ABSTRACT
Sir Ronald Fisher, upon discovering the work of W.S.Gossett (developed a test of mean differences between two groups, “student t-test,” or simply the t-test), extended it into his idea for an analysis of variance (ANOVA) technique. The analysis of variance technique was based on the idea that variance could be used to indicate whether sample means differed. For example, if three groups had the same average math score, then the variance (standard deviation) of the means would be zero, implying that the sample means do not vary (differ). As the sample means become more different, the variance increases. When sample means are similar in value they are called homogeneous, when they become more different in value they are called heterogeneous. The basic idea of variance indicating sample mean differences can be understood using the following two sets of mean scores, which indicate similar grand means but different variances:
The sample means are all the same in SET A; hence the variance is zero. The sample means are different in SET B; hence the variance is greater than zero. As sample means become different in value, the variance will become larger.
