Q–Q plots are also used to compare two theoretical distributions to each other. This can provide an assessment of "goodness of fit" that is graphical, rather than reducing to a numerical summary. Q–Q plots are commonly used to compare a data set to a theoretical model.
A Q–Q plot is generally a more powerful approach to do this than the common technique of comparing histograms of the two samples, but requires more skill to interpret. The use of Q–Q plots to compare two samples of data can be viewed as a non-parametric approach to comparing their underlying distributions. Q–Q plots can be used to compare collections of data, or theoretical distributions.
Q–Q plots can also be used as a graphical means of estimating parameters in a location-scale family of distributions.Ī Q–Q plot is used to compare the shapes of distributions, providing a graphical view of how properties such as location, scale, and skewness are similar or different in the two distributions. If the distributions are linearly related, the points in the Q–Q plot will approximately lie on a line, but not necessarily on the line y = x. If the two distributions being compared are similar, the points in the Q–Q plot will approximately lie on the line y = x. Thus the line is a parametric curve with the parameter which is the number of the interval for the quantile. A point ( x, y) on the plot corresponds to one of the quantiles of the second distribution ( y-coordinate) plotted against the same quantile of the first distribution ( x-coordinate). First, the set of intervals for the quantiles is chosen.
In statistics, a Q–Q (quantile-quantile) plot is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other. The curved pattern suggests that the central quantiles are more closely spaced in July than in March, and that the July distribution is skewed to the left compared to the March distribution. A Q–Q plot comparing the distributions of standardized daily maximum temperatures at 25 stations in the US state of Ohio in March and in July.
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