Mann-Whitney U - Statistics

Statistical Tests: Mann-Whitney U Page 1/3

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Q1. The best use of the Mann-Whitney U test will be for the comparison of which of the following types of data.

a)Parametric unpaired data ✔ ✗

b)Non-parametric paired data ✔ ✗

c)Continuous, non-parametric, unpaired data ✔ ✗

d)Categorical unpaired data ✔ ✗

e)Categorical paired data ✔ ✗

Feedback:

The answer is c). The Mann-Whitney U is a non-parametric test for assessing whether two independent or unpaired samples of observations come from the same distribution.

Q2. Which of the following statements you believe to be True when considering the Mann-Whitney U test?

a)It uses the ranking the data values. ✔ ✗

b)It is the equivalent of the paired t-test. ✔ ✗

c)It is used when the distribution of the data is skewed. ✔ ✗

d)It assumes that the standard deviations of the two independent groups are equal ✔ ✗

Feedback:

The correct answers are a) & c). a) is True. Data values are ranked during the calculation. b) is False. The Mann-Whitney U test is the non parametric equivalent of the independent samples t-test. c) is True. If the data is skewed, the assumption of Normality for the independent samples t-test is not met and the non-parametric alternative which is distribution free is required, d) Is False. Calculation of standard deviations and considerations of variance are not required for non parametric tests.

Q3. The accuracy of diagnosis of femoral hernia in referrals to a district general hospital over a period of 5 years was studied and related to clinical outcome. A correct diagnosis was made in only 36 of 98 cases (60 urgent, 38 routine) before admission to hospital. The median length of post-operative stay of urgent admissions was 7 days (range 4-50) when a correct initial diagnosis was made and 10 days (range 4-50) when the initial diagnosis was incorrect (P = 0.07, Mann-Whitney test). (Corder, A.P. Postgrad Med J (1992) 68, 26 – 28). Which of the following statements, if any, are true?

a)The Null hypothesis for this study would have been. There is no difference in the length of stay of patients with correct or incorrect diagnoses using the Mann Whitney U test. ✔ ✗

b)An alternative hypothesis for this study could be. Patients with correct diagnosis will stay in hospital about 3 days less compared to those with an incorrect diagnosis. ✔ ✗

c)Although the Mann-Whitney test was used, it could have been replaced by the independent samples t-test because there were 60 urgent cases. ✔ ✗

d)The results show there was no significant difference in the length of stay for correct and incorrect diagnoses of 3 days. ✔ ✗

Feedback:

The correct answers are a) and d). a) This is True. However the Null hypothesis does not need to mention the statistical test. This would be mentioned in a statistical analysis plan for the study. In doing so we are also deciding in advance that the length of stay data will be skewed. This would be justified if we had existing data to support this assumption. b) This is False. The Alternative hypothesis should state that there is a difference in the length of stay. It should not say if this will be greater or less and should not quantify it, even if we had preliminary data from elsewhere. c) This is False. It is the distribution of the data that is important and the median and range demonstrate that the data is skewed so a non-parametric test is required. d) This is True. The P-value was 0.07 so it did not reach the usual level of significance of 0.05.

Q4. The following chart shows triglyceride readings collected from male and female subjects.

Which of the following options would you choose to test whether there was a difference between the triglyceride levels in male and female subjects?

a)Perform an independent samples t-test ✔ ✗

b)Perform a Mann-Whitney U test ✔ ✗

c)Transform the data and replot the data ✔ ✗

d)Transform the data and perform a Mann-Whitney U test ✔ ✗

e)Transform the data and perform an independent samples t-test ✔ ✗

Feedback:

The correct answer is c). The best option would be to transform the data using a logarithmic transformation and plot a histogram of the transformed data. Then if the transformed data is Normally distributed we could undertake an independent samples t-test. We would not do a t-test (a) on skewed data, we could perform a Mann-Whitney U test (b), but as the t-test is more powerful we should explore the effects of transformation first. Note that if the Mann-Whitney U test is significant on the raw data, then we would expect transformed data that was Normally distributed to be significant. Options (d) is not sensible because the Mann-Whitney U test does not assume anything about the underlying distribution of the data, it is based on ranking, so transformation will not add anything. Option (e) does not allow for visualising the transformed data. The transformation may not result in a variable that follows a normal distribution in which case the t-test would be inappropriate.

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