DDBA 8307B Week 6 Post Hoc Comparison Note Example

Which Pair Carries the Difference: A Post Hoc Note on Average Repair Costs at an Insurer's Four Network Body Shops, Naming the Pairs That Differ, the Pairs That Cannot Be Told Apart and Why Neither Finding Says What Causes the Gap

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Walden University

DDBA 8307B: Quantitative Business Data Analysis Using SPSS

Instructor Name

Month Day, Year

Which Pair Carries the Difference: A Post Hoc Note on Average Repair Costs at an Insurer's Four Network Body Shops, Naming the Pairs That Differ, the Pairs That Cannot Be Told Apart and Why Neither Finding Says What Causes the Gap

From "Any Difference" to "Which Difference"

A composite regional auto insurer in Missouri sends collision claims in the Kansas City area to four network body shops, labeled here A, B, C and D. Its claims director asked whether average repair costs differ among them. A one-way analysis of variance on 416 claims closed in the first half of 2026 answered the first question: they do, F(3, 412) = 15.72, p < .001, with eta squared of .10, meaning shop membership accounts for about a tenth of the variation in repair cost. But the analysis of variance says only that at least one shop differs from at least one other. It does not say which. This note reports the follow-up comparisons that answer that, and what they cannot say.

The Shops

Table 1

Repair Costs by Shop

Closed collision claims, January to June 2026; total-loss claims excluded.

The Pairwise Comparisons

With four shops there are six pairs. Comparing each pair with a separate t-test would raise the chance of finding a difference by luck. Tukey's honestly significant difference procedure, run in SPSS as a post hoc test, adjusts for the number of comparisons. Field (2018) recommends Tukey's procedure when group sizes are similar and variances roughly equal, as they are here; Levene's test was not significant.

Table 2

Tukey Comparisons of Mean Repair Cost

Differences are row shop minus column shop; adjusted p values from Tukey's procedure.

What the Comparisons Show

One shop carries the difference. Shop C's average repair cost is $470 to $710 higher than each of the other three, and each of those differences is clear after adjustment. Among A, B and D, no pair can be told apart: their averages differ by $70 to $240, and the adjusted p values are well above .05. "Cannot be told apart" is not the same as "the same." The data are consistent with small differences among A, B and D that this sample is too small to detect. Lakens (2013) recommends reporting effect sizes alongside tests for exactly this reason; the differences among A, B and D are small relative to the spread in costs within each shop.

Why Neither Finding Says What Causes the Gap

It would be easy to read the result as "Shop C charges more." The data do not show that. Claims were not assigned to shops at random. The insurer's dispatchers send claims to the shop nearest the customer or the one with an opening, and Shop C is the only one of the four certified to repair aluminum-body trucks and several luxury brands. If Shop C receives more expensive vehicles and more complex damage, its higher average could reflect what it repairs rather than what it charges. The analysis compares averages; it does not hold the vehicle or the damage constant.

Why the Overall Test Came First

Running six t-tests without first checking the overall analysis of variance would have risked reporting a chance difference as real. With six comparisons each at the .05 level, the chance of at least one false difference is well above five percent. The overall test establishes that some difference exists; Tukey's procedure then locates it while keeping the overall error rate controlled. The order matters as much as the procedures themselves.

What Would Answer the Causal Question

Two steps would help. First, the claims data include vehicle make, model year and an estimate of damage severity at first notice. An analysis of covariance, adjusting for those, would show whether Shop C's costs remain higher for comparable repairs. Second, a sample of claims could be reviewed by an independent appraiser, comparing each shop's estimate with the appraiser's for the same damage. Appelbaum et al. (2018) ask that reports separate what a design can establish from what it cannot; this note does that by naming Shop C's difference and declining to say why it exists.

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

Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). SAGE Publications.

Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, Article 863. https://doi.org/10.3389/fpsyg.2013.00863