STATS3- non-parametric hypothesis tests

5 types of parametric hypothesis tests

• z-test

• 1 sample t-test

• paired t-test

• independent group t-test

• pearson’s r

degrees of freedom for parametric hypothesis tests

• z-test: 0

• 1 sample t-test: n-1

• paired t-test: n-1

• independent group t-test: total sample size-2

• pearson’s r: n-2

3 assumptions of parametric tests

• normally distributed populations

• sd of populations should be approximately equal

• theres no extreme scores in data set

what is the mann-whitney test the non-parametric alternative for

independent t-test

4 steps to carry out mann-whitney test

1. rank all scores from each group lowest to highest (include tied ranks)

2. substitute scores in each group with their rank

3. work out the smallest possible sum of ranks for each group

4. work out actual sum of ranks for each group & calculate difference from step 3

   • mann-whitney value = smallest number from step 4

what to do with p-value when doing a 1 tailed mann-whitney test

p-value/2

what is the wilcoxon test the non-parametric alternative for

paired t-test

3 steps to carry out wilcoxon test

1. calculate difference post-pre for each score

2. rank differences smallest - largest

   • ignore 0 difference & sign of difference

3. split ranks into positive and negative

   • wilcoxon value = sum of ranks in least occurring difference column (positive or negative)

what does a small wilcoxon score (t) suggest

more evidence for difference

what is the spearman’s rho test the non-parametric alternative for

pearson’s r

what values does spearman’s rho range from

-1 - 1

spearman’s rho formula

when can spearman’s rho test only be used

if theres no tied ranks

5 steps to carry out spearman’s rho test

1. convert scores in each group (X & Y) to ranks (2 different rank columns)

2. calculate the difference in ranks

3. square the difference

4. calculate the sum of squared differences

   • use spearman’s rho formula

what + when is the 1-variable chi square test used for

• relationships between frequency data in categorical variables

• if observed frequencies are different from whats expected (equally distributed)

4 steps to carry out 1-variable chi square test

1. calculate difference between expected (under null hypothesis) and observed frequencies

2. (E-O)²

3. (E-O)²/E

4. chi square = sum of step 4

degrees of freedom for 1-variable chi square test

n-1

what tail of significance do you look at for 1-variable chi squre test

one-tailed significance, 0.05

what is the 2×2 chi square test of association used for

relationship between 2 categorical variables

how to calculate expected values for 2×2 chi square test

(row total x column total)/sample total

4 steps for 2×2 chi square test

1. hypothesis: x association/relationship

2. calculate expected values

3. calculate chi square value

4. convert to critical value

degrees of freedom for 2×2 chi square test of association

(number of rows - 1) x (number of columns - 1)