Definition and Classes of ANOVA Table
The ANOVA Table stands for Analysis of Variance which is used as a statistical technique or test in detecting the differences in population means, or whether or not the means of different groups are all equal when you have more than two populations. It gets its name ANOVA not from what it does, but how it is done. ANOVA uses variance samples to find out the differences between population means. Sir Ronald Fisher introduced this term in 1918. In 1921 his first application of the analysis of variance or ANOVA was published. Then it became known when it was included in Fisher’s 1925 book Statistical Methods for Research Workers. ANOVA is very helpful because they have an advantage over a two-sample t-test which when used increases your chances of committing an error.
The three classes of ANOVA Table models are: Fixed-effects models that assume that the data came from normal populations. Random effects models assume that the data describes a hierarchy of different populations wherein their differences are limited by the hierarchy. This ANOVA table model is also used when the treatments are not fixed. And last is the mixed-effect model that describes the situation where both fixed and random effects are known.
One-way ANOVA Table is used to test for difference from among three groups since testing the differences for a two-group can be done using a t-test. To make sure that the results of a one-way ANOVA can be considered reliable, assumptions like response variable must be normally distributed, independent samples, population variances are equal and group responses should be independent and identically distributed should be met. For the two-way ANOVA Table, which is the extension to the one-way ANOVA, there are two independent variables. To consider the results as reliable, samples must be independent, groups must have same sample size, population variance must be equal and the populations from which the samples were taken must be normally distributed.