Hypothesis Testing: Significance, Effect Size, and Power
3 important questions on Hypothesis Testing: Significance, Effect Size, and Power
When testing a hypothesis we are trying to collect evidence of whether the null hypothesis is unlikely to be true.
Why do we do this?
- Falsificationism.
- It's easier to prove that something is wrong than to prove that something is right.
- We can never prove the alternative hypothesis directly about the population.
- We can only show the likelihood of the null hypothesis being false.
When we use the z-test for significance testing, there are two decisions that directly affect the critical z value.
Can you name them?
- The level of significance (⍺).
- Whether your alternative hypothesis is directional, non-directional.
- E.g., Directional H1 > 6; non-directional H1 ≠ 6.
- If ⍺ = 0.05 (5%), you search in the z-table for z=0.05 when H1 is directional, but for z=0.025 when it is non-directional.
- Because for non-directional, we have to take into account that the score might be situated above, but also below 6.
Your alternative hypothesis may be directional or non-directional.
When you opt for a directional hypothesis, what criterium must be fulfilled?
- You need to have prior evidence that the hypothesis may be directional.
- I.e., you have prior evidence that H1 may be higher/lower than H0.
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