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Example of a Mann-Whitney U-Test
A physician is interested in the effect of an anaesthetic on reaction times. Two groups are compared, one with (A) and one without (B) taking the anaesthetic. Subjects had to react on a simple visual stimulus. Reaction times are not normally distributed in this experiment, so data is analysed with the Mann-Whitney U-Test for ordinal scaled measurements. The table below shows the rank-ordered data: | Mean RT | Rank
| Group | 131
| 1
| B
| 135
| 2
| A
| 138
| 3.5
| B
| 138
| 3.5
| B
| 139
| 5
| A
| 141
| 6
| B
| 142
| 8
| B
| 142
| 8
| A
| 142
| 8
| B
| 143
| 10
| B
| 144
| 11
| A
| 145
| 12
| B
| 156
| 13
| B
| 158
| 14
| A
| 165
| 15
| A
| | 167 | 16
| B
| 171
| 17
| A
| 178
| 18
| A
| 191
| 19
| B
| 230
| 20
| B
| 244
| 21
| A
| 245
| 22
| A
| 256
| 23
| A
| 267
| 24
| A
| 268
| 25
| A
| 289
| 26
| A
|
Table showing Ranked Measures for each Group separately: | | Group A
| Group B
| | | 2
| 1
| | | 5
| 3.5
| | | 8
| 3.5
| | | 11
| 6
| | | 14
| 8
| | | 15
| 8
| | | 17
| 10
| | | 18
| 12
| | | 21
| 13
| | | 22
| 16
| | | 23
| 19
| | | 24
| 20
| | | 25
| | | | 26
| | | | | | Sum of Ranks
| 231
| 120
| Average Ranks
| 16.5
| 10
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The observed Z value is greater than the Z-value (5%, two-tailed). The anaesthetic group shows significantly slower reaction times than the non-anaesthetic group. BrightStat Output of this example This is a fictive example.
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Descriptives 