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:
= 595 - 477.04
SStotal = 117.96
= 507.13 - 477.04
SSamong = 30.08
SSwithin = 117.96 - 30.08 = 87.88
*(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).