Learn how to perform an Analysis Of VAriance (ANOVA) in R to compare 3 groups or more. See also how to interpret the results and test the assumptions
ANOVA (ANalysis Of VAriance) is a statistical test to determine whether two or more population means are different. In other words, it is used to compare two or more groups to see if they are significantly different.
In practice, however, the:
Note that there are several versions of the ANOVA (e.g., one-way ANOVA, two-way ANOVA, mixed ANOVA, repeated measures ANOVA, etc.). In this article, we present the simplest form only — the one-way ANOVA1 — and we refer to it as ANOVA in the remaining of the article.
Although ANOVA is used to make inference about means of different groups, the method is called “analysis of variance”. It is called this because it compares the “between” variance (the variance between the different groups) and the variance “within” (the variance within each group). If the between variance is significantly larger than the within variance, the group means are declared to be different. Otherwise, we cannot conclude one way or the other. The two variances are compared to each other by taking the ratio (between variance/within variance) and then by comparing this ratio to a threshold from the Fisher probability distribution (a threshold based on a specific significance level, usually 5%).
This is enough theory regarding the ANOVA method for now. In the remaining of this article, we discuss it from a more practical point of view, and in particular, we will cover the following points:
## install.packages("palmerpenguins") library(palmerpenguins)
The dataset contains data for 344 penguins of 3 different species (Adelie, Chinstrap and Gentoo). The dataset contains 8 variables, but we focus only on the flipper length and the species for this article, so we keep only those 2 variables:
library(tidyverse) dat <- penguins %>% select(species, flipper_length_mm)
(If you are unfamiliar with the pipe operator (
%>%), you can also select variables with
penguins[, c("species", "flipper_length_mm")]. Learn more ways to select variables in the article about data manipulation.)
summary(dat) ### species flipper_length_mm ### Adelie :152 Min. :172.0 ### Chinstrap: 68 1st Qu.:190.0 ### Gentoo :124 Median :197.0 ### Mean :200.9 ### 3rd Qu.:213.0 ### Max. :231.0 ### NA's :2
Flipper length varies from 172 to 231 mm, with a mean of 200.9 mm. There are respectively 152, 68 and 124 penguins of the species Adelie, Chinstrap and Gentoo.
library(ggplot2) ggplot(dat) + aes(x = species, y = flipper_length_mm, color = species) + geom_jitter() + theme(legend.position = "none")
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Statistics for Data Science and Machine Learning Engineer. I’ll try to teach you just enough to be dangerous, and pique your interest just enough that you’ll go off and learn more.
The agenda of the talk included an introduction to 3D data, its applications and case studies, 3D data alignment and more.
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