Explain why the t-statistic helps

Q: Explain why the t-statistic helps

This question evaluates understanding of the t-statistic, standardized effect sizes, standard errors, hypothesis testing, and interpretation of statistical evidence within the Statistics & Math domain, and it targets conceptual understanding with practical application implications.

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Question

Suppose you estimate an effect size $\hat{\beta}$ in a regression model or an A/B test and compute a standard error $SE(\hat{\beta})$ .

Explain why the t-statistic

$t = \frac{\hat{\beta}}{SE(\hat{\beta})}$

is often a useful summary of evidence. What does it capture that the raw coefficient or mean difference does not?

Discuss how it connects to p-values and confidence intervals, what assumptions are required, and in what situations relying on the t-statistic can be misleading.

Explain why the t-statistic helps

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Solution

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