Week 5 Conclusion: Hypothesis Testing → Assessing Relationships and Associations

Question 1

Statistical inference on Relationships and Associations
Hypothesis Testing
1. Set Hypothesis (& set α)
Null hypothesis (H₀): ____
H0: ____
Alternative hypothesis (H₁ or Hₐ or HA): ____
HA: ____

Answer 1

Null hypothesis (H₀): A statement that assumes no relationship exists in the population.
H0: parameter = # (H0: p = ⅙)
Bloom’s ability to detect the station with the LC urine samples is no different than guessing.
𝑯𝟎: 𝒑 = 𝟏/𝟔

Alternative hypothesis (H₁ or Hₐ or HA): A statement that contradicts the null hypothesis, suggesting a relationship does exist.
HA: parameter >/</≠ #
(>/< is one-tailed hypothesis, ≠ is two-tailed)
Bloom does better than just guessing the station with the LC urine sample.
𝑯𝑨: 𝒑 > 𝟏/𝟔

Question 2

2. ____
3. ____

Answer 2

2. Calculate test statistic

3. Simulate sampling distribution of test statistic assuming null hypothesis is true
Randomly generate samples (SRS) under the assumption that the null hypothesis is true.

Randomly generate samples under the assumption that Bloom’s ability is no different than guessing (i.e. the chance Bloom gets it right on each run p=⅙)

Question 3

4. ____
   p-value = ____
   → ____
   A small p-value = ____

We can end up with a small p-value in one of two ways:
1. H0 is true: ____
2. H0 is not true.
The ____ the p-value, the more we tend to side with #2.

Answer 3

p-value = the probability of observing a statistic that is as extreme as (or more extreme than) the observed sample statistic under the assumption that the null hypothesis is true.
→ the proportion of values in the estimated sampling distribution that are as extreme (or more extreme) than the test statistic calculated from the sample data.

A small p-value = there is a small probability of observing a statistic that is as extreme as (or more extreme than) the observed sample statistic under the assumption that the null hypothesis is true.
We can end up with a small p-value in one of two ways:
1. H0 is true: we select an unusual sample (i.e.,one with an extreme value of the test statistic) by chance.
2. H0 is not true.
The smaller the p-value, the more we tend to side with #2 (i.e., the more “evidence” we have against H0).

Question 4

5. Make a conclusion
   Reject H0 if ____
   Significance level (𝜶) = ____
   - ____
   - ____
   Note: ____

Answer 4

Reject H0 if p-value ≤ α

Significance level (𝜶) = the cut-off for how unusual/extreme the test statistic has to be under the assumption that H0 is true to reject that assumption that H0 is true.
Set in advance of obtaining p-value.
α can be chosen to be any number, but typically α = 0.05 is used.

NOTE: better to report the p-value and comment on the strength of evidence against H0.