Lecture 17: Non-Parametric Tests

Question 1

When do we do a non-parametric test (3)

Answer 1

1. When assumptions are violated
2. When the variable is ordinal
3. When unsure about outliers

Question 2

What is the assumption

Answer 2

Having independent random samples

Question 3

What are the hypotheses

Answer 3

H0: equal population distributions (implies equal mean ranking)
Ha: unequal mean ranking (two-sided)
Ha: higher/lower mean ranking (one-sided)

Question 4

What is the test statistic

Answer 4

The difference between sum of rankings

Question 5

How do we deal with ties in ranked data

Answer 5

We add the ranks that the ties we supposed to have and then divide that by the amount of numbers that are tied

Question 6

What are 4 non-parametric tests and their assumptions

Answer 6

1. Wilcoxon rank-sum test
   —> 2 independent samples (independent samples t-test)
2. Wilcoxon signed rank test
   —> 2 paired samples (paired samples t-test)
3. Kruskal-Wallis test
   —> independent with more than 2 samples; one-way ANOVA
4. Friedman’s ANOVA
   —> within subjects ANOVA

Question 7

What is the sum of ranks

Answer 7

Adding the values assigned to each rank in the group

Question 8

What is the minimum/maximum rank sum

Answer 8

The values of the rank added together; if you have rank 1-20 (each with an assigned data point), and group 1 is rank 1-10 and group 2 is rank 11-20 then the minimum rank sum = 1+2+3+4+5+6+7+8+9+10=55 and the maximum rank sum = 11+12+13+14+15+16+17+18+19+20=155

Question 9

What is the procedure for a Wilcoxon signed rank test

Answer 9

Take absolute differences (difference between scores without sign) between scores, rank the absolute differences, sum the differences that have a positive sign

Question 10

What is the test statistic of the Kruskal-Wallis test and what distribution does it have

Answer 10

The squared ranks in each of the groups combined, a chi-squared distribution