L5: MANN-WHITNEY TEST Flashcards
(25 cards)
What does non-parametric mean?
Distribution-free (does not assume a specific data distribution)
Does not require normality or equal variances (homogeneity)
Often used when data violates assumptions of parametric tests
What is ordinal data?
Data that shows order or ranking but the intervals between values are not necessarily equal.
Example: Movie ratings (1 star, 2 stars, 3 stars…), class rankings
- tells you the direction about info from one direction to another
What are some common non-parametric tests, and what type of data do they use?
Common tests: Mann-Whitney U, Wilcoxon Signed Ranks, Kruskal-Wallis, Friedman
They use ordinal (ranked) data, which is easier to interpret but gives limited information compared to interval/ratio data
What are the key features and limitations of non-parametric tests?
Make few/no assumptions about population distribution (distribution-free)
Use ranking of ordinal data; no means or variances used
Interval data is often converted to ordinal or nominal
Simpler but less sensitive than parametric tests
Higher chance of missing significant effects, so parametric tests are preferred when possible
What are non-parametric tests?
Statistical tests that don’t assume a specific data distribution (like normality). They work with ranked or ordinal data and are useful when parametric test assumptions aren’t met.
What kind of data does the Mann-Whitney test use?
Uses ranked data, not means
When do we use the Mann-Whitney tests?
To compare two independent groups on one measure when data isn’t normally distributed
What does Mann-Whitney test checks?
Whether one group tends to have higher or lower ranks than the other groups
What does it mean if there is a real difference?
One groups scores are mostly higher so ranks cluster at one end
What does it mean if there is no difference?
The ranks of both groups are mixed evenly
What does it mean if scores from two samples are clustered at opposite ends of the ranks?
It suggests a systematic difference between the two treatments
Q: What does it mean if two samples are intermixed evenly along the rank scale?
It indicates no consistent difference between the treatments.
What is the Mann-Whitney U test?
A non-parametric alternative to the independent t-test for comparing two unrelated samples.
Can the sample sizes be different in the Mann-Whitney U test?
Yes, sample sizes don’t have to be equal
What are the assumptions of the Mann-Whitney U test?
Observations must be independent, and the dependent variable should be continuous and doesn’t need to be normally distributed.
Why should there be few tied scores in the Mann-Whitney U test?
Because it relies on ranking continuous data, many tied scores can affect results and require caution
What is the purpose of assumption testing?
To decide which statistical test to use (Student t-test or Mann-Whitney U).
What assumptions do we test before choosing the test?
Normal distribution of data and equal variances between groups
Which test do we use if assumptions are met?
Independent samples t-test.
Which test do we use if assumptions are NOT met?
The non-parametric Mann-Whitney U test.
How do you perform a Mann-Whitney U test?
Combine and order all data values from both groups.
Assign ranks to each value (smallest = rank 1).
Sum the ranks for each group separately.
Use these rank sums to calculate the test statistic and evaluate the null hypothesis.
How do you assign ranks in the Mann-Whitney U test?
Order all scores from fastest (smallest) to slowest (largest).
Assign ranks 1, 2, 3, … to each score based on position.
If scores tie, assign them the average rank of their positions (middle point).
How do you calculate the expected rank sum for each group under the null hypothesis (H0) in the Mann-Whitney U test?
Expected rank sum for group = n × (N + 1) / 2
n = number of participants in the group
N = total number of participants in both groups
Under H0, both groups should have about equal mean ranks
Then calculate sum rank scores for group A
Calculate the sum of B
Then we have sum rank scores
