This example deals with two sets of sample data from two
contrasting urban areas, area X and area Y, with the aim of comparing them and
demonstrating differences. There are eight pairs of data in this example.
Tests of significance are used to tell us whether the
differences between the two sets of sample data are truly significant or whether
these differences could have occurred by chance. Tests of significance tell us
the probability level that differences between the two areas, X and Y are due to
chance.
First, examine the two data sets to decide whether differences
appear to exist which warrant further investigation.
The sample sets are:
Area X: 7; 3; 6; 2; 4; 3; 5; 5
Area Y: 3; 5; 6; 4; 6; 5; 7; 5
Area
Mean
Median
Mode
X
4.38
4.5
5
Y
5.13
5.0
5
The difference between the means for the two sets of data
warrants further investigation, to test the statistical significance of the
difference.
THE MANN-WHITNEY U TEST
Stage 1: Call one sample A and the other B.
Stage 2: Place all the values together in rank order (i.e. from
lowest to highest). If there are two samples of the same value, the 'A' sample
is placed first in the rank.
Stage 3: Inspect each 'B' sample in turn and count the number
of 'A's which precede (come before) it. Add up the total to get a U value.
Stage 4: Repeat stage 3, but this time inspect each A in turn
and count the number of B's which precede it. Add up the total to get a second U
value.
Stage 5: Take the smaller of the two U values and
look up the probability value in the table below. This gives the percentage
probability that the difference between the two sets of data could have occurred
by chance.
Example: Is there a significant difference in the
quality of the architecture between El Raval (site 3); and El Raval (site 4)?
Stage 1:
Site 3: (Sample A) 7; 3; 6; 2; 4; 3; 5;
5
Site 4: (Sample B) 3; 5; 6; 4; 6; 5; 7; 5
Stage 2:
A
A
A
B
A
B
A
A
B
B
B
A
B
B
A
B
2
3
3
3
4
4
5
5
5
5
5
6
6
6
7
7
Stage 3:U= 3+4+6+6+6+7+7+8 = 47
Stage 4:U= 0+0+0+1+2+2+5+7 = 17
Stage 5:U= 17
The critical value from the table = 6.5
The probability that the quality of the architecture measured
in Site 4 is better than Site 3 just by chance is 6.5 per cent.
If you find that there is a significant probability that the
differences could have occurred by chance, this can mean:
1. Either the difference is not significant and there is little
point in looking further for explanations of it, OR
2. Your sample is too small. If you had taken a larger sample,
you might well find that the result of the test of significance changes: the
difference between the two areas becomes more certain.
It is not possible to tell which of these conclusions is the
correct one from the result of the test itself. Statistics are only a tool and
can never replace good geographical thinking.
