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 statistic. Q–Q plots are commonly used to compare a data set to a theoretical model. A Q–Q plot is generally more diagnostic than comparing the samples' histograms, but is less widely known. 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 identity line y = x. This defines a parametric curve where the parameter is the index of the quantile interval. 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). In statistics, a Q–Q plot ( quantile-quantile plot) is a probability plot, 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. Otherwise, the data fit the Weibull(1,2) model well. Three outliers are evident at the high end of the range. The deciles of the distributions are shown in red.
A Q–Q plot of a sample of data versus a Weibull distribution. The linearity of the points suggests that the data are normally distributed. The median of the points can be determined to be near 0.7 A normal Q–Q plot comparing randomly generated, independent standard normal data on the vertical axis to a standard normal population on the horizontal axis. The offset between the line and the points suggests that the mean of the data is not 0. The points follow a strongly nonlinear pattern, suggesting that the data are not distributed as a standard normal ( X ~ N(0,1)). This Q–Q plot compares a sample of data on the vertical axis to a statistical population on the horizontal axis. A normal Q–Q plot of randomly generated, independent standard exponential data, ( X ~ Exp(1)).
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