week 6 - wilcoxon rank-sum and wilcoxon sign rank-test

Question 1

what are parametric tests

Answer 1

• t-tests and ANOVA
• Rely on the assumption that the data comes from a normally distribution population
• What if the assumption of normality is violated?
• You can conduct non-parametric tests
• Non-parametric tests are more flexible:
• Data does not need to come from a normally distributed population

Question 2

how do non-parametric tests work

Answer 2

• do not use the values of the dependent variable
• data is ranked using the values of the DV
• analysis then carried out on the ranks

Question 3

what don’t we just always perform non-parametric tests

Answer 3

• non parametric tests have less statistical power
• more likely to result in type II error

Question 4

how do we assess normality in designs with two independent groups

Answer 4

• Q-Q plots
• shapiro-wilk test
• data in each group should follow a normal distribution

Question 5

what are Q-Q plots

Answer 5

• Plots values you would expect to get if the distribution was normal against your observed values.
• Expected values are a straight diagonal line observed values are dots
• If normally distributed, dots fall mostly on top of line
• if not normally distributed points do not fall on line

Question 6

what is the interpretation of the Shapiro-Wilk test

Answer 6

• p ≤ .05 data is not assumed to come from a normally distributed population
• parametric tests not appropriate
• consider non-parametric tests
• p > .05 data is assumed to come from a normally distributed population
• parametrics tests may be appropriate - proceed with other assumptions checks

Question 7

which approach is better

Answer 7

• shapiro-wilk less subjective but likely to give significant p-value frequently with large sample sizes
• consider both outcomes together
• if the group sample size is <50 rely on the shapiro wilk
• if group sample size is >50 rely on Q-Q plot

Question 8

what is the theory behind the Wilcoxon rank sum test

Answer 8

• order the DV from small to large
• rank the DV from small to large
• add up ranks per group
• correct for the number of people in groups
• minus the mean rank from each groups sum of ranks

Question 9

what if at least one group doesn’t meet the normality assumption

Answer 9

• conduct non-parametric alt of unrelated samples t-test (Wilcoxon rank-sum test)
• also used if there is a two independent groups with no repeated measures
• Mann-whitney test

Question 10

what is the direction of the results

Answer 10

• parametric - report mean
• non-parametric - median is typically prefered

Question 11

what is the exact method

Answer 11

• we know the null hypothesis is true
• how often is the difference that appears as large as the difference in the true data

Question 12

what is the monte carlo method

Answer 12

• creates lots of databases that are the same as the sample
• assigns groups randomly

Question 13

what is the normal approximation with continuity correction

Answer 13

• assumes that the sampling distribution of the W statistic is normal
• produces a standard error
• can be used to calculate z and than a p-value
• applies a continuity correction

Question 14

which is the default method

Answer 14

• Sample size < 50 in all group and no tied ranks = exact method
• Sample size ≥ 50 in any group OR tied ranks = normal approximation with continuity correction

Question 15

why is my W different when calculated manually

Answer 15

• If you were to calculate W manually, W should be the smallest value (sum of ranks – mean rank)
• In R, W is reported for the first factor level
• Doesn’t affect significance, so not something you need to worry about
• You can just report what R outputs

Question 16

what are the assumptions of normality

Answer 16

• the difference between timepoint 1 and timepoint 2 should be normally distributed
• calculate a difference score for each participant and assess normality of this difference score

Question 17

what is the Wilcoxon signed-rank test

Answer 17

• Alternative to the related samples t-test
• Appropriate if you have a design with only two repeated measures (all participants contribute data at both timepoints)

Question 18

what is the theory behind the Wilcoxon signed-rank test

Answer 18

• calculate the difference between the conditions
• note the sign of the difference
• calculate the ranks
• add up the positive and negative ranks separately

Question 19

does the V differ depending on how I enter the variables in the code

Answer 19

• V is always the sum of positive ranks but whether ranks are positive or negative will differ depending on the way you enter the variables into the function