Hypothesis Testing

Question 1

Who is included in a population?

Answer 1

Current members and future members.

Question 2

Why is a sample of a population used?

Answer 2

Because it is not feasible to collect data on the entire population, a sample is used to tell us about the theoretical population.

Question 3

What is needed before collecting data from a sample?

Answer 3

The theoretical population must be defined in order to understand how generalisable the inferences from the sample are. The sample must be representative of the population.

Question 4

What are the key considerations for a random sample?

Answer 4

1. Each individual from the population must have an equal chance of being included.
2. The inclusion of one individual must not affect the inclusion of another.

Question 5

What is stratified random sampling?

Answer 5

A method in which populations are broken down into smaller divisions and samples taken from these in order to ensure the sample is representative of the entire population.

Question 6

Why is the normal distribution important in medical research?

Answer 6

1. To understand the central tendency and variability of the data to allow for summarising and interpretation of large datasets.
2. For use of parametric statistical tests such as t-tests and ANOVA.
3. For predictive modelling and risk assessment.
4. For quality control in order to set limits and identify outliers.

Question 7

What is the standard error?

Answer 7

A measure of the variability between sample means.
It quantifies the difference between the mean measured from a sample and the mean measured from the theoretical population.

Question 8

What is the standard deviation?

Answer 8

A measure of how far the mean is from other points in the dataset.
It is the variability in the population/sample mean.

Question 9

What does the null hypothesis state?

Answer 9

That there is no difference between populations.

Question 10

What does the alternate hypothesis state?

Answer 10

That there is a difference between populations.

Question 11

What do you have to assume about a sample in order to test a hypothesis?

Answer 11

1. The sample is representative.
2. The sample is independent.
3. The sample has homogenous variance.
4. The sample is normally distributed.

Question 12

What can you assume if the sample size is > 30?

Answer 12

That the distribution of the sample mean is approximately normal (no matter the distribution of the data).

Question 13

When should you use the normal distribution?

Answer 13

If the sample size is > 30 and assumptions are met.

Question 14

When should you use the t-distribution?

Answer 14

If the sample size < 30 and assumptions are met.

Question 15

What should you do if assumptions are not met?

Answer 15

First, try to transform the data.
If the transformed data still does not meet the assumptions, use a non-parametric test.

Question 16

What is the limiting factor for categorical data?

Answer 16

The accuracy of the instrument used to measure the value.

Question 17

What is categorical data known as if it can only take 2 distinct values?

Answer 17

Dichotomous or binary.

Question 18

What is a type I error?

Answer 18

A false positive - the null hypothesis is rejected when it is true.

e.g., you say there is a difference between groups when there isn’t one

Question 19

What is a type II error?

Answer 19

A false negative - the null hypothesis is not rejected when it is false.

e.g., you say there isn’t a difference between groups when there is one.

Question 20

What is the power of a test?

Answer 20

The probability of not rejecting the null hypothesis when it is false.

e.g., the probability of not making a type II error.

Question 21

What is the p-value?

Answer 21

A measure of the strength of the evidence against the null hypothesis.
A small p-value indicates that the null hypothesis is unlikely to be true.

Question 22

What is a confidence interval?

Answer 22

The range of values estimated from a sample within which the true population value is likely to be found.

Question 23

What does a 95% confidence interval mean?

Answer 23

That if a random sample was drawn 100 times, 95 out of the 100 times the sample would contain the true population parameter.

Question 24

How do you calculate the 95% CI?

Answer 24

95% CI for the mean is (x - 1.96 x SE) to (x + 1.96 x SE)

Question 25

What test should you use to compare one group to a known value?

Answer 25

Parametric = One sample t-test.

Non-parametric = sign test.

Question 26

What test should you use to compare 2 paired groups?

Answer 26

Parametric = paired t-test.

Non-parametric = Wilcoxon signed-rank test.

Question 27

What test should you use to compare 2 independent groups?

Answer 27

Parametric = unpaired t-test.

Non-parametric = Wilcoxon rank sum test.