Week 5 Conclusion: Hypothesis test (randomization test)

Question 1

Hypothesis Testing (randomization test): when ____, comparing ____ to ____.
1. State hypothesis
Null hypothesis (H0): ____
H0: ____
Alternative hypothesis: ____
Ha: ____

Answer 1

Null hypothesis (H₀): A statement that assumes no relationship exists in the population.
H0: parameter1 = parameter2/parameter1 - parameter2 = 0

Alternative hypothesis (H₁ or Hₐ or HA): A statement that contradicts the null hypothesis, suggesting a relationship does exist.
HA: parameter1 ≠ parameter2/parameter1 - parameter2 ≠ 0
(>/< is one-tailed hypothesis, ≠ is two-tailed)

Question 2

2. Calculate the test statistic
   ____
   Why?
   In hypothesis tests, ____
   In randomization test, ____

Answer 2

2. Calculate the test statistic
   p1-p2 =

Why?
In hypothesis tests, the null distribution is already known based on probability theory, so we can directly compare individual values..
In randomization test, the null distribution is built dynamically by reshuffling the data multiple times

Question 3

3. Randomization Test: Simulate sampling distribution of test statistic assuming null hypothesis is true.
   ____
   → ____

Answer 3

Randomly generate samples assuming the null hypothesis is true.
→ re-randomize all units in two treatment groups (with their responses) without replacement to the 2 treatment groups.

Question 4

4. Assess evidence against null hypothesis
5. Make a conclusion

Answer 4

4. Assess evidence against null hypothesis
5. Make a conclusion