Q: What does Cohen's d tell me?

Cohen's d = |x̄ − μ₀| / s measures the standardized effect size — how large the difference is relative to the variability. Conventions: d = 0.2 (small), d = 0.5 (medium), d = 0.8 (large). With a large sample, even a trivially small difference can be statistically significant (small p-value), so Cohen's d gives the practical importance.

Q: How are hypothesis tests used in CAE and quality control?

Common applications in CAE and quality engineering include: verifying statistical significance of differences between material test batches, comparing simulation results against experimental measurements, evaluating before/after performance of design improvements, and parameter sensitivity analysis. The two-sample t-test is particularly useful for comparing two process conditions or new vs. old designs.

Question 1

When should I use a z-test versus a t-test?

Accepted Answer

Use a z-test when the population standard deviation σ is known. Use a t-test when σ is unknown and estimated from the sample (standard deviation s). In practice, σ is rarely known, so t-tests are far more common. For large samples (n ≥ 30), the t-distribution approximates the normal distribution, so both tests give nearly identical results.

Question 2

What does the p-value mean?

Accepted Answer

The p-value is the probability of observing a test statistic as extreme as — or more extreme than — the one computed, assuming the null hypothesis H₀ is true. If p < α (significance level), we reject H₀ and conclude there is a statistically significant effect. Note: p-value measures evidence against H₀, not the size of the effect.

Question 3

What does Cohen's d tell me?

Accepted Answer

Cohen's d = |x̄ − μ₀| / s measures the standardized effect size — how large the difference is relative to the variability. Conventions: d = 0.2 (small), d = 0.5 (medium), d = 0.8 (large). With a large sample, even a trivially small difference can be statistically significant (small p-value), so Cohen's d gives the practical importance.

Question 4

How are hypothesis tests used in CAE and quality control?

Accepted Answer

Common applications in CAE and quality engineering include: verifying statistical significance of differences between material test batches, comparing simulation results against experimental measurements, evaluating before/after performance of design improvements, and parameter sensitivity analysis. The two-sample t-test is particularly useful for comparing two process conditions or new vs. old designs.

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