Empirical Distribution Tests

Select menu: Stats | Distributions | Empirical Tests

This test assesses how well the empirical data approximates a particular theoretical distribution. Note: usually the particular parameters of the distribution are not known and these have to be estimated first to obtain the expected values.

After you have imported your data, from the menu select
Stats | Distributions | Empirical Tests.
Fill in the fields as required then click Run.

You can set additional Options before running the analysis and save the results by clicking Store.

Available data

This lists variates that are available for analysis. Double-click on a name to copy it into the input field, or type the name in directly.

Data values

This specifies the name of the variate that will be used in the empirical distribution test.

Distribution

This provides a dropdown list of the range of continuous distributions that the observed data can be tested against.

Parameters

If you select Specify, the named fields give the numerical values for the parameters of the selected distribution. If you select Estimate, the parameters will be estimated using the DPROBABILITY procedure.

For some distributions, a constant can be added to the distributional parameters. If you select Specify, the value given is used as the minimum data value (which is normally zero for these distributions). When estimating the parameters of these distributions, you can also attempt to estimate the constant by selecting Estimate, although this quite commonly fails.

Goodness-of-fit test statistics

You may select the tests statistic to be used for the empirical distribution test. You can calculate probabilities using either the Traditional tests non-parametric probabilities, or the superior Likelihood ratio tests as documented in the EDFTEST procedure.

Anderson-Darling	This measures the deviation between the observed and theoretical cumulative distributions, but gives more weight to the tails than the Kolmogorov-Smirnov test.
Cramer-von Mises	This measures the sum of squared deviations between the observed and theoretical cumulative distributions.
Kolmogorov-Smirnov	This measures the maximum deviation between the observed and theoretical cumulative distributions.

Each test may be more powerful than the others in certain situations, but in general the Kolmogorov-Smirnov test statistic is the least powerful.

Action buttons

Run	Run the analysis.
Cancel	Close the dialog without further changes.
Options	Opens a dialog where you can specify additional options and settings for the analysis.
Defaults	Right-click this button to display a shortcut menu that lets you reset the latest user stored defaults or the Genstat default settings
Store	Opens a dialog to specify names of structures to store the results from the analysis. The names to save the structures should be supplied before running the analysis.

Action Icons

	Pin	Controls whether to keep the dialog open when you click Run. When the pin is down the dialog will remain open, otherwise when the pin is up the dialog will close.
	Restore	Restore names into edit fields and default settings.
	Clear	Clear all fields and list boxes.
	Help	Open the Help topic for this dialog.