BUSI 820 Week 4 Discussion Forum 4 Main Thread Example

Discussion Forum 4: Main Thread and Forum 3 Reply

BUSI 820 Quantitative Research Methods, Discussion Forum 4 Main Thread (with the Forum 3 reply)

Thread by [Student Name]

The data set is illustrative, generated for this page with a fixed random seed and analyzed with the statistics SPSS reports for a cross-tabulation; the bank, the classmate and the prompt are composites standing in for the course's own; the book is real; the week, points and readings follow Liberty's public course guide for BUSI 820.

The bank's leaders keep asking whether hybrid schedules are driving turnover. In my illustrative data set, I recorded whether each of the 186 tellers and personal bankers left within the following 12 months, a nominal variable with two categories, alongside work arrangement, a nominal variable with three. Morgan et al. (2020) recommend cross-tabulation with a chi-square test of independence when both variables are nominal, with phi or Cramér's V as the measure of association. Table 1 shows the cross-tabulation.

Before reading the test, I checked the expected counts. The smallest, for rotating staff who left, is 8.1, so every cell exceeds 5 and the chi-square approximation is appropriate. The Pearson chi-square was 0.30 with 2 degrees of freedom, p = .86, and Cramér's V was .04. In words, the percentage who left was slightly higher among hybrid and rotating staff than among on-site staff, but the differences were small, and data like these would be very likely if work arrangement and leaving were unrelated in the population. Cramér's V confirms that any association is negligible.

What should the bank conclude? A nonsignificant result means the data give no evidence that hybrid schedules drive departures; it does not prove that they never do. The hybrid and rotating groups are small, 44 and 27 employees, so the test had limited power to detect a modest difference. A five-point gap in departure rates would matter to the bank financially, yet a sample of this size could easily miss it. Using the effect size index w that Cohen (1988) defined for chi-square tests, detecting even a small association of w = .10 with 2 degrees of freedom and 80 percent power would require about 964 employees, and a small-to-medium association of w = .20 about 241, more than this bank's whole sample. Two conclusions follow. First, leaders should stop treating hybrid schedules as the obvious cause of turnover, because these data do not support it. Second, the question deserves a larger sample, pooling two or three years of records, before the policy is either defended or abandoned. Meanwhile, the earlier forums suggested that supervisor support relates to intention to leave more strongly, which is where attention may be better spent.

Reply to Grace (Forum 3)

Grace, your Forum 3 thread proposed an independent-samples t test to compare days absent between nurses on eight-hour and twelve-hour shifts. Your descriptive statistics from Forum 2 showed that days absent had a skewness of 2.4, well beyond the range of minus 1 to plus 1 that Morgan et al. (2020) treat as approximately normal. With groups of 38 and 41, that skew is a concern. Morgan and colleagues describe the Mann-Whitney U test as the nonparametric alternative when the dependent variable is ordinal or badly skewed, and it compares the groups' rank distributions rather than their means. You could run both and report whether they agree, but I would lead with the Mann-Whitney result and report medians, since a few nurses with long absences could pull the means apart. Would a log transformation of days absent, as I used for tenure, give you a third option to compare?

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for introductory statistics: Use and interpretation (6th ed.). Routledge.