01 / 06 · Welch t-test
Teaching example. Synthetic data.
Does a new formulation make a stronger material?
Compare the strength of standard and new material formulations. We care about both the evidence for a difference and its magnitude.
16 specimens · 2 formulations
- Mean difference: second group minus first
- 5
- 95% confidence interval
- 2.746 … 7.254
- Two-sided p
- 0.000405
Inspect the original observations
| Observation | Standard formulation | New formulation |
|---|---|---|
| 1 | 8 | 11 |
| 2 | 10 | 16 |
| 3 | 9 | 13 |
| 4 | 11 | 18 |
| 5 | 7 | 12 |
| 6 | 12 | 15 |
| 7 | 10 | 17 |
| 8 | 9 | 14 |
Calculated by the Linza engine from this example’s data. Opening it in the editor runs a fresh calculation.
Why this method
Welch compares means of two independent groups without requiring equal variances. A paired test is inappropriate: specimens from different formulations have no matched partners. With eight specimens per group, check outliers and whether distributional assumptions are reasonable.
Explore the theory: Comparing two groups →Work through it in Linza
Open the example. In Data, check the two columns with eight separate specimens each. In Analyses, compare the mean difference and its interval. Points on the chart are specimens; vertical intervals describe each group mean. These are different from the difference interval below the chart.
Open a copy and recalculateTry changing one condition
In a copy, subtract 5 MPa from every value of the new formulation. What happens to the mean difference and the within-group spread?
Show the explanation
The means become equal and their difference becomes zero. The spread within the new formulation stays the same because every point moved by the same amount. A zero observed effect does not establish equality in the population.
Data and reproducibility
Teaching studies with synthetic data. The scenarios reflect practical questions, but do not report real experimental findings.