Free Online One Way ANOVA Calculator and Dashboard

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

Input tab

The sidebar of the Input tab contains the input for the one way ANOVA model. The model accepts one independent categorical variables known as factor, and one dependent continuous variable. Input the name of the independent categorical variable in the “Factor Name” box and the category of each subject in the “Factor Values” box, separated by “,” or “;”. Note that the factor should have at least 3 distinct categories (known as factor levels). In our example the factor is “Drug” and its categories are “1” , “2”, “3” and “4” representing four different types of drugs produced by a pharmaceutical company. Note that the app also accepts text instead of numbers in the “Factor Name box”. For example, we could have inputted the factor levels as “Drug1”, “Drug2”, “Drug3” and “Drug4”.

In the “Dependent Variable Name” and “Dependent Variable Values” boxes, input the data for the dependent variable. In our case, it represents the Free Thyroxine level in the blood. 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 & ANOVA Model tab

In the Group Statistics box, the table shows the number of elements/subjects in each group/treatment level, together with the mean and standard deviation of the dependent variable for each group. On our example, we have 4 treatment levels corresponding to each drug type and each treatment level has size 10. The groups have a different means. In fact, Drug 2 displays the largest mean Free Thyroxine levels whereas Drug 3 displays the smallest mean Free Thyroxine levels. In the first row we have the plot of the distribution of the dependent variable. In our example, this plot gives as an idea that the effect on the Free Thyroxine levels is not equal across the groups. In the first row, we state the One-Way ANOVA model and give the parameter estimates. The $\tau_i$ ‘s represent the effect of treatment $i$ on the dependent variable.

The table in the ANOVA F-test box shows the data for the F-test that tests whether there is a significant difference between the effects of the treatment levels. A $p$ -values in green show a significant difference in the effects with a confidence level of at least 90%. Complementing this table, in the same row, the F-distribution is plotted. The blue lines split the graph in the acceptance and rejection region, using 90%, 95% and 99% confidence level. The R square and the Adjusted R square values quantify how much of the variation is explained by the ANOVA model.

Diagnostics and Post-Hoc Analysis tab

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 is equal across all groups. In the first plot of the first row, the residual are plotted against the fitted values. For the assumption to be satisfied, one must see similar spread of the residual over the fitted values. This is accompanied with the Levene Test.

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 histogram should be bell-shape and symmetric mimicking the normal distribution. In the Q-Q plot, if the data is normally distributed, the data’s quantile values should be close to the diagonal straight line. The result of the Shapiro Test of Normality is also provided.

In the last box of the first row we also give the Tukey HSD test, which is a post-hoc test that tests 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. In our example, we see that there is a significant difference between the mean readings of all pairs of groups except for the pair (Drug 1, Drug 4). Hence Drug 1 and Drug 4 seem to have a similar effect on the mean level of Free Thyroxine.