Question

ANOVA Worksheet

Chapter 13 “Too Groups Too Many”

An analysis of variance (also known as ANOVA) is used to test the difference between and within groups when there are more than two levels (in comparison to the t-test).

F-test Statistic

“Simple ANOVA involves testing the difference between the means of more than two groups on one factor or dimension” (Salkind, 2017).

Equation for simple ANOVA:

F= MS_between

MS_within In simple words: the variance between groups divided by the variance within groups.

1. Calculate F ,by hand, for the following data using the table below:

Group 1 Scores	Group 2 Scores	Group 3 Scores
58	67	89
67	73	90
54	82	87
69	78	92
72	81	89
59	76	79
67	79	82

ANOVA
Scale
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups
Within Groups
Total

2. How is this interpreted? (assume a p < .05)

Answer 1

Solution-

ANOVA Table-

	Sum of square	DF	Mean Square	F value	P-value
Between Groups	1882.286	2	941.143	30.251	0.0000 yes, significant
Within Groups	560	18	31.111
Total	2442.286	20

by the test results p < 0.05

So, we have enough evidence to claim that groups of scores are significantly different.

◆ ANOVA calculation and results-