CIs and Hypothesis Tests

Question 1

How can CIs be adjusted for small sample sizes?

Answer 1

By using student’s t distribution

Question 2

What is the t-distribution?

Answer 2

A symmetric probability distribution that depends on a parameter called degrees of freedom

Question 3

What do degrees of freedom represent?

Answer 3

The information content of a sample of information - in simple situations, this is based on sample size

Question 4

How does the visualisation of the t-distribution differ from the Normal distribution?

Answer 4

It has wider tails and is slightly narrower around the mode

Question 5

What are the assumptions when using a t-distribution to calculate CI?

Answer 5

Normal distribution

Observations are independent - the value of any one observation cannot influence the value of another

Question 6

For samples of size greater than what value, is there little difference between t and Normal distribution?

Answer 6

30

Question 7

What are the assumptions when calculating CI for a difference between two samples?

Answer 7

Normal distribution in both groups
Population variability (SD) approximately the same in each groups
Observations are independent
Sample is representative of the population

Question 8

What is the null hypothesis?

Answer 8

A statement to the effect that there is no mechanism of interest or. that the groups to. be. compared are exactly equivalent

Question 9

What is the p value?

Answer 9

The probability that we could have obtained the observed data (or that data were more unusual or extreme) assuming that the Null hypothesis is true

Question 10

Describe the stages in forming a hypothesis (significance) test

Answer 10

Define the appropriate Null hypothesis
Calculate the relevant test statistic
Compare the observed value of the Test Statistic to its reference t-distirbution, assuming the Null hypothesis is true to obtain a p value
Inspect the p-value to decide. whether or not to reject the Null hypothesis

Question 11

What is the alpha or significance level?

Answer 11

The probability that we would reject the Null hypothesis when the Null hypothesis is true

Question 12

A type I error is a false positive. T/F?

Answer 12

True

Question 13

What is power in a study?

Answer 13

Power is the probability of correctly finding a significant result. It is calculated as 1 - beta

Question 14

What letter denotes the likelihood of a type II error (false negative)?

Answer 14

Beta

Question 15

What factors affect the Power of a study?

Answer 15

The true size of the effect being studies
The variability of the data
The number of observations available
Size of sample chosen

Question 16

What are the assumptions for the hypothesis test?

Answer 16

Observations are independent from each other

Observations have been sampled from a Normal distribution

Question 17

What are the assumptions for a two-sample hypothesis test?

Answer 17

Observations are independent from each other
Observations have been sampled from a Normal distribution
Variability of measurement in the two groups is equal in population terms

Question 18

What is a paired t-test?

Answer 18

This is simply a one-sample t-test carried out on the. set of difference

Question 19

What is the additional assumption applied to a paired t test?

Answer 19

That the pairs are positively correlated with each other

Question 20

Why are CIs generally considered superior to hypothesis tests?

Answer 20

The CI method provides additional information about the magnitude of the differences revealed by the data which allows us to assess the clinical relevance of any apparently statistically significant effect or consider the precision of any statements we make about the lack of evidence of an effect