Topic 9 - Hypothesis Testing

Question 1

L.O.

Answer 1

LO7 [capstone] Given real multivariate data and a problem, formulate an appropriate hypothesis and perform a range of hypothesis tests.
LO8 Interpret the p-value, conscious of the pitfalls associated with testing.

Question 2

Proportion Tests

Answer 2

Used to determine if the percentage of a certain outcome in a sample differs significantly from an expected proportion.
- Type of hypthesis test

Question 3

HATPC framework

Answer 3

H: Hypothesese
A: Assumptions
T: Test statistic
P: P-Value
C: Conclusion

Question 4

H: Null and Alternate Hypotheses

Answer 4

H0:
Assumes that the differnce between the OV and the EV is due to chance alone
- Describes the defult scenario, nothing new occuring
Contains: =

H1:
Assumes that the differnce between the OV and the EV is NOT due to chance alone
- Describes what we think is happening
Contains: ≠ < >

Question 5

A: Assumptions

Answer 5

If assumptions not stated, the conclusions given by the Hypothesis Test is NOT transparent
- If assumptions are not justified, conclusion may be invalid
- The assumptions are statistically driven and not just assumed by us

Question 6

T: Test Statistic

Answer 6

A standardised measure of how far away of what we observe is from what we expected.

Test Stat =
(OV - EV) / SE

Question 7

P: P-value

Answer 7

• A way of weighing up whether a sample is consistant with H0.

P-value = Probability of observing the test statistic if H0 is true.

Question 8

C: Conclusion

Answer 8

Interpret the p-value to accept/ reject the H0 and H1.

P> 0.05 = retain H0 (greater than)
P< 0.05 = reject H0 (less than)

Question 9

Meaning of the test statistic

Answer 9

Shows the number of standard errors away from the EV.

eg. (26 - 23.2) / 2.2

= 1.3
The OV is 1.3 SE away from EV.

This can then be worked into a P-value

Question 10

Finding P-value from test statistic when Test stat = 1.3

Answer 10

P value is the chance of observing 1.3 or more extreme under the H0.

Using Pnorm in R:
P(test stat) ≈ 0.097

Question 11

Size of the P-value

Answer 11

The significance of the P-value is determined by the predefined threshold α (by convention 0.05)

If the P-value is 0.097, then P> 0.05,
The H0 is retained

Question 12

C: Conclusion

Answer 12

Statistical conclusion:

Since a P> 0.05, we must retain the H0.

If P< 0.05, we must reject H0.

Question 13

Effect of H1 on the P-value

Answer 13

One sided H1:
- Specifies the direction of H1.
- eg. p>0.8

Two sided H1:
- Does NOT specify the direction
- eg. p≠0.8
- In this case, we must double the P value to account for both sides.