Genies+R

Grass Bush Grass Bush Grass Bush

1 Black Orange Yellow

11 1 8 2 Black Green Orange Red

6 7 5 2 3 Black Green Orange Yellow

9 3 2 6 4 Black Green Orange Red

5 4 6 5 5 Black Orange Red Yellow

10 6 1 3 6 Black Green Orange Red

8 5 2 5

Chi Test Results: Null hypothesis: There is no significant difference between the frequencies of polymorphism in the two different habitats. There is not any significant variation between the expected and observed values. Alternative hypothesis: There is significant difference between the frequencies of polymorphism in the two different habitats. There is significant variation between the expected and observed values.

2.166667 || 17/6= 2.83333 ||  ||
 * || **Black**  || **Green** || **Orange** || **Red** || **Yellow** || **Total** ||
 * **1** || 11 || 0 || 1 || 0 || 8 || 20 ||
 * **2** || 6 || 7 || 5 || 2 || 0 || 20 ||
 * **3** || 9 || 3 || 2 || 0 || 6 || 20 ||
 * **4** || 5 || 4 || 6 || 5 || 0 || 20 ||
 * **5** || 10 || 0 || 6 || 1 || 3 || 20 ||
 * **6** || 8 || 5 || 2 || 5 || 0 || 20 ||
 * **Total** || 49 || 19 || 22 || 13 || 17 || 120 ||
 * **Expected** || 49/6= 8.166667 || 19/6= 3.166667 || 22/6= 3.66667 || 13/6=

As our expected value for both Red and Yellow fall below 3, we decided to group together Orange and Red in one category and Yellow and Green in another category.
 * || **Black**  || **Green/yellow** || **Orange/red** || **Total** ||
 * **1** || 11 || 8 || 1 || 20 ||
 * **2** || 6 || 7 || 7 || 20 ||
 * **3** || 9 || 9 || 2 || 20 ||
 * **4** || 5 || 4 || 11 || 20 ||
 * **5** || 10 || 3 || 7 || 20 ||
 * **6** || 8 || 5 || 7 || 20 ||
 * **Total** || 49 || 36 || 35 || 120 ||
 * **Expected** || 49/6=8.166667 || 36/6= 6 || 35/6=5.83333 ||  ||


 * Grass 1 || Black || Green/yellow || Orange/red || Total ||
 * Observed || 11  ||  8  ||  1  ||  20  ||
 * Expected || 6.66667  ||  6.66667  ||  6.66667  ||   ||
 * (O-E)2 || 18.7777778  ||  1.77777778  ||  32.1111111  ||   ||
 * (O-E)2/E || 2.8166667  ||  0.266667  ||  4.8166667  ||  7.9  ||
 * P-value ||  ||   ||   ||  0.019255  ||


 * Shrub 1 || Black || Green/yellow || Orange/red || Total ||
 * Observed || 6 || 7 || 7 || 20 ||
 * Expected || 6.66667 || 6.66667 || 6.66667 ||  ||
 * (O-E)2 || 0.44444  ||  0.11111  ||  0.11111  ||   ||
 * (O-E)2/E || 0.06666597  ||  0.01666649  ||  0.01666649  ||  0.099999  ||
 * P-value ||  ||   ||   ||  0.951229  ||


 * Grass 2 || Black || Green/yellow || Orange/red || Total ||
 * Observed || 9  ||  9  ||  2  ||  20  ||
 * Expected || 6.66667  ||  6.66667  ||  6.66667  ||   ||
 * (O-E)2 || 5.444444  ||  5.444444  ||  21.77778  ||   ||
 * (O-E)2/E || 0.81666619  ||  0.81666619  ||  3.26666537  ||  4.89999775  ||
 * P-value ||  ||   ||   ||  0.08629369  ||


 * Shrub 2 || Black || Green/yellow || Orange/red || Total ||
 * Observed || 5  ||  4  ||  11  ||  20  ||
 * Expected || 6.66667  ||  6.66667  ||  6.66667  ||   ||
 * (O-E)2 || 2.77777  ||  7.11111  ||  18.77778  ||   ||
 * (O-E)2/E || 0.41666529  ||  1.06666597  ||  2.81666559  ||  4.29999685  ||
 * P-value ||  ||   ||   ||  0.11648428  ||


 * Grass 3 || Black || Green/yellow || Orange/red || Total ||
 * Observed || 10  ||  3  ||  1  ||  20  ||
 * Expected || 6.66667  ||  6.66667  ||  6.66667  ||   ||
 * (O-E)2 || 11.111111  ||  13.44444  ||  32.11111  ||   ||
 * (O-E)2/E || 1.66666582  ||  2.01666499  ||  4.81666409  ||  8.4999949  ||
 * P-value ||  ||   ||   ||  0.01426422  ||


 * Shrub 3 || Black || Green/yellow || Orange/red || Total ||
 * Observed || 8  ||  5  ||  7  ||  20  ||
 * Expected || 6.66667  ||  6.66667  ||  6.66667  ||   ||
 * (O-E)2 || 1.777778  ||  2.77778  ||  0.111111  ||   ||
 * (O-E)2/E || 0.26666657  ||  0.41666679  ||  0.01666664  ||  0.7  ||
 * P-value ||  ||   ||   ||  0.70468821  ||

Majority our p values (excluding Grass 1 and 3) are greater than 0.05. If the p value is greater than 0.05 it is likely that the distribution is random and thus there is no significant difference in the frequency of polymorphism between the habitats. Therefore we fail to reject the null hypothesis at 5% significance.

On the other hand, for Grassland 1 and 3 the p value is less than 0.05, it is likely that the distribution is not random therefore we reject the null hypothesis in favour of the alternative hypothesis.