RES 710 Week 8 Applying Statistics Example

From Analysis to Decision: Applying Statistics to a Credit Union Service Problem

[Student Name]

University of Phoenix

RES/710: Statistical Research Methods and Design I

Week 8 Assignment

[Instructor Name]

[Date]

The learner, the credit union, its members and all data are composites written for a model paper.

Over seven weeks, the operations director at the invented western Michigan credit union defined variables, described a member survey, sampled and weighted it, tested hypotheses, compared groups, measured correlations and appraised a vendor's study. This final report brings those analyses together for the board, which must decide whether to invest in branch staffing, queue displays or neither, and sets out what the director's dissertation will add.

The Problem and Questions

Member satisfaction has fallen four points on the credit union's 100-point index over two years, and members' likelihood to recommend has declined. Branch managers blame waits; the digital team points to channel shifts. The report addresses three questions:

Q1: How long do members wait, and how satisfied are they?

Q2: How is waiting, recorded and perceived, associated with satisfaction?

Q3: How does satisfaction differ by channel?

Matching Questions to Analyses

Appelbaum et al. (2018) set out reporting standards for quantitative research that call for clear descriptions of participants and sampling, measures and their reliability, the analysis used for each hypothesis, effect sizes with confidence intervals and an account of any departures from the plan. The report follows those standards.

Q1 is answered with descriptive statistics suited to each variable's shape: medians and percentiles for skewed waits, means and standard deviations for the satisfaction scale and weighted estimates with intervals. Q2 uses Welch's t test at the 10-minute service standard, Pearson's r on log-transformed wait, Spearman's rho and a partial correlation controlling for age. Q3 uses Welch's t test comparing app and branch members, with an explicit note about confounding.

Findings for Q1: Waits and Satisfaction

The median recorded wait was 5.2 minutes, with the middle half of members waiting 2.6 to 9.8 minutes; one member in ten waited more than 16.5 minutes. Long waits clustered at Friday lunchtime, when the chance of waiting over 15 minutes was 31 percent, against 12 percent overall. Weighted mean satisfaction was 5.45 on a 7-point scale, 95% CI [5.38, 5.52], below the board's target of 5.6, though by a small margin (d = -0.17). The share of promoters fell from 45 to 41 percent, z = -2.81, p = .005.

Findings for Q2: Waiting and Satisfaction

Among branch members, those who waited longer than the 10-minute standard rated satisfaction 0.88 points lower, t(219) = 6.96, p < .001, d = 0.70, 95% CI for the difference [0.63, 1.13]. Across all members with a recorded wait, log wait correlated with satisfaction at r(990) = -.41, 95% CI [-.46, -.36], and the relationship was steepest in the first 10 minutes. Members believed they waited 1.6 minutes longer than recorded, and perceived wait was more strongly associated with satisfaction (rho = -.52) than recorded wait (rho = -.40), a difference that was itself significant. Controlling for age left the relationship nearly unchanged.

The clock matters, but the member's sense of the wait matters more.

Findings for Q3: Channel

App members rated satisfaction 0.7 points higher than branch members, t(643) = 9.12, p < .001, d = 0.58. Because app members are younger, do simpler transactions and never wait in line, this difference cannot be attributed to the app itself.

In Plain Terms

Most members are served quickly, but a predictable group, Friday lunch visitors at four high-volume branches, waits much longer, and those members are noticeably less satisfied. How long a wait feels matters at least as much as its length. App users are happier, but the reasons are unclear. Overall satisfaction is a little below target, and advocacy has slipped.

A Common Comparison Error

Regional managers have asked which branches "have a significant wait problem." Gelman and Stern (2006) showed that the difference between a significant and a nonsignificant result is not necessarily significant itself; a branch whose wait-satisfaction correlation reaches p < .05 and another whose correlation does not may not differ meaningfully. The report therefore does not label branches by significance. Instead, it presents each branch's median wait and mean satisfaction with intervals in a single chart and flags branches only when a direct comparison with the network shows a difference.

Assumptions and Limitations

The analyses rest on several conditions. The survey covers active members only, and respondents were older and more often branch users than the frame; weights correct for those differences but not for unmeasured ones. Standard errors from simple formulas understate uncertainty because members are clustered in branches; final estimates use survey software that accounts for this. Every finding about waiting and channel is correlational: staffing, transaction complexity and members' moods could produce the associations. And the satisfaction scale, though reliable (alpha = .89), was measured after a single transaction.

Recommendations

First, the board should not buy queue displays for all branches on the vendor's evidence, which Week 7 found weak. Second, the credit union should run a randomized pilot at its 12 busiest branches for three months: six receive an extra teller during Friday and Monday peaks, and, crossing that factor, six receive queue displays, so each branch falls into one of four combinations. This design tests both minutes and perception. Third, branch managers can act now on the service standard by shifting staff breaks away from Friday lunch, a no-cost change.

Registering the Pilot in Advance

Nosek et al. (2018) argued that preregistration, specifying hypotheses and analysis plans before seeing outcome data, distinguishes confirmatory tests from exploratory findings and reduces the risk of reporting chance results as discoveries. The director will register the pilot's hypotheses, primary outcome (mean satisfaction on the four-item scale), secondary outcomes (recorded and perceived wait, promoter share), sample sizes and analysis model with the credit union's analytics committee before the pilot starts, and any additional analyses will be labeled exploratory.

Power for the Pilot

With 12 branches and about 60 surveyed members per branch per month, the pilot will gather roughly 2,100 responses over three months. Because branches, not members, receive the changes, the effective sample size is smaller than the raw count; the director will estimate the design effect from this year's survey and adjust the number of months if needed to detect a difference of 0.3 points.

What the Dissertation Will Add

RES 720 and the dissertation will add multiple regression, so the relationship between waiting and satisfaction can be estimated while holding channel, age, tenure, transaction type and branch constant; multilevel models to treat branches as a level of analysis; and, if the pilot proceeds, analysis of a randomized comparison that can support causal claims. Week 1's variable definitions and Week 2's descriptive groundwork make those analyses possible.

Reflection

At the start of the course, the director planned to report average wait and average satisfaction. She now reports medians for skewed variables, effect sizes and intervals for every test, checks assumptions before trusting numbers and distinguishes what data can show from what they cannot. Those habits shaped every recommendation here.

Conclusion

Integrating descriptive statistics, hypothesis tests, t tests and correlation answered the board's three questions: waits are mostly short but predictably long at peaks, longer and especially longer-feeling waits are linked to lower satisfaction and channel differences remain unexplained. Reported to professional standards and kept within the limits of correlational data, the findings support low-cost changes now and a preregistered randomized pilot before larger investments.

References

Appelbaum, M., Cooper, H., Kline, R. B., Mayo-Wilson, E., Nezu, A. M., & Rao, S. M. (2018). Journal article reporting standards for quantitative research in psychology: The APA Publications and Communications Board task force report. American Psychologist, 73(1), 3-25. https://doi.org/10.1037/amp0000191

Gelman, A., & Stern, H. (2006). The difference between "significant" and "not significant" is not itself statistically significant. The American Statistician, 60(4), 328-331. https://doi.org/10.1198/000313006X152649

Nosek, B. A., Ebersole, C. R., DeHaven, A. C., & Mellor, D. T. (2018). The preregistration revolution. Proceedings of the National Academy of Sciences, 115(11), 2600-2606. https://doi.org/10.1073/pnas.1708274114