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What is a non parametric form of a two-sample t-test?

Mann-Whitney test


How does a Mann-whitney test work?

If the two samples are drawn from the same population, we would expect to receive a random sample of the ranks and therefore the sum of the ranks would be approximately equal


What are the technicalities of a Mann whitney test?

assumes that the data can be uniquely ranked
Ho is that both groups' observations been sampled from the same distribution
Less powerful than a two-sample t-test. This difference is usually only noticed in small samples


What is done in the case of tied observations?

give tied observations the average of the ranks that would have been used for them if the values were different


What are the assumptions for calculating the confidence intervals of the medians in Mann whitney tests?

the distributions have the same shape
The distributions only vary by their medians not their variability
these are very similar to the assumptions for parametric tests and sometimes it would be more appropriate to use these


Give an example of the non-parametric version of a one-sample t-test

Wilcoxon signed ranks rest


Describe the wilcoxon signed rank test

ranks are calculated based on the differences between the observations and the target value


Notes on the wilcoxon signed rank test

holds only when the differences are non zero
assumes the observations come from a population with a symmetrical distribution - usually only if data is normal . if it doesn't use a sign test- much lower power
It is possible to calculate confidence intervals for the median


Describe the WIlcoxon matched pairs test

when there are two measurements of the same quantity o each individual in a single sample
Ho- values of first measurement are approximately equal to the measurement of he second measurement
calculate the difference between each individual pair of measurements, then carry out test based on ranks of the within pair differences


Notes on Wilcoxon matched pairs test

effectively Wilcoxon signed rank test
only holds when differences are non-zero
assume from a symmetrical distribution


What is the name of a method for non-parametic analysis of variance ?

The Krushal-Wallis test


Describe the Krushal-Wallis test

mathematical extension of the Mann whitney test
Ho- different groups come from populations with the same distribution
Use bonferroni to account for multiple testing


Describe the use of transformations

variables that do not follow the normal distribution can sometimes be made to do so through transformation
- need to transform back before making conclusions
- log transformation is the only one that can be used to make interpretable CIs
If two groups are being compared need to use the same transformation