Introduction to Between-Subjects Analysis of Variance: Preliminaries (2 of 4)
The first question the experimenter was interested in was whether background noise has any effect at all. That is, whether the null hypothesis: µ1 = µ2 = µ3 is true where µ1 is the population mean for the "no noise" condition, µ2 is the population mean for the "moderate noise" condition, and µ3 is the population mean for the "loud noise" condition. The experimental design therefore has one factor (noise intensity) and this factor has three levels: no noise, moderate noise, and loud noise.
Analysis of variance can be used to provide a significance test of the null hypothesis that these three population means are equal. If the test is significant, then the null hypothesis can be rejected and it can be concluded that background noise has an effect.
In a one-factor between- subjects ANOVA, the letter "a" is used to indicate the number of levels of the factor (a = 3 for the noise intensity example). The number of subjects assigned to condition 1 is designated as n1, the number of subjects assigned to condition 2 is designated by n2, etc.