Statistics

Question 1

What assumptions are required for parametric tests to be valid?

Answer 1

Observations are independent.
Observations are drawn from a normally distributed population.
Different groups must have equal variance.
Data must be at an interval scale at least.

Question 2

What are the two most common issues with experimental data that prevent the use of parametric tests?

Answer 2

Not knowing the underlying distribution of the data.

Data not being in the interval scale.

Question 3

What assumptions are required to carry out non-parametric tests?

Answer 3

Observations are independent.

Sometimes: data are drawn from a continuous underlying distribution.

Question 4

Main benefits of non-parametric tests?

Answer 4

Smaller sample size required.
Can use more forms of data.
Less impact from outliers.

Question 5

What is the main downside of non-parametric tests?

Answer 5

Tests have less power

Question 6

What does it mean when a test has less power?

Answer 6

Harder to reject the null hypothesis when it is false

Question 7

What are the four scales of data?

Answer 7

Nominal
Ordinal
Interval
Ratio

Question 8

Characterise nominal data

Answer 8

Data is categorised, no order

Question 9

Characterise ordinal data

Answer 9

Data is categorised and ordered

Question 10

Characterise interval data

Answer 10

Numerical differences between numbers has some meaning

Question 11

Characterise ratio data

Answer 11

Scale has a natural zero point at origin

Question 12

What are the two one-sample parametric tests?

Answer 12

Binomial and chi-squared

Question 13

When can you use the binomial test?

Answer 13

When population consists of only two classes

Question 14

What scale of data is required at least for the binomial test?

Answer 14

Nominal scale

Question 15

When to use the chi-squared test?

Answer 15

When population consists of at least two classes

Question 16

What is the minimum scale of data required for the chi-squared test?

Answer 16

Nominal scale

Question 17

What are the three two-sample non-parametric tests?

Answer 17

Fisher exact test
Mann-Whitney U test
Wilcoxon test

Question 18

When to use the Fisher exact test?

Answer 18

Two independent samples that consist of two classes

Question 19

What is the minimum scale of data required for the Fisher exact test?

Answer 19

Data can be nominal or ordinal

Question 20

How to calculate the Fisher exact test statistic?

Answer 20

Calculate the probability of a more extreme outcome than the most extreme observed, keeping marginal totals fixed.

Question 21

What experimental design is the Mann-Whitney U test used for?

Answer 21

Between-subject design

Question 22

What element of samples data does the Mann-Whitney U test examine?

Answer 22

The distribution and differences in the distribution

Question 23

What scale of data is required at the minimum for the Mann-Whitney U test?

Answer 23

Ordinal scale

Question 24

What is the general intuition of the Mann-Whitney U method?

Answer 24

Pool all data and rank each observation. If distributed similarly would expect to see similar sum of ranks for each sample.

Question 25

What experimental design is the Wilcoxon test used for?

Answer 25

Within-subject design

Question 26

When you can carry out the Mann-Whitney U test or the Wilcoxon test, which should you prefer?

Answer 26

The Wilcoxon test is stronger

Question 27

What is the minimum scale of data required for the Wilcoxon test?

Answer 27

Ordinal scale

Question 28

Describe the method of the Wilcoxon test

Answer 28

Look at differences in paired observations. Pool all differences and rank them. Add a minus sign to any negative observations. Compare positive and negative sum of ranks. If treatment had no effect, sums of ranks should be similar.

Question 29

Name the two k-sample non-parametric tests

Answer 29

Kruskaw-Wallis test | Jonckheere test

Question 30

What are the differences in expected group order that separate between the Kruskaw-Wallis and Jonckheere tests?

Answer 30

Group order is random in Kruskaw-Wallis test, while groups are ordered a priori in Jonckheere test.

Question 31

What is the minimum scale of data required for the Kruskaw-Wallis test?

Answer 31

Ordinal scale

Question 32

What element of the data does the Kruskal-Wallis test consider?

Answer 32

The median of each group

Question 33

Describe the general method of the Kruskaw-Wallis test

Answer 33

All observations are converted in to a single series. Observations are ranked. Sum of ranks should be similar for each group if medians are the same.

Question 34

What is the minimum scale of data required for the Jonckheere test?

Answer 34

Ordinal scale

Question 35

What do you expect of the groups to use the Jonckheere test?

Answer 35

Groups have an expected rank order a priori

Question 36

Describe the general method of the Jonckheere test

Answer 36

Count the number of times an observation in group i is preceded by an observation in group j

Question 37

In what case are the MWU, W, KW and J tests poor choices?

Answer 37

When there are lots of ties when ranking data

Question 38

What is type 1 error

Answer 38

Falsely rejecting the null hypothesis when it's true

Question 39

What is type 2 error

Answer 39

Failing to reject the null hypothesis when it is false

Question 40

What is the power of the test?

Answer 40

1 - the type 2 error rate

Question 41

How to improve the power of the test?

Answer 41

Increase sample size Reduce error variance Increase treatment level variance

Question 42

How to reduce the error variance

Answer 42

Randomisation and blocking

Question 43

How to increase treatment level variance

Answer 43

Reduce number of treatments and increase spread

Question 44

When can you not use only two treatments in an experiment?

Answer 44

When a non-linear relationship is expected