10- The analysis of variance (ANOVA)
2 min read
Create some data
group <- rep(c('A1','A2', 'A3'), times=4) value <- runif(12, 10, 20) df1 <- data.frame(group, value) df1 group <- rep(c('A1','A2', 'A3'), times=4) value <- runif(12, 10, 20) year <- as.factor(c(rep("2010",6), rep("2020",6))) df2 <- data.frame(value,group,year) # dataframe
library(ggplot2) ggplot(df1, aes(x = group, y = value)) + geom_boxplot()
One way ANOVA
It uses to examine statistically significant differences between two samples means.
df1.anova <- aov(value ~ group, data=df1) df1.anova summary(df1.anova) # extract the p-value and F value summary(df1.anova)[][1,4:5]
Interpret the result:
P-value ≤ α: The differences between some of the means are statistically significant.
P-value > α: The differences between the means are not statistically significant.
p-value of df1 = 0.9358 > 0.05, so we can not reject the null hypothesis (means are equal) and conclude that means are equal.
Two way ANOVA
A two-way ANOVA, has two independents. The style of two way ANOVA is:
df2.anova <- aov(value ~ group*year, data=df2) summary(df2.anova) # extract the p-value and F value: summary(df2.anova)[][1,4:5] summary(df2.anova)[][2,4:5] summary(df2.anova)[][3,4:5]
Analysis of covariance
df2.anova <- aov(value ~ group+year, data=df2) summary(df2.anova) # extract the p-value and F value: summary(df2.anova)[][1,4:5]
TukeyHSD(df1.anova) #Tukey Honest Significant Differences TukeyHSD(df2.anova)
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