Quantile-Quantile and Probability Charts

Quantile-Quantile (Q-Q) Chart

  • The quantile-quantile (Q-Q) chart is a graphical representation for assessing if two variables come from populations with a common distribution.
  • The graph includes 100 points (percentiles); for example, the 0.4 or 40% quantile is the points at which 40% of the data fall below and 70% fall above that point. A reference line connects the 0-percentile to 100-percentile.
Example Graph

Q-Q Graph of Fisher Iris Data*

Spine Chart

  • Q-Q chart does not convey information about the type of distribution (as seen in the given examples above). It only conveys information about similarity between the distributions of the two variables used to generate the graph.
  • If the two variables come from a population with the same distribution, the percentile points displayed on a Q-Q chart should fall approximately along this reference line. The larger of departure from the reference line, the larger the difference between the populations represented by two variables.

* Source of data: Fisher (1936), reproduced by Andrews and Herzberg (1985): Andrews, D. F. and Herzberg, A. M. (1985). Data - A Collection of Problems from Many Fields for the Student and Research Worker. Springer-Verlag, New York.