Chi-Square Tests

Figure 1. Chi-Square Tests
Chi-Square Tests

The Probit Analysis procedure produces two chi-square tests of different aspects of the model:

  • The Pearson goodness-of-fit chi-square statistic is used to test the null hypothesis that the model adequately fits the data.
  • The Parallelism test checks to see whether the assumption of equal slopes across factor levels is reasonable. If the Parallelism test is significant, you need to perform separate analyses for each site.

If the null hypotheses of these tests are true, the statistics have chi-square distributions with the displayed degrees of freedom. If the significance value of a given test is small (less than 0.05), then the model does not adequately fit the data. In this case, the data do not violate the model assumptions.

Figure 2. Cell counts and residuals
Cell counts and residuals

The goodness-of-fit statistics are based on the cell counts and residuals table. Cells in the table represent the cross-classification of Site of offer and Value of offer. Note that the values of Value of offer shown are the natural logarithms of the actual values.

  • Thus, the first row of the table pertains to customers visiting the online store who were offered a 15% rebate.
  • The observed responses column reports the number of cases observed in the data file that are in the cross-classification.
  • The expected responses column reports the number of cases you would expect to see in the cell if the model is correct.
  • The residuals are measures of the difference between the observed and predicted values. Large residuals can indicate cells that are not well fit by the model.

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