Section 8 (Pgs 94-108) Flashcards
Basically, when are non-parametric methods used?
When the variables are not normally dsitributed
When the data is skewed
What do non-parametric methods use instead of the actual values of the data?
Ranks of the data
Are non-parametric methods more or less powerful than parametric methods?
Why?
Less powerful
They do not utilise all the data
What 3 variables are most likely to warrant the use of non-parametric methods?
Counts
Ranks
Scores
What can sometimes achieve normality for counts, ranks and scores?
Square root transformation
What should you always do before deciding on non-parametric methods?
Explore methods of transforming the data
What should you look at to determine whether data is normally distributed?
Normal plot
Box-and-whisker diagram
Shaprio-Wilk statistic
Coefficient of skewness
What is the most appropriate measure of centre in normally distributed data?
Mean
Is not normally distributed data normally symmetrically or non-symmetrically distributed?
Non-symmetrically (skewed)
What is the most appropriate measure of centrality in non-normally distributed data?
Median
When is non-parametric tests of the average of a single sample indicated?
Data is not plausibly normal (normal plot, box-and-whisker plot, shapiro-wilk statistic, coefficient of skewness)
Transformations to address the problem cannot be found
Sample size is small?
What 2 non-parametric procedures can be used to test hypothesis about the median of a single sample?
Sign test
Wilcoxon signed rank sum test
What principle is the sign test based on?
The numbers of observations above and below the hypothesised median
If the null hypothesis is true, these should be equal
Which out of the sign test and the wilcoxon signed rank sum test is preferable?
Why?
Wilcoxon signed rank sum test
Based on ranks and therefore incorporates some measure of the actual values
Why is the sign test sometimes used instead of the wilcoxon signed rank sum test?
Data must be approximately symmetrically distributed for the wilcoxon signed rank sum test
In the sign test, what is the hypothesised median normally approximately distributed to?
What is the other option?
Normal distribution
Binomial distribution
What does n in the sign test equal?
The number of observations not equal to the reference median
Why is a correction for continuity included in the sign test?
As the data (which is discrete) is being approximated to the normal distribution (which is continuous)
In what does the sample size affect the ability to reject a null hypothesis?
It is difficult to obtain sufficient evidence to reject a null hypothesis with a small sample size
In what way does sample size determine the ability of study to detect a real effect?
A large sample size makes it easier for a study to detect a real effect
What is the proper phrase for the ability of a study to detect a real effect?
Power of the study
For a sample size of <25, what is the test statistic in the Wilcoxon signed rank sum test?
W
For a sample size of >25, what is the test statistic in the Wilcoxon signed rank sum test?
Z
How do you rank data in the Wilcoxon signed rank sum test?
Determine the difference between each value and the hypothesised median
Ignore the signs and zero difference, rank the differences in order of magnitude
Determine the sum of the positive (and negative) ranks above (and below) the hypothesised value
The test statistic W is the smaller of the 2 rank sums
When are the results from non-parametric and parametric tests comparable?
When the assumptions for the parametric test are met
When are observations dependent (paired)?
If they are applied to the same individual or to individuals matched for factors likely to affect the outcome
What non-parametric test is used to compare dependent samples?
Wilcoxon matched pairs rank sum test
What non-parametric test is used to compare independent samples?
Mann-Whitney Test
In basic terms, how do you do the Wilcoxon matched pairs rank sum test?
By applying the Wilcoxon signed rank sum test to the differences between the pairs of measurements
What test statistic is used for the Mann-Whitney if neither n1 or n2 is >10?
T
What test statistic is used for the Mann-Whitney if either n1 or n2 is >10?
Z
In the Mann-Whitney, when comparing U to T, why is U more useful?
It provides information about actual probability - the probability that a randomly selected observation from the smaller group will be smaller than a randomly selected observation from the larger group
