# Introduction to Between-Subjects Analysis of Variance: Preliminaries (3 of 4)  If the sample size is the same for all of the treatment groups, then the letter "n" (without a subscript) is used to indicate the number of subjects in each group. The total number of subjects across all groups is indicated by "N." If the sample sizes are equal, then N = (a)(n); otherwise,

N = n1 + n2 + ... + na.

Some experiments have more than one between-subjects factor. For instance, consider a hypothetical experiment in which two age groups (8-year olds and 12-year olds) are asked to perform a task either with or without distracting background noise. The two factors are age and distraction.

Assumptions
Analysis of variance assumes normal distributions and homogeneity of variance. Therefore, in a one-factor ANOVA, it is assumed that each of the populations is normally distributed with the same variance (σ²). In between-subjects analyses, it is assumed that each score is sampled randomly and independently. Research has shown that ANOVA is "robust" to violations of its assumptions.  