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I fumbled the analogy part more than I should have.
Start by defining a p-value in plain language as the probability of seeing data as extreme as yours if there were truly no effect. Then use a concrete everyday analogy to illustrate this, and explicitly correct common misinterpretations by contrasting what a p-value is not. Finally, tie it back to the business context, emphasizing that statistical significance does not imply practical importance.
Pro tip: Use an analogy that resonates with the interviewer's domain—like a medical test or a store promotion—to make the concept stick, and always clarify that a p-value is not the probability that the null hypothesis is true, but rather the probability of the data given the null.
State that a p-value is the probability of observing data at least as extreme as what you got, assuming there is no real effect (the null hypothesis is true). Avoid jargon like 'null hypothesis' initially; instead say 'if nothing were going on.'
Choose an everyday scenario, such as flipping a coin to test if it's fair. If you flip 10 times and get 9 heads, the p-value is the probability of getting 9 or more heads if the coin were fair. A low p-value suggests the coin is likely not fair.
Clarify that a p-value is not the probability that the null hypothesis is true, nor does it measure the size or importance of an effect. It only indicates how surprising the data are under the null.
Explain that a small p-value does not mean the effect is large or meaningful. For example, a tiny improvement in conversion rate could be statistically significant with a large sample but not worth implementing.
Tie the explanation to A/B testing at CVS Health: a p-value helps decide if an observed difference in metrics like click-through rate is likely due to chance, but business decisions should also consider effect size, cost, and impact.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Went straight to Wilcoxon and felt pretty confident about it.
Start by clarifying the goal: comparing paired differences in blood pressure before and after a low-sodium diet. Given the skewed distribution with outliers and small sample size (n=12), the Wilcoxon signed-rank test is more appropriate because it does not assume normality. Walk through the assumptions of both tests, explain how you'd check them (e.g., Shapiro-Wilk, histogram, Q-Q plot), and discuss handling ties and zeros in the Wilcoxon test, then recommend an appropriate effect size like r or Cohen's d for paired data.
Pro tip: Mention that with n=12, the central limit theorem doesn't apply, so normality is crucial; also note that the Wilcoxon test assumes symmetric distribution of differences, which you should check. If the distribution is not symmetric, consider a sign test or bootstrapping.
Confirm that the data are paired (same patients before and after) and that we are interested in the median difference in blood pressure. Note the small sample size (n=12) and the presence of skewness and outliers.
Paired t-test assumes differences are normally distributed (or large n). Wilcoxon signed-rank test assumes differences are symmetrically distributed around the median (not necessarily normal) and that observations are independent.
Use a histogram, Q-Q plot, and Shapiro-Wilk test to assess normality of differences. For Wilcoxon, check symmetry via a histogram or by comparing mean and median. With n=12, formal tests have low power, so visual inspection is key.
Given skewness and outliers, choose Wilcoxon signed-rank test. For ties, use average ranks; for zeros, either discard them (reducing n) or use a method that handles zeros (e.g., Pratt's method). Report how you handled them.
For Wilcoxon, report r = Z/√N (or rank-biserial correlation). For t-test, Cohen's d for paired data. Interpret the effect size in context and state the conclusion in plain language.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying that Welch's t-test estimates the difference in means while the Wilcoxon rank-sum test estimates the probability that a random observation from one group exceeds a random observation from the other (or a shift in medians under certain assumptions). Then discuss when each is preferred given the unequal variances, heavy tails, and small sample sizes, and finally explain how to complement the chosen test with confidence intervals (e.g., bootstrap or Hodges-Lehmann) and a robust effect size (e.g., Cliff's delta or Glass's delta).
Pro tip: In practice, with heavy-tailed data and small samples, the Wilcoxon test often has better power and validity, but always report a robust effect size and confidence interval to convey practical significance—especially in healthcare where stakeholders care about magnitude, not just p-values.
Explain that Welch's t-test estimates the difference in population means (with a correction for unequal variances), while the Wilcoxon rank-sum test estimates the probability that a randomly selected value from one group is greater than a randomly selected value from the other (or a shift in location under symmetric distributions).
Discuss that Welch's t-test assumes approximately normal sampling distributions or large samples; with n=18 and 25 and heavy tails, the central limit theorem may not hold, making the t-test unreliable. The Wilcoxon test does not assume normality but assumes similar distribution shapes if interpreting as a median shift; it is more robust to outliers and skewness.
Prefer Wilcoxon when distributions are heavy-tailed, variances are unequal, and sample sizes are small, as it is more robust and often more powerful. Use Welch's t-test if the data are not severely non-normal and the mean difference is the parameter of interest, but consider transformations or bootstrap alternatives.
For Welch's t-test, report the confidence interval for the mean difference. For Wilcoxon, report a confidence interval for the Hodges-Lehmann estimate of the median difference or use bootstrap methods to obtain a confidence interval for the probability of superiority (or Cliff's delta).
Use Cliff's delta (or Vargha-Delaney A) for the Wilcoxon test, which quantifies the probability of superiority and is robust to non-normality. For Welch's t-test, consider Glass's delta or Hedges' g, but note their sensitivity to non-normality. Always interpret effect size in the context of hospital length of stay to assess practical significance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.