Quantile-Quantile Plots - Advanced Tab

Graphical Analytic Techniques

Use the options on the Advanced tab of the Quantile-Quantile Plots Startup Panel to create a Quantile-Quantile plot using a variety of distributions.

Variables. Click the Variables button to display a standard variable selection dialog box, in which you select the variable(s) to be plotted. If you select more than one variable, a sequence of graphs (one for each variable selected) will be produced. The selection made will be displayed below the Variables button.

Distribution. Select the desired theoretical distribution for this graph. Additional options available in this box are dependent on the distribution selected.

Parameters. Specific parameters are available for some of the distributions. In those cases, the parameter options will be displayed when the distribution is selected. Click the desired plot link below for more information.

Normal

Gamma

Beta

Lognormal

Exponential

Rayleigh

Extreme Value

Weibull

Probability scale. Select this check box to scale the upper x-axis nonlinearly, according to the probability values given in the respective box (by default, .01, .05, .1, .25, .5, .75, .9, .96, .99). Vertical grid lines will be positioned along these percentiles. If this check box is cleared, then no scale will be displayed on the upper x-axis.

Plot layout. Specify the plot layout.

Multiple plots in one graph. When you have chosen more than one variable to be plotted, select the Multiple plots in one graph check box to create an overlaid quantile plot. When this check box is selected, several quantile plots will be displayed in the graph, one for each selected variable. A different point marker and color is used for each of the multiple variables and referenced in the legend so that individual plots representing different variables can be discriminated in the graph. When this check box is cleared, separate graphs will be generated for each variable.

Fitting line. The options in this group box pertain to the fitting line. Two types of fitting lines are available:

Display linear fit. STATISTICA calculates and displays the linear fitting line when this check box is selected. The equation of the linear fitting line (Y=a + bx, given in the third title of the resulting Q-Q plot) provides estimates for the Threshold (a, location) and the Scale (b) parameters of the specified distribution.

Custom fit. Custom-define a fitting line to be included in the graph (in addition to the linear fit) by selecting the Custom fit check box and then entering user-defined Scale and Threshold (location) values. This option is useful for comparing the linear fitting line (see above) with custom fitting lines based on known distributions in the family of distributions.

Note that both the linear fit and custom fit lines can be displayed in the graph by selecting both check boxes.

Adjustments. Use these options to adjust the values used in the determination of the theoretical quantiles: [(i - rankadj)/(n + nadj)] where i is the i'th ordered observation, n is the number of non-missing values and rankadj and nadj are user-defined adjustments to ensure that this quantity is greater than 0 and less than 1, see below.

Ranks. Specify the rank adjustment (rankadj; by default, .375), which is added to the ranks of the observed values when the theoretical quantiles are computed.

N. Specify the sample size adjustment (nadj; by default, .25), which is added to the observed sample size when the theoretical quantiles are computed.

For more information, see Hahn and Shapiro, 1967.