Goodness of Fit Analysis Tools

Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides the Goodness of Fit data analysis tool, which supports the following tests:

• Two-Sample Kolmogorov-Smirnov Test
• One-Sample Anderson-Darling Test
• Two-Sample Anderson-Darling Test
• Chi-square Goodness of Fit Test

We now give three examples of the use of this data analysis tool.

Two Sample Kolmogorov-Smirnov Test

We now show how to perform Example 1 of Two Sample Kolmogorov-Smirnov Test using the Goodness of Fit data analysis tool. Press Ctrl-m and double-click on the Goodness of Fit option from the main menu (or from the Misc tab of the MultiPage interface). Fill in the dialog box that appears as shown in Figure 1.

Figure 1 – Goodness of Fit Tests data analysis tool

Upon clicking on the OK button, the output shown in range E3:F11 of Figure 2 appears.

Figure 2 – Two Sample KS Test

In this example, the input data (range A3:C13) is in the form of a frequency table. The data analysis tool can also be used with data in raw data format. E.g. for Example 2 of Two Sample Kolmogorov-Smirnov Test, when the dialog box in Figure 1 appears, enter J3:K11 (see Figure 3 of Two Sample Kolmogorov-Smirnov Test) in the Input Range and select the Kolmogorov-Smirnov (raw) test.

One Sample Anderson-Darling Test

To repeat Example 2 of Anderson-Darling Test, press Ctrl-m, choose the Goodness of Fit data analysis tool, and fill in the dialog box that appears as shown in Figure 1 with Input Range A3:A18 and select the One sample Anderson-Darling, Moments, and Gamma options. After pressing the OK button, the output shown in Figure 3 is displayed.

Figure 3 – Anderson-Darling data analysis tool

Note that the Beta and Uniform options are not supported for the Anderson-Darling test. The Regression option is only valid for the Weibull distribution.

Note too that when the Specify parameters option is selected, you need to explicitly enter values for Param1 and possibly Param2. If you select the Normal option, enter the mean and standard deviation in the Param1 and Param2 fields. For the Expon option, enter the lambda value in Param1. For the other distribution choices, enter the alpha and beta values in Param1 and Param2. These fields are ignored when the Generic option is chosen.

Chi-square Goodness of Fit

To repeat Example 1 of Chi-square Goodness of Fit Test, press Ctrl-m, choose the Goodness of Fit data analysis tool, and fill in the dialog box that appears as shown in Figure 1 with Input Range A3:B11 and select the Chi-square Goodness of Fit, Moments, and Normal options. After pressing the OK button, the output shown on the left side of Figure 4 is displayed.

Figure 4 – Chi-square goodness of fit data analysis

This is the same output that we saw on the left side of Figure 2 of Chi-square Goodness of Fit Test. To repeat the analysis with the specific values of 2 and 1 for the mean and standard deviation, respectively, we follow the same steps as described above, except that we choose the Specify parameters option instead of the Moments option. The output is shown on the right side of Figure 4. This output is the same as we saw on the right side of Figure 2 of Chi-square Goodness of Fit Test.

Reference

D’Agostino, R. B., Stephens, M. A. (1986) Goodness-of-fit techniques. Marcel Dekker, Inc.
https://dblp.org/rec/journals/sac/Genz04.html