Question 1

What is Welch's t-test?

Accepted Answer

Welch's t-test compares the means of two independent groups without assuming equal variances. Unlike Student's t-test, it adjusts the degrees of freedom using the Welch-Satterthwaite equation, making it robust to unequal sample sizes and variances. Most statisticians recommend always using Welch's test as the default, since it performs well even when variances are equal.

Question 2

What is Cohen's d?

Accepted Answer

Cohen's d is a standardized measure of the difference between two group means, expressed in pooled standard deviation units: d = (M₁ − M₂) / SD_pooled. Cohen's benchmarks: d = 0.2 (small), d = 0.5 (medium), d = 0.8 (large). Always report d with a confidence interval — the point estimate alone is insufficient.

Question 3

What is Pearson correlation?

Accepted Answer

Pearson correlation coefficient (r) measures the linear association between two continuous variables. Values range from −1 (perfect negative) to +1 (perfect positive). $	ext{R}^{2}$ gives the proportion of variance in Y explained by X. Correlation does not imply causation, and r is sensitive to outliers and restricted range.

Question 4

Why use Fisher z for correlation CI?

Accepted Answer

The sampling distribution of r is skewed (especially when |r| is large), so computing a CI directly on r gives inaccurate coverage. The Fisher z transformation z = ½ ln((1+r)/(1−r)) has an approximately normal distribution, enabling accurate CI computation. The CI is then back-transformed to the r scale.

Question 5

Should I use raw data or summary statistics?

Accepted Answer

Use raw data whenever possible — it allows the tool to verify assumptions and compute exact statistics. Summary statistics (n, mean, SD) are useful when you only have published results from another study, but you lose the ability to check for outliers or non-normality.

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