In the second row, the assumption of the normality of the residuals is tested.
One of the assumptions of ANOVA (required for the F-test to make sense) is that the variance of all the groups are equal. The first two boxes of the first row test for the equality of variance across the groups. The Adjusted R square is the R square adjusted for the number of parameters in the model relative to the number of observations. 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. R square is the proportion of the variation in the dependent variable resulting from the model. In the last row we have an analysis and breakdown of the variation. The blue lines split the graph in the acceptance and rejection region, using 90%, 95% and 99% confidence level. Complementing this table, in the same row, the F-distribution is plotted for each of the three tests. P-values in green show significance of effects with a confidence level of at least 90%. 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. The estimated parameters of this equation are given in row 1 of the dashboard. The gamma values are the terms of interaction resulting from the combinations of treatments of the two factors. 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 first box displays the equation of the full ANOVA model. This results in non-parallel lines and an indication of interaction between the two factors. 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. 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. 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 first row we have two plots of the group means. The sizes of the groups are also displayed in a colour-coded tile plot in the groups sizes box. 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 different combinations of the categories of the two independent factors produce a number of groups. In the same tab, the input is grouped and shown as a table, on the right side of the screen. In our case, it represents the score of a test carried out on the subjects. In the “Readings” box input the values of the dependent continuous variable. 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. Input the data about the second factor in a similar way in the boxes provided. Note you can input “M” or “Male” instead of “1”, the app would still work. Note in our example the first factor is “Gender” and its categories are “1” and “2” representing “Male” and “Female” respectively. 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 “ ”. The model accepts two independent categorical variables and one dependent continuous variable. The sidebar of the Input tab contains the input for the two way ANOVA model.
How to use and interpret the Two Way ANOVA calculator and dashboard Input
Free Online Two Way ANOVA Calculator and Dashboard