NOT DONE Mann-Whitney and Wilcoxon tests

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Last updated 10:12 AM on 10/8/26
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7 Terms

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Why Mann-Whitney

Unrelated design (Independent groups design)

Ordinal level of measurement - data based on an ‘unsafe scale’ (subjective ratings of happiness) - Converted to ranks for the purposes of the statistical test

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Mann-Whitney example

Aim

A study of the effects of age was conducted to see if there is a difference in perceived happiness between younger and older people.

18 people were given a questionnaire and 1 question asked them to rate their general level of happiness.

1-20 scale (1 = extremely unhappy, 20 = extremely happy)

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Mann-Whitney example

Hypotheses

Alternative hypothesis: There is a difference in happiness ratings between younger people (Group A) and older people (Group B) (2-tailed)

Null hypothesis: There is no difference in happiness ratings between younger people (Group A) and older people (Group B)

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Mann-Whitney example

Table of ranks

To rank the ratings you need to consider data from Group A and B at the same time.

The lowest number has a value of 1. In the case where 2 data items are the same, you add up the rank they would both get and give the mean for those ranks.

E.g. The rating of 12 appears 4 times, at position 7,8,9,10. They are all given the rank of 8.5 (the mean of the 4 numbers.

With a lot of multiple ranks it may be good to use a frequency table

Calculate the sum of the ranks for Group A (RA) and Group B (RB)

<p>To rank the ratings you need to consider data from Group A and B at the same time.</p><p>The lowest number has a value of 1. In the case where 2 data items are the same, you add up the rank they would both get and give the mean for those ranks.</p><p>E.g. The rating of 12 appears 4 times, at position 7,8,9,10. They are all given the rank of 8.5 (the mean of the 4 numbers.</p><p>With a lot of multiple ranks it may be good to use a frequency table</p><p>Calculate the sum of the ranks for Group A (R<sub>A</sub>) and Group B (R<sub>B</sub>)</p>
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Mann-Whitney example

Formula for U

Calculate the smaller value for U which in this case is Group A (RA < RB) (U=UA, Number of participants in Group A is now referred to as NA)

U = UA = RA - [NA(NA+1)]/2

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Mann-Whitney example

U calculation

UA = 65.5 - [10(10+1)]/2

UA = 65.5 - (110)/2

UA = 65.5 - 55 = 10.5

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Mann-Whitney example

Calculated and critical values

U = 10.5

The critical value of U for a 2-tailed test at the 0.05 level where NA = 10 and NB = 8 is 17

U < Critical value of U. The result is significant so we can reject the null hypothesis and accept the alternative hypothesis