MST 7000 Module 6 Written Assignment: Order Days and Return Reasons With Chi-Square Example

Mondays, Beds and Photographs: Two Chi-Square Tests on Orders and Returns

Student Name

MBA in Data Analytics, Thomas Edison State University

MST-7000: Managerial Statistics

Mentor Name

Month Day, Year

Mondays, Beds and Photographs: Two Chi-Square Tests on Orders and Returns

Test 1: Are Orders Spread Evenly Across the Week?

Customer service staffs the same number of agents every day, on the assumption that orders arrive evenly. I counted 700 orders over four weeks by the day they were placed.

Anderson et al. (2011) set out the goodness-of-fit test: for each category, square the gap between observed and expected counts, divide by the expected count and add the results, using k minus 1 degrees of freedom. Pearson (1900) introduced this criterion. With 6 degrees of freedom, the statistic of 14.48 exceeds the critical value of 12.59, and CHISQ.DIST.RT(14.48,6) gives a p-value of 0.025. The null hypothesis of equal daily orders is rejected. Monday contributes more than half the statistic: customers browse over the weekend and order on Monday. A single four-week window could reflect one unusual week, such as a Monday sale, so I repeated the count for the previous four weeks, 684 orders. Monday again had the highest count, 121 against an expected 97.7, and the service team's call logs show the same Monday peak.

Test 2: Do Return Reasons Depend on Product Category?

The returns team groups 180 returns last quarter by reason and category.

Expected counts, in parentheses, are each row total times column total divided by 180; all exceed 5, meeting the test's condition. The statistic is 10.37 with (3 minus 1) x (3 minus 1) = 4 degrees of freedom, above the critical value of 9.49, and CHISQ.TEST on the observed and expected ranges gives p = 0.035. Return reason and category are not independent.

What Drives the Dependence

The largest gaps between observed and expected counts are tables returned as damaged, 18 against 13.9; tables returned as not as pictured, 12 against 19.4; and beds returned as not as pictured, 28 against 23.3, while beds are returned as damaged less often than expected. Glass-topped tables break in transit, and bed frames look different from their photographs, where they are shown with bedding and lighting that hide their finish. Agresti (2019) recommends examining such cell contributions or standardized residuals after a significant test, since the test itself does not say where the dependence lies. Beds were returned as not as pictured far more often than as damaged, which points to the website rather than to shipping.

Limits

Both tests describe association, not cause. The returns sample covers one quarter, and customers may choose the reason that sounds most acceptable. The independence test also treats each return as a separate customer decision, so I removed two repeat returns by the same customers before counting the 180.

Recommendations

Add two customer service agents on Mondays and move one from Sunday. Reshoot bed photographs in plain light with close views of the finish, and refer glass tables to the packaging review already under way.

References

Agresti, A. (2019). An introduction to categorical data analysis (3rd ed.). Wiley.

Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2011). Essentials of modern business statistics with Microsoft Excel (5th ed.). South-Western Cengage Learning.

Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine, 50(302), 157-175. https://doi.org/10.1080/14786440009463897