Case Study 7—Measuring Differences in Pre- and Postincident Sales Using Two Sample t-Tests versus Regression Models
Atypical lost profits case begins with the plaintiff complaining that sales, and ergo profits, have declined from a base period due to the alleged actions of the defendant. For the damages expert, whether he or she works for the plaintiff or the defendant, the first item on the to-do list is to test that assertion. This case study presents two tools that can be used to test the assertion of declining sales over time. Both tools will be demonstrated and the results obtained from each will be compared and contrasted.
Preliminary Tests of the Data
ABC Retailer is a convenience store that also sells gasoline. Its sales fell off dramatically after a customer's truck backed into the pump island and rendered the pumps unable to dispense gasoline. Subsequent issues with the Department of Environmental Protection prevented a quick replacement of the pumps, and so the losses dragged on. Figure 7.1 shows seven months of sales before the incident and eight months of sales after the incident. We want to compare the averages of the two periods to determine whether a significant difference exists between them. In order to test for this difference, we use the two-sample t-statistic. This test requires that the data be near–bell shaped, and the skewness and kurtosis amounts indicate that this is approximately so. But before we apply the t-test, we need to determine if the ...