Plot: QQ

The options described here are used to modify the existing Quantile-Quantile plot using a variety of distributions. Various options are available on this tab for specifying the parameters of the distribution that you select for your plot. It also provides options that can be used to adjust the ranks and the sample size for determining the theoretical quantiles. These options are available in the QQ dialog as well as on the QQ tab of the Plot Layout dialog and via the Graph Options dialog.

Plot. Use the Plot drop-down box to select the plot to which you want to make changes. If you have several plots in one graph, you assign names to each plot using the Name field on the Plot: General tab.

Distribution. The Distribution group box provides a list of the theoretical distributions from which you can select a distribution for the Quantile-Quantile plot (Normal, Beta, Exponential, Extreme, Gamma, Lognormal, Rayleigh, Weibull). Specific parameters are required for the distributions: Beta, Gamma, Lognormal, and Weibull, while no parameters are required for the distributions: (Normal, Exponential, Extreme, and Rayleigh) as will be indicated when you select the distribution. See also the description of Quantile-Quantile plots in the Glossary for additional details on how these plots are constructed.

Do not assign average ranks to tied observations. This check box is selected by default, which enables you to see all data points, even the ties. When this check box is not selected, the "tied" points will overlap.

Parameters. STATISTICA offers three ways to supply the parameter(s) required for fitting the Beta, Gamma, Lognormal, or Weibull distribution in the Quantile-Quantile plot and are described below.

  1. If you want to use the default values, then first select the desired distribution and then clear the Compute parameters from: check box. If you selected the Beta distribution, then STATISTICA will fit the standardized Beta distribution using the default values of the shape parameters (Shape 1 = 1, Shape 2 = 1). If you selected the Gamma, Lognormal, or Weibull distributions, then STATISTICA will fit the standardized selected distribution using the default value of the shape parameter (Shape = 1).

  2. If you want to supply your own values for the shape parameter(s), then you first need to clear the Compute parameters from: check box. You can then specify the desired values in the Shape1 and Shape 2 fields (for the Beta distribution), or a value in the Shape field (for the Gamma, Lognormal, or Weibull distribution).

  3. If you want to compute (estimate) the shape parameters, then you need to select the Compute parameters from: check box. In that case, you can also enter the threshold ("offset") value in the Threshold field as well as the scale value in the Scale field, if the selected distribution is Beta. If the selected distribution is Gamma, Lognormal, or Weibull, then you need to specify only the threshold value in the Threshold field. The shape parameter(s) will then be estimated either by using the maximum likelihood (see below) or by matching moments approximation. Note that the maximum likelihood method is not available for estimating the shape parameter of the Lognormal distribution.  

Refer to the description of the respective distributions to learn more about the respective parameterizations.

Use Max. Likelihood. Select the Use Max. Likelihood checkbox to use the maximum likelihood method to estimate the Shape parameter(s) of the distribution (see Evans, Hastings, & Peacock, 1993, for details). If this check box is cleared, then the method of matching moments will be used. Note that the Use Max. Likelihood check box will only be available if the selected distribution is Beta, Gamma, or Weibull and the Compute parameters from: check box is selected.

Adjustments. Use the Adjustments group box to adjust the values which are used in the determination of the theoretical quantiles; these are computed as:

Theoretical Quantile = [(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.

Ranks. Enter the rank adjustment (rankadj; by default, .375) which is subtracted from the ranks of the observed values when the theoretical quantiles are computed in the Ranks field.

N. Enter the sample size adjustment (nadj; by default, .25) which is added to the original sample size in the N field. For more information, see Hahn and Shapiro, 1967.