Sometimes, you are just curious to know whether a sample is normally distributed. Sometimes, you NEED to know whether it is or not because normality is a prerequisite for performing a specific test.
To check whether your sample is normally distributed, you may use
shapiro.test() which performs the Shapiro-Wilks normality test. In this test, the null hypothesis H0 states that the sample has a normal distribution. Accordlingly, the p-value that results from the test represents the chance that the sample originates from a normal distribution. A low value (typically under 0.05) would thus indicate that the sample is not likely to be normally distributed.
Let’s take an example.
To visualize the sample, we first create a histogram of the vector
data1 to which we add a line representing the normal density curve:
data1 <-c (11.25, 10.00, 9.68, 10.52, 8.77, 9.92, 8.62, 10.21, 9.09, 10.36) hist(data1, col="red", xlim=c(7,13), prob=TRUE) x <- seq(7,13,0.1) curve(dnorm(x,mean=mean(data1), sd=sd(data1)), 7, 13, col="blue", add=TRUE)
Now let’s run the test:
Apparently, the p-value is rather high. The null hypothesis H0 is NOT rejected, meaning that your sample is very likely to be normally distributed.