Lecture 24 - Chance 2

Question 1

P-value

Answer 1

The probability of obtaining a study estimate (or one further from the null) when there is no association, purely due sampling error (chance)

Question 2

Null hypothesis H0

Answer 2

Really is no association in the population. Parameter equals null value. (RR,OR = 1) and (RD = 0)

Question 3

The alternative hypothesis (HA)

Answer 3

Really is an association in the population
- Parameter does not equal null value

Question 4

e.g OR = 2.3

Answer 4

Statement: If really unlikely, estimate unlikely to be due to sampling error and can reject H0
- the study association unlikely to be due to chance

Question 5

What is Type-I error

Answer 5

Incorrectly rejecting the null hypothesis when it is true. This error occurs when the p-value is less than 0.05, but there is actually no association in reality.

Question 6

p < 0.05

Answer 6

• Reject H0
• Accept HA
• Association is statistically significant

Question 7

p > 0.05

Answer 7

• Fail to reject H0 (accepting)
• Reject HA
• Association is not statistically significant

Question 8

e.g. OR = 2.1, p=0.01

Answer 8

The probability of a OR of 2.1 or further from the null, when the null hypothesis is true, is 0.01. Since p-value is less than 0.05 the association is statistically significant. We reject the null hypothesis and accept the alternative hypothesis. Chance is an unlikely explanation of the study finding

Question 9

Type-II errors

Answer 9

Incorrectly fail to reject the full hypothesis H0, when it should be rejected.
- Typically due to a small sample size.
- Bigger sample size = smaller p value
- Smaller sample size = bigger p value

Question 10

Relation of p-value with C.I

Answer 10

You can see whether a p-value is greater or less than 0.05 with a 95% C.I

Question 11

How to find out if 95% C.I includes null value

Answer 11

• Yes, it includes null value
• p > 0.05
• Not statically significant

Question 12

If 95% doesn’t include the null value

Answer 12

• No
• p < 0.05
• statistically significant

Question 13

interpreting OR = 2.1 (95% C.I 1.2 - 3.8)

Answer 13

We are 95% C.I that the true value of the RR lies between 1.2 and 3.8. This is statically significant association at the 0.05 level as the 95% C.I does not include the null value of 1. Chance is unlikely explanation of the study finding

Question 14

Why are p-value are problematic

Answer 14

• Arbitrary threshold
• Only about H0
• Nothing about importance

Question 15

Arbitrary threshold

Answer 15

• Statistical significance threshold is arbitrary and artificial. Refers to a cutoff point that is chosen based on convention rather than inherent scientific reasoning.

Question 16

Only about H0

Answer 16

• Just give evidence about consistency with the null hypothesis
• Don’t say anything about precision

Question 17

Nothing about importance

Answer 17

Statistical significance is not clinical significance
- Don’t say anything about whether the results are valid, useful or correct
- Absence of statically significant association is not evidence of absence of a real association