The variance of the distribution of the outcome is the same across all predicted values (assessed by visually inspecting the residual plot).Д®xample 1: Performing a two-way ANOVA in R.

The population of values for the outcome are normally distributed across all predicted values (assessed by confirming the normality of the residuals).

The outcome all numeric predictors are linearly related.

The population variances of each group are equal.

The population of each group of each predictor is normally distributed.

H A: While controlling for all other predictors in the model, the outcome variable is linearly related to the predictor variable. H o: While controlling for all other predictors in the model, the outcome variable is not linearly related to the predictor variable. Hypotheses (GLM): Each predictor will have its own set of hypotheses: H A: The mean of the outcome variable does differ based on the predictor variable, controlling for all other predictors in the model.

H o: The mean of the outcome variable does not differ based on the predictor variable, controlling for all other predictors in the model. Hypotheses (ANOVA): Each predictor will have its own set of hypotheses: General Linear Model Equation (for k predictors): A general linear model, also referred to as a multiple regression model, produces a t-statistic for each predictor, as well as an estimate of the slope associated with the change in the outcome variable, while holding all other predictors constant. A multi-factor ANOVA is similar to a one-way ANOVA in that an F-statistic is calculated to measure the amount of variation accounted for by each predictor relative to the left-over error variance. A multi-factor ANOVA or general linear model can be run to determine if more than one numeric or categorical predictor explains variation in a numeric outcome.

How to run a two way anova in excel