ANOVA Calculator

The one-way analysis of variance (ANOVA) is an extension of independent two-sample t-test is used in studying differences between two or more group means, while the two-way ANOVA evaluates simultaneously the effect of two grouping variables on a response variable. ANOVA uses F-statistic and its corresponding p-value to determine whether data comes from the same population. A significant p-value suggests that some of the group means are different. Being an omnibus test statistic, ANOVA can’t be used to determine which specific groups were statistically significantly different from each other. Hence post hoc tests, such as Tukey multiple pairwise-comparisons and Pairwise t-test are used in evaluating mean difference between specific pairs of groups. The model assumes that each factor is randomly sampled, independent, and belongs to a normally distributed population with unknown but equal variances. The data can be visualized with box plots and bar plots. Assumptions are verified by analyzing model residuals. Simultaneously, multiple comparison tests, such as Shapiro-Wilk, Bartlett, and Flinger are performed to ascertain conclusions on normality, check homogeneity of variances. Finally, alternative analysis to One-way ANOVA includes Welch One-way test that makes no assumptions of equal variances and the non-parametric Kruskal-Wallis rank sum test, which is used when neither assumptions are met.