Group+23+R

Grass Shrub Grass Shrub Grass Shrub

1 Black Green Orange Yellow

5 8 2 5 2 Black Green Red Yellow

3 5 1 11 3 Black Green Orange Red Yellow

5 6 1 1 7 4 Black Green Red Yellow

6 4 4 6 5 Black Green Orange Red Yellow

6 2 4 1 7 6 Black Green Red Yellow

3 8 2 7


 * || Black || Green || Orange || Yellow || red ||  ||
 * Grass 1 || 5 || 8 || 2 || 5 || 0 || 20 ||
 * Shrub 1 || 3 || 5 || 0 || 11 || 1 || 20 ||
 * Grass 2 || 5 || 6 || 1 || 7 || 1 || 20 ||
 * Shrub 2 || 6 || 4 || 0 || 6 || 4 || 20 ||
 * Grass 3 || 6 || 2 || 4 || 7 || 1 || 20 ||
 * Shrub 3 || 3 || 8 || 7 || 7 || 2 || 20 ||
 * ||  ||   ||   ||   ||   || 120 ||

We decided that as green and yellow jelly babies close in colour and difficult to distinguish that we would group them together Reject null hypothesis because the value is greater then 12.59 which is the 5% critical value (see table),
 * Grass || Black || Green & Yellow || Orange || red ||  ||
 * || 5 || 13 || 2 || 0 ||  ||
 * || 5 || 13 || 1 || 1 ||  ||
 * || 6 || 9 || 4 || 1 ||  ||
 * Observed || 16 || 35 || 7 || 2 ||  ||
 * Expected || 15 || 15 || 15 || 15 ||  ||
 * O-E || 1 || 10 || -8 || -13 ||  ||
 * (O-E)2 || 1 || 100 || 64 || 169 ||  ||
 * (O-E)2/E || 0.066667 || 6.666666667 || 4.266667 || 11.26667 || **22.26667** ||
 * d.f |||| (4-1)x(3-1) = 6 ||  ||   ||   ||
 * d.f |||| (4-1)x(3-1) = 6 ||  ||   ||   ||

(d.f. = degrees of freedom)
 * Shrub || Black || Green & Yellow || Orange || red ||  ||
 * || 3 || 16 || 0 || 1 ||  ||
 * || 6 || 10 || 0 || 4 ||  ||
 * || 3 || 15 || 0 || 2 ||  ||
 * Observed || 12 || 41 || 0 || 7 ||  ||
 * Excepted || 15 || 15 || 15 || 15 ||  ||
 * O-E || -3 || 26 || -15 || -8 ||  ||
 * (O-E)2 || 9 || 676 || 225 || 64 ||  ||
 * (O-E)2/E || 0.6 || 45.06666667 || 15 || 4.266667 || 64.93333 ||
 * d.f |||| (4-1)x(3-1) = 6 ||  ||   ||   ||
 * d.f |||| (4-1)x(3-1) = 6 ||  ||   ||   ||


 * Shrub || Black || Green & Yellow || red ||  ||
 * || 3 || 16 || 1 ||  ||
 * || 6 || 10 || 4 ||  ||
 * || 3 || 15 || 2 ||  ||
 * Observed || 12 || 41 || 7 ||  ||
 * Excepted || 15 || 15 || 15 ||  ||
 * O-E || -3 || 26 || -8 ||  ||
 * (O-E)2 || 9 || 676 || 64 ||  ||
 * (O-E)2/E || 0.6 || 45.06666667 || 4.266667 || 49.93333 ||
 * d.f |||| (4-1)x(3-1) = 6 ||  ||   ||
 * d.f |||| (4-1)x(3-1) = 6 ||  ||   ||

In the table above we see that even when the orange snails are omitted from the test (as there were 0 of them) the result is still significant.

Both tests yielded a significant result (rejection of the null hypothesis), this means that we would expect to see deviations from the expected value as large as this less than 5% of the time if the null hypothesis were true. This implies that it is likely that there is a significant difference in the type of snails that live in grassy and shrub areas. The large present of the green/yellow may imply that they are the best adapted snail either environment (grass and shrub land)

Freedom //(df)// |||||||||||||||||||||| **Probability** (//p//)
 * Degrees of

||
 * || 0.95 || 0.90 || 0.80 || 0.70 || 0.50 || 0.30 || 0.20 || 0.10 || 0.05 || 0.01 || 0.001 ||
 * 1 || 0.004 || 0.02 || 0.06 || 0.15 || 0.46 || 1.07 || 1.64 || 2.71 || 3.84 || 6.64 || 10.83 ||
 * 2 || 0.10 || 0.21 || 0.45 || 0.71 || 1.39 || 2.41 || 3.22 || 4.60 || 5.99 || 9.21 || 13.82 ||
 * 3 || 0.35 || 0.58 || 1.01 || 1.42 || 2.37 || 3.66 || 4.64 || 6.25 || 7.82 || 11.34 || 16.27 ||
 * 4 || 0.71 || 1.06 || 1.65 || 2.20 || 3.36 || 4.88 || 5.99 || 7.78 || 9.49 || 13.28 || 18.47 ||
 * 5 || 1.14 || 1.61 || 2.34 || 3.00 || 4.35 || 6.06 || 7.29 || 9.24 || 11.07 || 15.09 || 20.52 ||
 * 6 || 1.63 || 2.20 || 3.07 || 3.83 || 5.35 || 7.23 || 8.56 || 10.64 || **12.59** || 16.81 || 22.46 ||
 * 7 || 2.17 || 2.83 || 3.82 || 4.67 || 6.35 || 8.38 || 9.80 || 12.02 || 14.07 || 18.48 || 24.32 ||
 * 8 || 2.73 || 3.49 || 4.59 || 5.53 || 7.34 || 9.52 || 11.03 || 13.36 || 15.51 || 20.09 || 26.12 ||
 * 9 || 3.32 || 4.17 || 5.38 || 6.39 || 8.34 || 10.66 || 12.24 || 14.68 || 16.92 || 21.67 || 27.88 ||
 * 10 || 3.94 || 4.86 || 6.18 || 7.27 || 9.34 || 11.78 || 13.44 || 15.99 || 18.31 || 23.21 || 29.59 ||
 * |||||||||||||||| Nonsignificant |||||| Significant ||

Source: R.A. Fisher and F. Yates, Statistical Tables for Biological Agricultural and Medical Research, 6th ed., Table IV, Oliver & Boyd, Ltd., Edinburgh, by permission of the authors and publishers.