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Normal Quantile-Quantile Plots in Rweb (Stat 3011)

For an example dataset we use the data for Exercise 6.37 on page 231 of the textbook. The dataset URL is

     http://superior.stat.umn.edu/~charlie/3011/ex0637.dat

If you submit the R command

     qqnorm(x)

you get a normal quantile-quantile plot of the data.

Ideally, the points in this plot should lie close to a straight line. They won't lie exactly on a straight line because of randomness, but they should be close. To help see the line, there is also a command to fit a line (not the regression line) to the plot. The two commands

     qqnorm(x)
     qqline(x)

make the plot and draw a line. Now it is even clearer that the four points on the right show a clear departure from linearity. These data do not appear to be normally distributed.

To tell whether that Q-Q plot is close enough to a straight line so that the data should be considered normally distributed is hard. Even data that are actually normally distributed will not be exactly on a line. To see this, do

     z <- rnorm(length(x))
     qqnorm(z)
     qqline(z)

Here z has exactly the same sample size as x and is exactly normally distributed by construction (rnorm is the Rweb function that generates normal random numbers). If the Q-Q plot for x looks no less linear than the Q-Q plot for z, then we can safely say that x is also normally distributed.

Since Q-Q plots are rather variable, especially if the sample size is small, you should probably make several Q-Q plots for known normal data (just repeat the three lines above). This will give you some idea of the statistical variability of Q-Q plots. If the Q-Q plot for x looks no less linear than any of the Q-Q plots for z, then we are even more confident that x is also normally distributed.