Nonparametric tests Flashcards
Nonparametric tests
Appropriate when outcome is CONTINOUS but NOT NORMALLY DISTRIBUTED
- Rank scores
- Continuous but subject to extremes
- Continuous but there are limits of detection (on high or low end of scale)
General Approach to Nonparametric tests
- Rank data
- Perform analysis on ranks
- Follow same 5 step procedure for hypothesis testing
Ranking data in nonparametric test
- Take Raw data: (7,5,9,3,0,2)
- Order it: (0,2,3,5,7,9)
- Rank it: (1,2,3,4,5,6)
How to rank data in nonparametric tests when you have two numbers that are the same
Average their RANK Raw data: (7,7,9,3,0,2) ordered: (0,2,3,7,7,9) ranked: (1,2,3,4.5,4.5,6) Where 7, 7 would have been 4 and 5-- average the 4 and 5)
Mann -Whitney U test
Tests with two independent samples
- continuous outcome that is not assumed to follow a normal distribution
- same as 2 sample T test
- comparing two populations
- H0: Two populations are equal
- H1: Two populations are not equal
Mann Whitney U test
- test statistic is a function of the sample sizes and the ranks of the observations.
- Test statistic is U
- Reject H0 if U <_ critical value
sign Test
- Test with matched samples or paired samples
- Equivalent to the paired t test
- Continuous outcome measured in matched or paired samples, differences are not assumed to follow a normal distribution
- Can use in more situations
- has to be ordinal level or above
- CAN NOT use nominal
- H0: Median difference is zero
- H1: Median difference >,< or not 0
Sign test
- test statistic is the smaller of the number of positive or negative signs ( of differences)
- Reject H0 if the smaller of the number of positive of negative signs < or = critical value
- Tells you if there is a change
Sign test
when taking the difference you can do after - before or before -after. Does not matter you just have to be consistent throughout.
sign test what to do when you have a 0
- some through it out
- or if you have even # assign one a + and one a -
- If odd # through it out
- looks at the sign of the change- is there more change in the direction of + or more in the direction of -?
Wilcoxon signed rank test
- tests with matched samples or paired
- continuous outcome measured in matched or paired samples, differences are not assumed to follow a normal distribution
- Improved version of the sign test- incorporates the direction of the change along with the magnitude
- H0: Median difference is zero
- H1: Median difference >,< or not 0
Wilcoxon signed rank test
- Test statistic is W, the smaller of W+ and W-, the sums of he positive and negative ranks of the differences scores
- Reject H0 if W< or = to critical value
Wilcoxon signed rank test
-Configure the same as the signed but add the sum of the ranks
Example W+=39 and W- = 31
Kruskal-Wallis Test
-Tests with more than two independent samples
-continuous outcome that is not assumed to follow a normal distribution
-K (k>2) independent samples
H0: K population medians are equal
H1: k population medians are not all equal
-test statistic is H
Kruskal Wallis test
- based on the ranks
- lessens the impact of outliers
