Previously I have shown how to analyze data collected using within-subjects designs using rpy2 (i.e., R from within Python) and Pyvttbl. In this post I will extend it into a factorial ANOVA using Python (i.e., Pyvttbl). In fact, we are going to carry out a Two-way ANOVA but the same method will enable you to analyze any factorial design. I start with importing the Python libraries that are going to be use.

# Month: March 2016

In an earlier post I showed four different techniques that enables one-way analysis of variance (ANOVA) using Python. In this post we are going to learn how to do two-way ANOVA for independent measures using Python.

First, we ar going to learn how to calculate the ANOVA table “by hand”. Second, we are going to use Statsmodels and, third, we carry out the ANOVA in Python using pyvttbl. Finally, as a bonus, we will also use Pingouin Stats, a newer Python package.

An important advantage of the two-way ANOVA is that it is more efficient compared to the one-way. There are two assignable sources of variation – supp and dose in our example – and this helps to reduce error variation thereby making this design more efficient.

Two-way ANOVA (factorial) can be used to, for instance, compare the means of populations that are different in two ways. It can also be used to analyse the mean responses in an experiment with two factors. Unlike One-Way ANOVA, it enables us to test the effect of two factors at the same time.

One can also test for independence of the factors provided there are more than one observation in each cell. The only restriction is that the number of observations in each cell has to be equal (there is no such restriction in case of one-way ANOVA).