An ANOVA is a statistical test used to check a quantitative variable between groups to find out if there’s a statistically significant difference between several population means. In practice, it is generally used to check three or more groups. Nevertheless, in theory, it could actually even be done with only two groups.1
In a previous post, we showed easy methods to perform a one-way ANOVA in R. On this post, we illustrate easy methods to conduct a one-way ANOVA by hand, via what is generally called an “ANOVA table”.
As an instance the tactic, suppose we take a sample of 12 students, divided equally into three classes (A, B and C) and we observe their age. Here is the sample:
We’re concerned about comparing the population means between classes.
Keep in mind that the null hypothesis of the ANOVA is that every one means are equal (i.e., age will not be significantly different between classes), whereas the choice hypothesis is that at the least one mean is different from the opposite two (i.e., age is significantly different in at the least one class in comparison with the opposite two). Formally, we have now:
- μA = μB = μC
- at the least one mean is different
As mentioned above, we’re going to do an ANOVA table to conclude the test.
Note that the ANOVA requires some assumptions (i.e., independence, equality of variances and normality). The aim of this post is for instance easy methods to do an ANOVA by hand and never easy methods to confirm these assumptions, so we suppose they’re met with none verification. See easy methods to test these assumptions in R in case you have an interest.