How to interpret data from Mann-Whitney U Test So I am doing a research project and I was told to d

Makayla Boyd

Makayla Boyd

Answered question

2022-06-12

How to interpret data from Mann-Whitney U Test
So I am doing a research project and I was told to do the Mann Whitney U Test. The research is examining male and female work experiences by them ranking statements from 1-6 (1 being strongly agree and 7 being strongly disagree). The goal is to see if their is a difference in work experience between the two groups. Using an online calculator these were my results: Key: 1st group/2nd group
Variable: Female/Male Observations: 720/936
Mean: 3.099/3.042 SD: 1.715/1.668
Mann-Whitney test / Two-tailed test:
U 341978.5
U (standardized) 0.532
Expected value 336960
Variance (U) 89023289.87
p-value (Two-tailed) 0.595
alpha 0.05
So I have all this great data. The first part makes sense to me but the data in the second part I don't know how to read/analyze. Can somebody explain. Thank you!

Answer & Explanation

Ryan Newman

Ryan Newman

Beginner2022-06-13Added 26 answers

U = 341978.5
This is the value of the Mann-Whitney U statistic, which is defined as
U = i = 1 n j = 1 m S ( X i , Y j ) , S ( X , Y ) = { 1 , Y < X 1 / 2 , Y = X 0 , Y > X .
Here, X i represents the response of the i t h person in the first group, which are women, and Y j is the response of the j t h person in the second group, which are men. However, this definition could have X and Y reversed, so you might want to double check.
U (standardized) 0.532
This is the standardized value of the U-statistic, equal to
U μ U σ U ,,
where μ U and σ U are given below. This standardized value is approximately normally distributed with mean 0 and variance 1, so 0.532 is a z-score; the more extreme it is, the more evidence there is to support the hypothesis that the two groups differ in their responses.
Expected value 336960
This is μ U = m n / 2, where m=936 and n=720.
Variance (U) 89023289.87
This is the sample variance of the U statistic,
σ U 2 = m n 12 ( ( m + n 1 ) i = 1 k t i 3 t i ( m + n ) ( m + n 1 ) )
where t i is the number of people sharing rank i, where your ranks range from 1 to k=7.
p-value (Two-tailed) 0.595
This is the conditional probability that, given there is no difference between the two groups, you would obtain a sample that is at least as extreme as the one you observed. It is a measure of the plausibility of the data you observed, assuming the null is true. Therefore, the smaller this value, the more evidence there is to favor rejecting the null hypothesis.
alpha 0.05
This is the predefined significance level of the test and is the maximum Type I error you are willing to accept--i.e., you wish to limit the probability of incorrectly rejecting the null hypothesis to be at most 5%. Since the p-value exceeds α, you do not reject H 0 and your conclusion is that the data furnishes insufficient evidence to suggest the two groups responded differently to the survey.

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