ANOVA

Comparison of means of two or more populations. A way to examine group of responses that are measured on interval or ratio scales.

Dependent variable must be metric. There must be one or more independent variable that is categorical. A categorical independent variable is called a factor. If there is a combination of categorical and metric variable, the technique is called ANCOVA. One way ANOVA is usually called so because there is only one categorical variable. If the mean is compared against n categorical variables, it is called an n-way ANOVA. A particular combination of factor levels is called a treatment.

ANOVA compares a continuous response variable(dependent) against a factor variable(independent)

ANCOVA compares a continuous response variable(dependent) against levels of factor variable while controlling for a continuous covariate.

Total Variation = Variation Within(SSerror) + Variation Between(SSx)

Eta^2 = Variation Between / Total Variation. Eta^2 is strength of effect.

Testing of hypothesis using F-statistic = [SSx/(c-1)]/[SSerror/(n-c)] with c-1 and n-c being degrees of freedom. n is the number of samples. c is the number of categories.

Assumptions of ANOVA
 * error terms are not correlated
 * error terms are normally distributed
 * the categorical of independent variables are fixed

For n-way ANOVA:

SStotal = SSx1 + SSx2 + SSx1x2 + SSerror. The eta^2 is called the overall effect or multiple eta^2. F is calculated using SSx1x2.

Interactions are shown on the graph

If parallel then there is no interaction.

If there is an interaction it can be ordinal or disordinal. Means that there is an interaction between the variables. Need to see if the effects are significant.

For disordinal, there can be crossing or non-crossing case.

Omega squared is used as an indicator of interaction.