Analysis of variance(Anova)

Abstract

In t-test, the difference between 2 sample means are tested for Significance. In ANOVA the differences between means of more than 2 samples are tested for significance. This is done by examining the variation within the whole groups of sample means. It consists of a comparison between 2 estimates of the overall variation (of the complete set of measurements included in the analyses), one estimate being based on the variance of sample means about the grand mean. The other based on the variance of the individual measurements about their treatment means. The first estimate is called treatment variance. The second estimate is called error variance. If the null hypothesis is true, the ratio of these estimates would approximate 1. If, on the other hand, the sample means estimates differ from the population or group means then the ratio would exceed 1, In practice, this ratio is calculated as F and the level of probability of obtaining such a ratio is determined if the null hypothesis were to be true.