Hypothesis Testing

1. What is hypothesis testing?

A statistical method used to determine whether an observed difference could be due to chance.

2. What is the null hypothesis (H₀)?

There is no real difference between the groups.

3. What is the alternative hypothesis (Hₐ)?

There is a real difference between the groups.

4. What is an effect size?

The magnitude or size of the difference between groups.

5. What is a Type I error?

Rejecting a true null hypothesis. Concluding that a difference exists when there is actually no difference (false positive).

6. What is a Type II error?

Failing to reject a false null hypothesis. Missing a real difference (false negative).

7. What is alpha (α)?

The probability of making a Type I error. Usually set at 0.05.

8. What is beta (β)?

The probability of making a Type II error.

9. What is statistical power?

The probability of detecting a real difference when one actually exists.

10. What is the relationship between power and beta?

Power = 1 − β.

What is a non-parametric test?

A statistical test that does not require normally distributed data.

9. Which test compares the means of two independent groups with approximately normal data?

10. Which test compares two measurements from the same individuals with normally distributed differences?

11. Which test compares two independent groups with non-normally distributed data?

12. Which test compares paired measurements when the differences are not normally distributed?

Independent samples t-test.

Paired t-test.

Wilcoxon rank-sum test (Mann–Whitney U test).

Wilcoxon signed-rank test.

What is the purpose of a QQ plot?

To assess whether data approximately follow a normal distribution

QRS times are compared between patients with and without IVT. The groups contain different patients, and the data are normally distributed. Which test should be used?

Independent samples t-test.

16. Cholesterol is measured at baseline and after six months in the same patients. The differences are normally distributed. Which test should be used?

Paired t-test.

17. Cholesterol is measured before and after treatment in the same patients. The differences are not normally distributed. Which test should be used?

Wilcoxon signed-rank test.

18. Researchers want to compare cholesterol changes between males and females. The change is calculated for each patient, and the differences are normally distributed. Which test should be used?

Independent samples t-test.

A study reports p = 0.003 with α = 0.05. What is the conclusion?

Reject H₀. The result is statistically significant.

A study reports a mean difference of 5 with a 95% CI of [-2, 12]. Is the result statistically significant?

A study reports p = 0.08. Does this prove that there is no difference between the groups?

No. Zero is included in the confidence interval.

No. There is insufficient evidence to reject H₀.

What factors are needed for sample size calculation?

Primary outcome, statistical test, expected means and SDs or proportions, alpha and desired power.

23. What happens to sample size when

the expected treatment difference decreases?

standard deviation increases?

power increases from 80% to 90%?

alpha decreases from 0.05 to 0.01?

Increases

A study has 80% power. What is beta?

β = 0.20 (20%).

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