By default, an Anderson-Darling test for normality is performed and the numerical results are displayed with the graph. The line forms an estimate of the cumulative distribution function for the population from which data are drawn. The grid on the graph resembles the grids found on normal probability paper. Normal plots use the values in the input column as x-values. Saves the graph in a Minitab Graphics Format (MGF) file Specifies the Kolmogorov-Smirnov goodness-of-fit test Specifies the Ryan-Joiner test (similar to Shapiro-Wilk test) Shows the percents at the reference x-scale positions Stat > Basic Statistics > Normality Test or Graph > Probability Plot Command Syntax NORMTEST C Q-Q plots tend to be preferred in research situations.īoth Q-Q and P-P plots can be used for distributions other than normal.Minitab material on test for Normality NORMTEST example

For the most part, the normal P-P plot is better at finding deviations from normality in the center of the distribution, and the normal Q-Q plot is better at finding deviations in the tails. In both, the points fall right on the line when normality has been met. That’s what I’ve described above.Ī P-P plot, one the other hand, plots the corresponding areas under the curve (cumulative distribution function) for those values. The Q-Q is plotting the quantiles-the actual values of X against the theoretical values of X under the normal distribution. As you do more of these, you’ll get better at reading them without the histogram. I find it helpful to always plot a histogram along with the Q-Q plot, to aid interpretation. You can see that it’s not matching a normal distribution well at all-there are too many low values and too few high values. The following Q-Q plot shows a positively skewed distribution. The further a point is from the line, the further it is from where a normal distribution would put it. So if each value is exactly where it should be, if the distribution is perfectly normal, every single point would fall right on the line. We don’t have easy ways to remember them, but those are the values plotted on the graph. Likewise, there is an exact value that the 17 th, the 42 nd, each of the 111 ordered values would have under a standard normal distribution. So the 3 rd value should be right around -2. Only 2.5% of the 111 points-about 3 of them-should have values at or below -2. So in a distribution of 111 points with a mean of 0 and standard deviation of 1, we know that the 56 th point must have a value of 0-in a normal distribution the median equals the mean. Because the distribution is symmetric, these same percentages apply above the mean.The final 2.5% are above 2 standard deviations below the mean.Another 12.5% are between one and 2 standard deviations below the mean.34% of points are between the mean and one standard deviation below the mean.The mean is 0 and the standard deviation is 1.Remember back to your intro stats class, when you learned these rules about a standard normal distribution: This concept is a little strange if you’re not used to it, so think through it a bit. On the Y axis are the values that you would have gotten if they came from a standard normal distribution with the same number of data points–111. If they didn’t, the plot would standardize them before plotting). (Note, these are standardized residuals, so they already have a mean of 0 and a standard deviation of 1. You can see that just like on the histogram, the values range from about -2.2 to 2.2. We have 111 observations in this data set, and you can see a histogram of the distribution on the right, and the corresponding Q-Q plot on the left.Īcross the bottom are the observed data values, sorted lowest to highest. The Q-Q plot plots every observed value against a standard normal distribution with the same number of points. There are two versions of normal probability plots: Q-Q and P-P. It’s more precise than a histogram, which can’t pick up subtle deviations, and doesn’t suffer from too much or too little power, as do tests of normality. A normal probability plot is extremely useful for testing normality assumptions.

Normal probability plot minitab