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
Most nonparametric methods perform analysis using:
Ranked Data
Which nonparametric test is more appropriate for testing the hypothesis that K population medians are equal (k>2)?
Kruskall Wallis Test
Which of the following nonparametric procedure is most appropriate for testing whether two populations (means or median) are equal?
Mann Whitney test
Which of the following is NOT true when determining sample size based on the confidence interval approach?
must specify type II error rate
Which test has a test statistic based on the counts of +’s and -‘s obtained from the difference in before and after scores?
Sign test
