Topic 9: Hypothesis Testing

Question 1

Why do we need Hypothesis Testing?

Answer 1

Hypothesis Testing is used to weigh up the given evidence (data) against the given hypothesis to make an evidence-based decisions/conclusions.

Question 2

Identify main steps to conduct hypothesis testing

Answer 2

• Set up research question: H: Hypothesis: H0 vs H1
• Weight up evidence:
  + A: Assumptions
  + T: Test statistics
  + P: p-value
• Explain conclusion: C: Conclusion

Question 3

Describe how hypotheses can be determined

Answer 3

• Null hypothesis (H0): a given hypothesis, assuming that the differences between OV and EV are due to chance alone
• Alternative hypothesis (H1): assumes that the differences between OV and EV are NOT due to chance alone
  + 2 sided: not equal to
  + 1 sided: > or <

Question 4

Explain why assumptions are important

Answer 4

Assumptions always exist, so without stating and justifying them, the data can be non-transpoarent and invalid.

Question 5

Identify and explain test statistics

Answer 5

Test statistic is the difference between OV and EV acquired from the null hypothesis.

TS = OV - EV / SD

Question 6

What is p-value and how can it be intepreted?

Answer 6

p-value is chance of observing the TS (or something more extreme) given that the null hypothesis is true.
This is a way to weigh up whether the sample data is consistent with H0.

• p-value is not the chance that H0 can be true.
• A large p-value doesn’t mean H0 is true; it can only be said that data is consistent with H0 or we retain H0. If p-value is small, we can conclude there is evidence against H0 and we reject H0.
• The use of significance level equal to 0.05 is not mandatory.

Question 7

In the Hypothesis Testing framework, what does the ‘box’ represent?

Answer 7

The null hypothesis

Question 8

Is this statement true or false?

“We say the null hypothesis is true if and only if the difference between the expected and observed value is too big.”

Answer 8

False
We cannot say for sure whether the null hypothesis is true or false. If the difference between the EV and OV is too big, we can only say there is evidence against the null hypothesis.