Lecture 1 - Hypothesis testing

Question 1

What is a Q-Q plot?

Answer 1

A quantile-quantile plot, i.e. a probability plot.
It is a graph that compares two probability distributions by plotting their quantiles against each other.

Question 2

You are tesing whether hormone levels differ between boys and girls. Describe the null and alternative hypothesis.

Answer 2

• Null: there is no difference in hormone levels between boys and girls.
• Alternative: there is a difference in hormone levels between boys and girls.

Question 3

Which two values are important to take into consideration when determining whether to reject H0 and accept Ha or to accept H0 and reject Ha?

Answer 3

• p-value: the probability of finding the observed results when the null hypothesis is true.
• significance level: the probability of rejecting the null hypothesis when the null hypothesis is actually true.

Question 4

How are the p-value and significance level used to determine whether to accept or reject H0?

Answer 4

• if p-value is higher than the signifcance level (e.g. p-value of 0.1 compared to significance level of 0.05), accept H0.
• if p-value is lower than the significance level (e.g. p-value of 0.001 compared to significance level of 0.05), reject H0.

Question 5

What is a type I and type II error?

Answer 5

• Type I error: mistakenly rejecting H0 while it is actually true.
• Type II error: mistakenly accepting H0 while it is actually false.

Question 6

Complete the sentences.

• The probability of a type I error is equal to …
• The probability of a type II error is denoted as …

Answer 6

• The probability of a type I error is equal to significance level α.
• The probability of a type II error is denoted as β.

Question 6

Independent sample t-test
What is it used for?

Answer 6

Used for comparing the means of two independent population means.

Question 6

Independent sample t-test
What assumptions need to be met?

Answer 6

• Outcome in both groups is normally distributed.
• Variances (SD^2) of both groups are equal

Question 7

Independent sample t-test
* What solutions is there if the outcomes in both groups are not normally distributed?
* How can equal variances be assumed?

Answer 7

• Either transform the outcome or use a non-parametric test (Mann-Whitney test).
• Levene’s test can be used. If the p-value of Levene’s test is ≥0.05, equal variances can be assumed.

Question 8

Paired sample t-test
What is it used for?

Answer 8

Used for comparing the means of two times measured, paired variables (e.g. baseline and follow-up measurement).

Question 9

Paired sample t-test
What assumptions need to be met?

Answer 9

• The mean difference between the two measurements are normally distributed.
• Variances of both groups are equal

Question 10

Paired sample t-test
What solution is there if the mean difference between two measurements are not normally distributed?

Answer 10

Transform the outcome or use a non-parametric test (Wilcoxon signed rank test).

Question 11

If α decreases, β will increase and vice versa. Ideally, you want both α and β to be as small as possible. How can you achieve the latter?

Answer 11

By increasing the sample size n.

Question 12

What is needed to determine the sample size n?

Answer 12

• The primary outcome measure
• The statistical test: the expected outcomes (means, SDs), significance level (α), and the desired power (1-β) of the study.

Standard choices: α = 0.05, 1-β = 0.8 or 0.9