Subjects One-Way ANOVA
example
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Between Subjects One-Way ANOVA example |
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:
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group
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test scores
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|||||||
| 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 = 24 | Sx32 = 125 |
| (Sx1)2 = 2304 | (Sx2)2 = 1024 | (Sx3)2 = 576 | |||
| M1 = 6 | M2 = 4 | M3 = 3 |
= 595 - 477.04
SStotal = 117.96
= 507.13 - 477.04
SSamong = 30.08
SSwithin = 117.96 - 30.08 = 87.88
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Source
|
SS
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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).