Free Online Two Way ANOVA Calculator and Dashboard

How to use and interpret the Two Way ANOVA calculator and dashboard

Input

The sidebar of the Input tab contains the input for the two way ANOVA model.  The model accepts two independent categorical variables and one dependent continuous variable. Input the name of the first independent categorical variable in the “Factor 1 Name” box and the category of each subject in the “Factor 1 Values” box, separated by “,” or “;”. Note in our example the first factor is “Gender” and its categories are “1” and “2” representing “Male” and “Female” respectively. Note you can input “M” or “Male” instead of “1”, the app would still work. Input the data about the second factor in a similar way in the boxes provided. In our example, it is Alcohol, with categories “1”, “2” and “3” representing “No alcohol” consumed, “2 pts beer” consumed and “4 pts beer” consumed, respectively. In the “Readings” box input the values of the dependent continuous variable. In our case, it represents the score of a test carried out on the subjects.

In the same tab, the input is grouped and shown as a table, on the right side of the screen.

Visualisation

The different combinations of the categories of the two independent factors produce a number of groups. In the Group Statistics box, the table shows the number of elements/subjects in each group, together with the mean and standard deviation of the dependent variable for each group. The sizes of the groups are also displayed in a colour-coded tile plot in the groups sizes box. In the first row we have two plots of the group means. Non-parallel lines in such plots is an indication of a presence of interaction whereas nearly parallel lines indicate that interaction is not present. In the second row, we have similar plots of the readings of the groups (displayed by a box plot) ordered by Factor 1 and Factor 2 respectively. In our case the non-alcohol treatment seems to affect males and females in a different way than the 2pts alcohol and 4pts alcohol treatments. This results in non-parallel lines and an indication of interaction between the two factors.

ANOVA model

The first box displays the equation of the full ANOVA model. The alpha values show the effect of the different treatments of Factor 1 and the beta values show the effect of the different treatments of Factor 2. The gamma values are the terms of interaction resulting from the combinations of treatments of the two factors. The epsilons are the error terms. The estimated parameters of this equation are given in row 1 of the dashboard.

The table in the ANOVA F-test box shows the data for the F-test that test whether Factor 1 is significant, Factor 2 is significant and whether the interaction between Factor 1 and Factor 2 is significant. P-values in green show significance of effects with a confidence level of at least 90%. Complementing this table, in the same row, the F-distribution is plotted for each of the three tests. The blue lines split the graph in the acceptance and rejection region, using 90%, 95% and 99% confidence level.

In the last row we have an analysis and breakdown of the variation. R square is the proportion of the variation in the dependent variable resulting from the model. This is broken down into 3 components: how much of the variation is explained by Factor 1, by Factor 2 and by the interaction of the two factors. The Adjusted R square is the R square adjusted for the number of parameters in the model relative to the number of observations.

Diagnostics and Post-Hoc Analysis

The first two boxes of the first row test for the equality of variance across the groups. One of the assumptions of ANOVA (required for the F-test to make sense) is that the variance of all the groups are equal. In the second row, the assumption of the normality of the residuals is tested. Again this is required in order to be able to use the F-distribution for the F-tests. The Tukey HSD test is a post-test that test the pairwise difference in the means of the groups. In the plot, for each pair of groups, we have the 95% Confidence Level range of difference in means, represented by a horizontal black line. If this line does not touch the dashed line (representing 0), it means that there is a statistical difference between the mean readings of the two groups.
Resource: https://aviatordao.com/win-calculator/