Hypothesis Tests of Proportions

Question 1

Define null hypothesis and alternative hypothesis:

Answer 1

Null hypothesis - is a statement of no effect or no difference
Alternative hypothesis - just contradicts the null hypothesis
In a hypothesis test, only if the evidence against the null hypothesis in the sample is strong enough (basis of P value) do we reject the null hypothesis and accept the alternative hypothesis

Question 2

Define P value:

Answer 2

P Value - the probability of observing a test statistic as, or more, extreme than that observed in your sample, in hypothetical repetitions of the study assuming that the null hypothesis is true
The P-value is compared with the significance level (usually 0.05)

Question 3

What are the 2 types of statistical error ?

Answer 3

Type I error occurs if the null hypothesis is rejected when it is true. The probability of this = the significance level usually 5%
Type II error occurs if the null hypothesis is not rejected when it is false

Question 4

Recognise the steps involved in conducting an hypothesis test:

Answer 4

State the hypotheses - null + alternative
Set the significance level - usually 0.05
Select appropriate statistical test - Chi-square test for categorical data
Calculate test statistic
Calculate P value
Accept or reject hypothesis

Question 5

When would you accept or reject the null hypothesis ?

Answer 5

If the p-value is less than or equal to the significance level (α), you reject null hypothesis
If the p-value is greater than the significance level (α), you fail to reject H₀.

Question 6

Understand the absolute risk reduction and relative risk:

Answer 6

The absolute risk reduction is the difference in risk between the two treatment groups
The relative risk (RR) or risk ratio is the risk in the treatment divided by the placebo group

Question 7

What is a Chi squared test used for ?

Answer 7

A Chi-squared test for a 2x2 contingency table is used to compare proportions between two independent groups.
It is commonly used in randomized controlled trials comparing an outcome with two categories

Question 8

Define the odds ratio and what its value indicates

Answer 8

the odds in the treatment group divided by the placebo group

An OR above 1 indicates that the risk is increased in the treatment group compared with the placebo group and a OR below 1 indicates that the risk is decreased in the treatment group