DDBA 8307B Week 4 t-Test Assumption Check Example

Auditing a Procedure's Promises Before Reading Its Result: An Assumption Check for Comparing Day and Night Shift Hourly Output at a Plastics Molding Plant, and What the Analysis Does When One Assumption Fails

Student Name

Walden University

DDBA 8307B: Quantitative Business Data Analysis Using SPSS

Instructor Name

Month Day, Year

Auditing a Procedure's Promises Before Reading Its Result: An Assumption Check for Comparing Day and Night Shift Hourly Output at a Plastics Molding Plant, and What the Analysis Does When One Assumption Fails

The Comparison

A composite injection molding plant in Grand Rapids, Michigan, makes plastic housings for small appliances on 12 presses running two 12-hour shifts. The operations manager believes the night shift produces less per hour and wants evidence that the gap is real before changing night staffing. The data are average parts per press-hour for each shift over the last quarter: 40 day shifts and 38 night shifts, after two shifts with plant-wide power outages were removed. The planned procedure is an independent-samples t-test comparing mean output between day and night shifts. Before reading its result, this check tests each condition the t-test assumes and states what the analysis will do if one fails.

Assumption 1: Independent Observations

The t-test treats every shift as unconnected to every other. Here each observation is a shift, but consecutive shifts share presses and molds, and a mold that runs poorly at the end of one shift may still run poorly at the start of the next. Field (2018) emphasizes that violations of independence are the most serious, because they distort standard errors in ways no correction for shape can fix. I checked whether output in one shift predicted output in the next by correlating each shift's output with the following shift's: the correlation was .12, small enough that treating shifts as independent is reasonable, though not perfect. The write-up will say so.

Assumption 2: Normal Distribution Within Each Group

Day-shift output looks roughly normal. Night-shift output does not: the Shapiro-Wilk test rejects normality, and the distribution is skewed to the left. The cause is visible in the lowest values. Three night shifts had output between 302 and 331, and the maintenance log shows a mold change on each of those nights, which stops a press for several hours. Mold changes are scheduled at night to avoid disrupting daytime deliveries. With 38 observations, the t-test is fairly robust to moderate skew, but these three shifts reflect a scheduling choice rather than night crews' performance.

Table 1

Normality and Spread by Shift

Computed in SPSS Explore with normality plots.

Assumption 3: Equal Variances

Levene's test for equality of variances gives F(1, 76) = 6.84, p = .011. The night shift's output varies much more than the day shift's, again partly because of the mold-change shifts. Delacre et al. (2017) argued that Welch's version of the test, built for unequal spreads, should be the default, because it loses little when spreads are equal and protects the result when they differ. The analysis will use Welch's test and report it.

What the Analysis Will Do

Three decisions follow. First, the main comparison will use Welch's t-test. On the full data, the day shift averaged 14.5 more parts per press-hour, Welch's t(61.2) = 2.58, p = .012, 95 percent confidence interval from 3.2 to 25.8. Second, a sensitivity analysis will repeat the test without the three mold-change shifts. Without them, the difference shrinks to 9.2 parts per press-hour, t(66.4) = 1.94, p = .056, with an interval from −0.3 to 18.7. Third, the write-up will report both and explain the difference.

Why Not Simply Transform the Data

A common response to skew is to transform the outcome, for example by taking logarithms, until it looks normal. That was considered and rejected. A log of parts per hour is harder for the operations manager to interpret, and the skew here comes from three identifiable shifts rather than from the general shape of the data. Addressing the cause, by examining those shifts directly, keeps the result in units the manager uses.

What the Check Changes About the Conclusion

The check changes what the manager should conclude. With all shifts, the night shift appears to produce less. Without the mold-change nights, the difference is smaller and less certain, and much of the gap reflects when the plant chooses to change molds. Tabachnick and Fidell (2019) note that outliers with a known cause should be reported and examined rather than silently removed; here the cause is itself a finding. Before changing night staffing, the manager might ask whether moving some mold changes to weekends would close most of the gap.

References

Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should by default use Welch's t-test instead of Student's t-test. International Review of Social Psychology, 30(1), 92-101. https://doi.org/10.5334/irsp.82

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

Tabachnick, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). Pearson.