One-Way ANOVA: An ANOVA hypothesis tests the difference in population means based on one characteristic or factor. a—–>b
“An example of when a one-way ANOVA could be used is if you want to determine if there is a difference in the mean height of stalks of three different types of seeds. Since there is more than one mean, you can use a one-way ANOVA since there is only one factor that could be making the heights different.
Two-Way ANOVA: An ANOVA hypothesis tests comparisons between populations based on multiple characteristics. a—->c<—-b “Suppose that there are three different types of seeds, and the possibility that four different types of fertilizer is used, then you would want to use a two-way ANOVA. The mean height of the stalks could be different for a combination of several reasons”
Multivariate analysis of variance (MANOVA): it is simply an ANOVA with several dependent variables. That is to say, ANOVA tests for the difference in means between two or more groups, while MANOVA tests for the difference in two or more vectors of means. a—–>c, b——>d, a——d, b—–>c