Notice how the points stray from the straight line. Standard normal distribution: QQ Plot transformed QQ Plot Map An example of using data transformationsĪ Normal QQ plot of an example dataset is presented here: As seen below, they are concentrated around the San Francisco Bay area (points shaded in pink on the map below). The location of the selected points are then highlighted in the ArcMap data view.
The Normal QQ Plot tool allows you to select the points that do not fall close to the reference line. The main departure from this line occurs at high values of ozone concentration. You can see that the points fall close to the 45-degree reference line. In the diagram below, the quantile values of the standard normal distribution are plotted on the x-axis in the Normal QQ plot, and the corresponding quantile values of the dataset are plotted on the y-axis. If the data is not normally distributed, the points will deviate from the reference line. If the data is normally distributed, the points will fall on the 45-degree reference line. Points on the Normal QQ plot provide an indication of univariate normality of the dataset. General QQ plot example Examining data distributions using QQ plots If the two datasets have identical distributions, points in the general QQ plot will fall on a straight (45-degree) line. These plots are created following a similar procedure as described for the Normal QQ plot, but instead of using a standard normal distribution as the second dataset, any dataset can be used. General QQ plots are used to assess the similarity of the distributions of two datasets. Normal QQ plot example How the general QQ plot is constructed Once these two cumulative distribution graphs have been generated, data values corresponding to specific quantiles are paired and plotted in a QQ plot (bottom graph in the figure below). The same process is done for a standard normal distribution (a Gaussian distribution with a mean of 0 and a standard deviation of 1, shown in the graph on the top right of the figure below). A cumulative distribution graph is produced by plotting the ordered data versus the cumulative distribution values (graph on the top left in the figure below). How the Normal QQ plot is constructedįirst, the data values are ordered and cumulative distribution values are calculated as ( i– 0.5) /n for the ith ordered value out of n total values (this gives the proportion of the data that falls below a certain value). Quantile-quantile (QQ) plots are graphs on which quantiles from two distributions are plotted relative to each other. An example of using data transformations.Examining data distributions using QQ plots.
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