Statistics Flashcards
What assumptions are required for parametric tests to be valid?
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.
What are the two most common issues with experimental data that prevent the use of parametric tests?
Not knowing the underlying distribution of the data.
Data not being in the interval scale.
What assumptions are required to carry out non-parametric tests?
Observations are independent.
Sometimes: data are drawn from a continuous underlying distribution.
Main benefits of non-parametric tests?
Smaller sample size required.
Can use more forms of data.
Less impact from outliers.
What is the main downside of non-parametric tests?
Tests have less power
What does it mean when a test has less power?
Harder to reject the null hypothesis when it is false
What are the four scales of data?
Nominal
Ordinal
Interval
Ratio
Characterise nominal data
Data is categorised, no order
Characterise ordinal data
Data is categorised and ordered
Characterise interval data
Numerical differences between numbers has some meaning
Characterise ratio data
Scale has a natural zero point at origin
What are the two one-sample parametric tests?
Binomial and chi-squared
When can you use the binomial test?
When population consists of only two classes
What scale of data is required at least for the binomial test?
Nominal scale
When to use the chi-squared test?
When population consists of at least two classes
What is the minimum scale of data required for the chi-squared test?
Nominal scale
What are the three two-sample non-parametric tests?
Fisher exact test
Mann-Whitney U test
Wilcoxon test
When to use the Fisher exact test?
Two independent samples that consist of two classes
What is the minimum scale of data required for the Fisher exact test?
Data can be nominal or ordinal
How to calculate the Fisher exact test statistic?
Calculate the probability of a more extreme outcome than the most extreme observed, keeping marginal totals fixed.
What experimental design is the Mann-Whitney U test used for?
Between-subject design
What element of samples data does the Mann-Whitney U test examine?
The distribution and differences in the distribution
What scale of data is required at the minimum for the Mann-Whitney U test?
Ordinal scale
What is the general intuition of the Mann-Whitney U method?
Pool all data and rank each observation. If distributed similarly would expect to see similar sum of ranks for each sample.
What experimental design is the Wilcoxon test used for?
Within-subject design
When you can carry out the Mann-Whitney U test or the Wilcoxon test, which should you prefer?
The Wilcoxon test is stronger
What is the minimum scale of data required for the Wilcoxon test?
Ordinal scale
Describe the method of the Wilcoxon test
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.
Name the two k-sample non-parametric tests
Kruskaw-Wallis test
Jonckheere test
What are the differences in expected group order that separate between the Kruskaw-Wallis and Jonckheere tests?
Group order is random in Kruskaw-Wallis test, while groups are ordered a priori in Jonckheere test.
What is the minimum scale of data required for the Kruskaw-Wallis test?
Ordinal scale
What element of the data does the Kruskal-Wallis test consider?
The median of each group
Describe the general method of the Kruskaw-Wallis test
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.
What is the minimum scale of data required for the Jonckheere test?
Ordinal scale
What do you expect of the groups to use the Jonckheere test?
Groups have an expected rank order a priori
Describe the general method of the Jonckheere test
Count the number of times an observation in group i is preceded by an observation in group j
In what case are the MWU, W, KW and J tests poor choices?
When there are lots of ties when ranking data
What is type 1 error
Falsely rejecting the null hypothesis when it’s true
What is type 2 error
Failing to reject the null hypothesis when it is false
What is the power of the test?
1 - the type 2 error rate
How to improve the power of the test?
Increase sample size
Reduce error variance
Increase treatment level variance
How to reduce the error variance
Randomisation and blocking
How to increase treatment level variance
Reduce number of treatments and increase spread
When can you not use only two treatments in an experiment?
When a non-linear relationship is expected
