# SmartRS

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
``````

Visualize data:

``````library(ggplot2)
ggplot(df1, aes(x = group, y = value)) +
geom_boxplot()
`````` #### One-way ANOVA

It is used to examine statistically significant differences between means of two or more groups.

``````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]
``````

#### Interpretation of the result:

If the p-value is less than or equal to the chosen significance level (α), we reject the null hypothesis and conclude that there is a statistically significant difference between at least two group means.

If the p-value is greater than α, we fail to reject the null hypothesis and conclude that there is no statistically significant difference between group means.

The p-value of df1 is 0.9358, which is greater than 0.05. Therefore, we cannot reject the null hypothesis (means are equal) and conclude that the means are equal.

#### Two-way ANOVA

A two-way ANOVA has two independent variables. The syntax for a two-way ANOVA is:

``````aov(dependent ~ as.factor(independent1) * as.factor(independent2), data=filename)
``````
``````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)
``````