Levene Test for Constant Variance

This test for constant variance does not depend on the error terms (e,) being normally distributed. That is, the test is very robust, even if the error terms are not normal, and is based on the size of the y, — y, = c, error terms. The larger the ej, the larger the Sy. Because a large Sy value may be due to a constant variance, the data set is divided into two groups, and 2- If say, the variance is increasing as the x, values increase, then the e lower values of should be less than the e upper values of ri2. 

FIGURE 8.10 High predictor variables vs. low predictor variables. 

Let us work out an example (Example 8.2). In a drug stability evaluation, an antimicrobial product was held at ambient temperature ( 68°F) for 12 months. The potency (%) through HPLC was measured, 10 colony-forming units (CPU) of Staphylococcus aureus (methicillin-resistant) were exposed to the product for 2 min, and the microbial reductions (logio scale) were measured. Table 8.2 provides the data. 

The regression model parameters are presented in Table 8.3. and the regression evaluation of the data in Table 8.2 are presented in Table 8.4. 

Without even doing a statistical test, it is obvious that, as months go by, the variability in the data increases. Nevertheless, let us perform the Modified Levene Test. 

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