Offwell Woodland & Wildlife Trust

Promoting the British Countryside

Home

About us Conservation Education Wildlife Habitats Maps Search Resources Sponsors

 


An Ecological Sampling Exercise
Processing & Interpreting Raw Data
Contents

Exercise Answers

wpeD1.jpg (5850 bytes)

Mann-Whitney U Test

Both spring-cut strips (2 & 4) had a lower % cover of Bluebells than the autumn-cut strips (1 and 3). This difference was most evident in strip 4. However, the difference in % Bluebell cover between strip 2 and strips 1 and 3 was not particularly marked. It is really necessary to test the data statistically to determine whether the observed differences are significant or not, before drawing any firm conclusions.

In order to determine whether the differences are statistically significant, a Mann-Whitney U Test has been performed on the data.

Calculations and Results

Comparison between results obtained for sections 1 (autumn cut) and 2 (spring cut)

Data arranged in order and ranked

The data on % Bluebell cover from both section 1 (orange) and 2 (green) is arranged in ascending order of % Bluebell cover, from lowest to highest and then ranked.

Sample 

5 5 . . 10 . . . . . . 20 20 . . . . . . . .
Rank 1.5 1.5 . . 6 . . . . . . 15 15 . . . . . . . .

Sample 

. . 8 8 . 10 10 15 15 15 15 . . 20 20 20 20 20 25 25 25
Rank . . 3.5 3.5 . 6 6 9.5 9.5 9.5 9.5 . . 15 15 15 15 15 20.5 20.5 20.5

Sample 

. 30 . 45 50 70 . . 90 . . . . . . . . . . . Sum
Rank . 23 . 25 26 27 . . 30 . . . . . . . . . . . 170

Sample 

25 . 40 . . . 80 85 . . . . . . . . . . . . Sum
Rank 20.5 . 24 . . . 28 29 . . . . . . . . . . . . 295

wpeF1.jpg (819 bytes)R1 = 170        n1 = 10

wpeC3.jpg (1196 bytes)R2 = 295         n2 = 20

To calculate values of U, where n1 and n2 are the number of samples from each section.

U1 = n1 x n2 + n2(n2 + 1 ) - wpeC3.jpg (1196 bytes)R2 

U1 = 10 x 20 + 20(20 + 1) - 295

U1 = 200 + 210 - 295

U1 = 115

 

U2 = n1 x n2 + n1(n1 + 1 ) - wpeC3.jpg (1196 bytes)R1  

U2 = 10 x 20 + 10(10 + 1) - 170

U2 = 200 + 55 - 170

U2 = 85

 

The smallest figure of U obtained in the calculations is then compared with the critical value of U for
n1 = 10 and  n2 = 20. This critical value is looked up in a table of critical values for the Mann Whitney U Test. The critical value in this case is 55.

If the smallest figure of U obtained is less than, or equal to this critical value, then the results are significantly different. The smallest value  (U2) was 85, which is larger than this critical value.  The observed difference between the data for % Bluebell cover between Section 1 and 2 is therefore not significant at the p = 0.05 level.

 

 

Comparison between results obtained for sections 2 (spring cut) and 3 (autumn cut)

 

Sample 

8 8 . . . . 10 10 . 15 15 15 15 . 20 20 20 20 20 . ..
Rank 2 2 . . . . 6.5 6.5 . 11.5 11.5 11.5 11.5 . 16.5 16.5 16.5 16.5 16.5 . ..

Sample 

. . 8 9 10 10 . . 13 . . . . 20 . . . . . 24 25
Rank . . 2 4 6.5 6.5 . . 9 . . . . 16.5 . . . . . 20 23

Sample 

25 25 25 25 . . 40 . . . . . . . . . . 80 85 . Sum
Rank 23 23 23 23 . . 27.5 . . . . . . . . . . 38.5 40 . 343.5

Sample 

. . . . 27 40 . 45 45 45 49 55 60 60 67 70 80 . . . Sum
Rank . . . . 26 27.5 . 30 30 30 32 33 34.5 34.5 36 37 38.5 . . . 476.5

 

wpeC3.jpg (1196 bytes)R1 = 343.5          n1 = 20

wpeC3.jpg (1196 bytes)R2 = 476.5          n2 = 20

U1 = n1 x n2 + n2(n2 + 1 ) - wpeC3.jpg (1196 bytes)R2 

U1 = 20 x 20 + 20(20 + 1) - 476.5

U1 = 400 + 210 - 476.5

U1 = 133.5

U2 = n1 x n2 + n1(n1 + 1 ) - wpeC3.jpg (1196 bytes)R1  

U2 = 20 x 20 + 20(20 + 1) - 343.5

U2 = 400 + 210 - 343.5

U2 = 266.5

 

The critical value of U for  n1 = 20 and  n2 = 20 is 127

Neither of the U values above are equal to or below this figure. The differences between section 2 and section 3 are therefore not significant at the p = 0.05 level.

 

Comparison between results obtained for sections 3 (autumn cut) and 4 (spring cut)

 

Sample 

. . . . . . . . . . . . . . 8 9 10 10 13 . .
Rank . . . . . . . . . . . . . . 14.5 16 17.5 17.5 19 . .

Sample 

0 0 0 0 0 1 1 1 1 2 4 6 6 8 . . . . . 15 .
Rank 3 3 3 3 3 7.5 7.5 7.5 7.5 10 11 12.5 12.5 14.5 . . . . . 20 .

Sample 

20 24 25 27 . 40 45 45 45 49 55 60 60 . 67 70 . 80 . . Sum
Rank 21 22 23 24 . 26 28 28 28 30 31 33 33 . 35 36 . 38 . . 520.5

Sample 

. . . . 30 . . .   . . . . 60 . . 75 . . . Sum
Rank . . . . 25 . . ..   . . . . 33 . . 37 . . .

220.5

wpeC3.jpg (1196 bytes)R1 = 520.5          n1 = 20

wpeC3.jpg (1196 bytes)R2 = 220.5          n2   = 18

U1 = n1 x n2 + n2(n2 + 1 ) - wpeC3.jpg (1196 bytes)R2 

U1 = 20 x 18 + 18(18 + 1) - 220.5

U1 = 360 + 171 - 220.5

U1 = 310.5

U2 = n1 x n2 + n1(n1 + 1 ) - wpeC3.jpg (1196 bytes)R1  

U2 = 20 x 18 + 20(20 + 1) - 520.5

U2 = 360 + 210 - 520.5

U2 =  49.5

The critical value of U for  n1 = 20 and  n2 = 18 is 112

The lowest U value (U2) of 49.5 is well below this figure. The differences between section 3 and section 4 are therefore significant at the p = 0.05 level.

 

Comparison between results obtained for sections 1 (autumn cut) and 4 (spring cut)

Sample 

. . . . . . . . . . . 5 5 . . . 10 . 20 20 30
Rank . . . . . . . . . . . 12.5 12.5 . . . 17 . 19.5 19.5 21.5

Sample 

0 0 0 0 0 1 1 1 1 2 4 . . 6 6. 8. .. .15 .. . ..
Rank 3 3 3 3 3 7.5 7.5 7.5 7.5 10 11 . . 14.5 14.5 16 . 18 . . ..

Sample 

. 45 50 . 70 . 90 . . . . . . . . . . . . . Sum
Rank . 23 24 . 26 . 28 . . . . . . . . . . . . . 203.5

Sample 

30 . . 60 . 75 . . . . . . . . . . . . . . .Sum
Rank 21.5 . . 25 . 27 . . . . . . . . . . . . . . 202.5.

wpeC3.jpg (1196 bytes)R1 = 203.5          n1 = 10

wpeC3.jpg (1196 bytes)R2 = 202.5          n2   = 18

U1 = n1 x n2 + n2(n2 + 1 ) - wpeC3.jpg (1196 bytes)R2 

U1 = 10 x 18 + 18(18 + 1) - 202.5

U1 = 180 + 171 - 202.5

U1 = 148.5

U2 = n1 x n2 + n1(n1 + 1 ) - wpeC3.jpg (1196 bytes)R1  

U2 = 10 x 18 + 10(10 + 1) - 203.5

U2 = 180 + 55 - 203.5

U2 =  31.5

The critical value of U for  n1 = 10 and  n2 = 18 is 48

The U2 value of 31.5 is below this figure. The differences between section 1 and section 4 are therefore significant at the p = 0.05 level.

 

Summary of Results

% Bluebell Cover Section 1 (autumn) Section 2 (spring) Section 3 (autumn) Section 1 (autumn)
  Section 2 (spring) Section 3 (autumn) Section 4 (spring) Section 4 (spring)
p = 0.05 level Not significant Not significant Significant Significant


Click here to return to the exercise answers

 

Answers Contents