Question 1

What does a p-value of 0.05 mean?

Accepted Answer

A p-value of 0.05 means there is a 5% probability of observing a test statistic this extreme (or more extreme) if the null hypothesis is true. It does NOT mean there is a 5% chance the null hypothesis is true. At the conventional α = 0.05 level, this result is right at the border of significance.

Question 2

Is a smaller p-value always better?

Accepted Answer

A smaller p-value provides stronger evidence against the null hypothesis, but it does not measure the size or importance of the effect. A very small p-value can result from a large sample with a trivially small effect. Always consider effect size alongside p-values.

Question 3

When should I use one-tailed vs. two-tailed test?

Accepted Answer

Use a two-tailed test (default) when you want to detect differences in either direction. Use a one-tailed test only when you have a strong a priori reason to test in one specific direction AND finding a difference in the opposite direction would be treated the same as no difference. One-tailed tests are more powerful but riskier.

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Interpretation

One-Tailed vs. Two-Tailed

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