Mann-Whitney U test Flashcards
What is meant by ordinal data?
Tells us about direction of one score to another i.e. rank
No mean or SD values - ranks give no info about distance between points so we can’t know that anything above a mean would be equal to anything below it
What are some advantages and disadvantages of non-parametric tests?
Useful where parametric assumptions not met - tests are distribution and assumption-free
However lack sensitivity and have a greater likelihood of failing to detect significant differences
What is the mann-whitney U test?
Non-parametric alternative for unrelated t-test, used to detect differences on one measure between TWO groups
Cannot use means, just “higher/lower” scores e.g. ranks in x condition will be systematically higher/lower than ranks in y condition
What are the null and alternative hypothesis for this test?
Null - no difference i.e. large and small scores mixed evenly in the two samples, so population medians should be equal
Alternative - real difference i.e. scores in one sample will generally be larger than in the other and if combined scores from each we should see them concentrated at either end of a distribution
What are 2 requirements of non-parametric tests?
Observations must be independent
DV should be continuous i.e. values may take on any value within a finite/infinite interval and can be counted, ordered and measured (i.e. no one should have exactly the same scores)
What are the steps in conducting this test?
Need to order scores from smallest to highest and then we can rank them i.e. position 1, 2, 3 etc - both samples will be mixed together in the ranking process
Once data are ranked we sum the ranks together - under the null we expect sums for each sample group to be roughly equal since they should both have roughly equal mean ranks
Can calculate what we expect the rank sums to be under H0 by n(N+1)/2, and we compare these to rank sums we actually calculate for each sample
What is the Mann-whitney formula?
For each sample we calculate:
(sample 1 x sample 2) + ((sample1(sample 1 +1))/2) - calculated rank sum
The Mann-whitney value will be the smaller of the values calculated when you have done this calculation for both samples - look this value up in the tables and our calculated value needs to be LESS/EQUAL to critical value to be significant
What is an alternative to the ranking method?
Assigning points - for each score in each group a point is given where beaten by another score in the OTHER GROUP and half a point each time there is a tie
Add points up and the U value will be the lower one
Smaller U values thus indicate few points and thus significant difference i.e. little overlap between the groups
For the largest possible difference one sample would have zero points
