Between Subjects One-Way ANOVA example

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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 = 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

 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