Welch’s Two-Sample t-Test: Assumptions, Inference, and Effect Size

All flashcards

What are independent samples?

Samples from two distinct groups whose observations are not paired with or dependent on one another.

What is the small-sample distribution condition?

For small samples, the population distributions should be approximately normal; strong outliers can also be problematic.

What does the standard error of a difference represent?

It estimates how much the difference between sample means typically varies from sample to sample.

Why does variability matter in a two-mean comparison?

A mean difference may arise by chance when individual observations vary substantially, so the difference must be judged relative to its standard error.

Why must Group 1 and Group 2 be labeled consistently?

The order in $\bar{x}_1-\bar{x}_2$ determines the sign of the difference and the direction of a one-sided test.

Quiz questions

1. How does Welch’s two-sample t-test handle the sample variances in its standard-error calculation?Answer: It uses both sample variances separately in the calculation.
2. Which statement about Welch-Satterthwaite degrees of freedom is correct?Answer: The estimate can be fractional and is often computed with software.
3. If Group 1 is hypothesized to have a larger population mean than Group 2, which alternative hypothesis fits?Answer: $H_a: \mu_1-\mu_2>0$
4. When a test gives $p>\alpha$, what is the appropriate conclusion?Answer: Fail to reject the null; the evidence is insufficient at the chosen level.
5. What does Cohen’s $d$ express?Answer: The mean difference in pooled-standard-deviation units.