Question

Explain the notions of mathematical differences, managerially relevant differences, and statistical significance. Can results be statistically significant and yet lack managerial importance? Explain your answer.

A retailer is interested in investigating whether doubling the value of manufacturer coupons will increase the number of shoppers. “Doubling” means that the store would give consumers a discount equal to twice the coupon face value, with the retailer absorbing the cost of the extra discount. Write the null and alternative hypotheses associated with this test that would need to be performed in order to provide this information. Also indicate the type of data that should be collected to best test the hypothesis, and the type of statistical test that would need to be performed.

Answer 1

Mathematical differences are the result obtained after subtracting one number from another. Provided the numbers are not exactly the same, they are mathematically different. It measures how one number is greater than or less than the other number. They determine how figures differ in terms of quantity (Spiegel & Lindstrom, 2000). Managerially important differences are the differences between numbers to the extent that the difference matters from a managerial perspective. The different is important or beneficial to the management as further as the process of decision making is concerned.

Finally, statistical significance is the difference that is so large that it is most likely to have resulted due to chance or sampling errors (Spiegel & Lindstrom, 2000). The significance is never certain hence tested at different confidence levels. In this regard, the results can be statistically significant and lack managerial importance. Statistical significance and managerial importance difference have a direct relationship. Therefore, a data might be statistically significance but yet so small as to be of little managerial or practical significance.