Rankit Plot

Assumption of normal distribution of data is an important prerequisite for some statistical tests (parametric) and regression methods. This assumption can be tested by using various graphical methods like rankit plots, normal probability plots and tests like Shapiro-Wilk or Kolmogorov-Smirnov tests.

A simple way to test the normality assumption could be to just look at the distribution of data as a histogram and see if it assumes a bell-shaped distribution that is characteristic of a normal or Gaussian distribution. If this is not the case, some transformations like log transformation can be attempted to see if now the new distribution takes more of a bell shaped curve.

Parameters like skewness and kurtosis can also be checked. Further, quantile distribution of values can be looked at to see if a given mass of distribution is falling below a given %ile position patterning the indicative trend of a normal distribution.

A graph plotting the rankits versus the data points is known as a rankit plot. If the sample is sufficiently large and comes from a normally distributed population, such a plot should approximate a straight line. Significant deviations from straightness can indicate evidence against normality of the distribution.

A rankit plot is quite simple to generate. We have a list of values with us whose normal distribution we wish to check. We need to get an equal number of data points from a normal distribution (mean 0, variance 1). We then plot these two lists against each other after sorting them both and putting corresponding ranks against each other as the x,y pairs.

A plot of particular interest to look at is a rankit plot of the 'standardized residuals'.

A script for obtaining a rankit plot on the given column is available at http://www.qsarworld.com/virtual-workshop.php.

References:

1. http://en.wikipedia.org/wiki/Normal_probability_plot

Cite This As:

Dogra, Shaillay K., "Rankit Plot" From QSARWorld--A Strand Life Sciences Web Resource.
http://www.qsarworld.com/qsar-statistics-rank-it-plot.php