A quantile-quantile (or q-q) plot is a graphical method for comparing two probability distributions by plotting their quantiles against each other. For example, suppose we were given the following set of data and are asked to check if it follows a normal distribution:
y1 ≤ y2≤ ...≤ yr≤ ...≤ yn
Fist, we need to compute the sample quantiles for each observation. To that end, yr, is the sample quantile of order p = r/(n+1), i.e., it is the
100r/(n+1) sample percentile. Next, we can compare the sample quantiles to the corresponding quantiles of the normal(0,1) distribution. In particular, since
z1-p = (qp-μ)/σ
we know that if the points follow a straight line, then the data is normally distributed and the slope of the line is the reciprocal of the standard deviation.
To use the qq-plot calculator below, input your sample data as a comma separated list and hit go! The code will compute the mean and standard deviation of the sample. Then,
it will plot the sample quantiles against the corresponding quantials of the standard normal distribution. Finally, it will plot the least squares regression for comparison and
gives the reciprocal of the slope of the fitted line.
x:
