Between
Subjects One-Way ANOVA
example

description | steps | calculator

Problem: Susan Sound predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all. She randomly divides twenty-four students into three groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with noise that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Their scores follow:

group
test scores
1) constant sound 7 4 6 8 6 6 2 9
2) random sound 5 5 3 4 4 7 2 2
3) no sound 2 4 7 1 2 1 5 5

x1
x12
x2 x22  x3 x32
7 49 5 25 2 4
4 16 5 25 4 16
6 36 3 9 7 49
8 64 4 16 1 1
6 36 4 16 2 4
6 36 7 49 1 1
2 4 2 4 5 25
9 81 2 4 5 25
Sx1 = 48 Sx12 = 322 Sx2 = 32 Sx22 = 148 Sx3 = 27 Sx32 = 125
(Sx1)2 = 2304   (Sx2)2 = 1024   (Sx3)2 = 729  
M1 = 6   M2 = 4   M3 = 3.375  

= 595 - 477.04

SStotal = 117.96

= 507.13 - 477.04

SSamong = 30.08

SSwithin = 117.96 - 30.08 = 87.88

Source
SS
df
MS
F
Among
30.08
2
15.04
3.59
Within
87.88
21
4.18
 

*(according to the F sig/probability table with df = (2,21) F must be at least 3.4668 to reach p < .05, so F score is statistically significant)

Interpretation: Susan can conclude that her hypothesis may be supported. The means are as she predicted, in that the constant music group has the highest score. However, the signficant F only indicates that at least two means are signficantly different from one another, but she can't know which specific mean pairs significantly differ until she conducts a post-hoc analysis (e.g., Tukey's HSD).


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  • Read a more detailed description of the One-way Analysis of Variance


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