Snatchers+R

Wood Bush Bush Bush Wood Wood

1 Black Green Orange Red Yellow

6 7 1 1 5 2 Black Green Orange Red

3 2 9 6 3 Black Green Orange Red

5 4 4 7 4 Black Green Orange Red

4 6 7 3 5 Black Green Orange Red Yellow

9 3 1 4 3 6 Black Green Red Yellow

5 8 4 3

__**Chi-Squared Analysis**__


 * =  ||||||= **Observed Frequencies** ||=   ||=   ||=   ||~   ||=   ||||||= **Observed Frequencies** ||=   ||=   ||=   ||
 * =  ||= Black ||= Green ||= Orange ||= Red ||= Yellow ||= Total ||~   ||=   ||= Black ||= Green ||= Orange ||= Red ||= Yellow ||=   ||
 * = Woods 1 ||= 6 ||= 7 ||= 1 ||= 1 ||= 5 ||= 20 ||~  ||= Bush 1 ||= 3 ||= 2 ||= 9 ||= 6 ||= 0 ||= 20 ||
 * = Woods 2 ||= 9 ||= 3 ||= 1 ||= 4 ||= 3 ||= 20 ||~  ||= Bush 2 ||= 5 ||= 4 ||= 4 ||= 7 ||= 0 ||= 20 ||
 * = Woods 3 ||= 5 ||= 8 ||= 4 ||= 3 ||= 0 ||= 20 ||~  ||= Bush 3 ||= 4 ||= 6 ||= 7 ||= 3 ||= 0 ||= 20 ||
 * = Total ||= 20 ||= 18 ||= 6 ||= 8 ||= 8 ||= 60 ||~  ||= Total ||= 12 ||= 12 ||= 20 ||= 16 ||= 0 ||= 60 ||
 * =  ||||||= **Expected Frequencies** ||=   ||=   ||=   ||~   ||=   ||||||= **Expected Frequencies** ||=   ||=   ||=   ||
 * =  ||= Black ||= Green ||= Orange ||= Red ||= Yellow ||= Total ||~   ||=   ||= Black ||= Green ||= Orange ||= Red ||= Yellow ||= Total ||
 * = Woods 1 ||= 6.666667 ||= 6 ||= 2 ||= 2.666667 ||= 2.666667 ||= 20 ||~  ||= Bush 1 ||= 4 ||= 4 ||= 6.666667 ||= 5.333333 ||= 0 ||= 20 ||
 * = Woods 2 ||= 6.666667 ||= 6 ||= 2 ||= 2.666667 ||= 2.666667 ||= 20 ||~  ||= Bush 2 ||= 4 ||= 4 ||= 6.666667 ||= 5.333333 ||= 0 ||= 20 ||
 * = Woods 3 ||= 6.666667 ||= 6 ||= 2 ||= 2.666667 ||= 2.666667 ||= 20 ||~  ||= Bush 3 ||= 4 ||= 4 ||= 6.666667 ||= 5.333333 ||= 0 ||= 20 ||
 * = Total ||= 20 ||= 18 ||= 6 ||= 8 ||= 8 ||= 60 ||~  ||= Total ||= 12 ||= 12 ||= 20 ||= 16 ||= 0 ||= 60 ||
 * = Total ||= 20 ||= 18 ||= 6 ||= 8 ||= 8 ||= 60 ||~  ||= Total ||= 12 ||= 12 ||= 20 ||= 16 ||= 0 ||= 60 ||

 As the expected frequencies of Red, Yellow & Orange are below 3, these polymorphisms must be grouped together (also based on our understanding of Jellybaby genetics). However, in the Bush habitat no yellow babies were found; they must be omitted from the analysis.
 * =  ||=   ||||||= **Observed Frequencies** ||=   ||=   ||~   ||=   ||=   ||||||= **Observed Frequencies** ||=   ||=   ||
 * =  ||= Black ||= Green ||||||= Orange, Red & Yellow ||= Total ||~   ||=   ||= Black ||= Green ||||||= Orange & Red ||= Total ||
 * = Woods 1 ||= 6.666667 ||= 6 ||||||= 7.333333333 ||= 20 ||~  ||= Bush 1 ||= 3 ||= 2 ||||||= 15 ||= 20 ||
 * = Woods 2 ||= 6.666667 ||= 6 ||||||= 7.333333333 ||= 20 ||~  ||= Bush 2 ||= 5 ||= 4 ||||||= 11 ||= 20 ||
 * = Woods 3 ||= 6.666667 ||= 6 ||||||= 7.333333333 ||= 20 ||~  ||= Bush 3 ||= 4 ||= 6 ||||||= 10 ||= 20 ||
 * = Total ||= 20 ||= 18 ||= 22 ||= 0 ||= 0 ||= 60 ||~  ||= Total ||= 12 ||= 12 ||||||= 36 ||= 60 ||
 * =  ||||||= **Expected Frequencies** ||=   ||=   ||=   ||~   ||=   ||||||= **Expected Frequencies** ||=   ||=   ||=   ||
 * =  ||= Black ||= Green ||||||= Orange, Red & Yellow ||= Total ||~   ||=   ||= Black ||= Green ||||||= Orange & Red ||= Total ||
 * = Woods 1 ||= 4 ||= 4 ||||||= 12 ||= 20 ||~  ||= Bush 1 ||= 4 ||= 4 ||||||= 12 ||= 20 ||
 * = Woods 2 ||= 4 ||= 4 ||||||= 12 ||= 20 ||~  ||= Bush 2 ||= 4 ||= 4 ||||||= 12 ||= 20 ||
 * = Woods 3 ||= 4 ||= 4 ||||||= 12 ||= 20 ||~  ||= Bush 3 ||= 4 ||= 4 ||||||= 12 ||= 20 ||
 * = Total ||= 12 ||= 12 ||||||= 36 ||= 60 ||~  ||= Total ||= 12 ||= 12 ||||||= 36 ||= 60 ||
 * = Total ||= 12 ||= 12 ||||||= 36 ||= 60 ||~  ||= Total ||= 12 ||= 12 ||||||= 36 ||= 60 ||

D.O.F = 4 (3-1 x 3-1) //p = 13.77777911// According to a table of P values, with 4 degrees of freedom 13.7778 is significant, with a //p// value between 0.05 and 0.001. We can reject the null hypothesis; there is a significant difference in the frequency of jelly babies in the woodland habitat & a low probability (< 5%) that sampling error would produce these results.
 * H o - There will be no significant differences in the frequency of jellybaby polymorphisms in the Woodland Habitat**
 * = O - E ||
 * Black || Green |||||| Orange, Red & Yellow ||  ||
 * 2.666667 || 2 |||||| -4.666666667 ||  ||
 * 2.666667 || 2 |||||| -4.666666667 ||  ||
 * 2.666667 || 2 |||||| -4.666666667 ||  ||
 * 8.000001 || 6 |||||| -14 ||  ||
 * = (O - E)2 (Woodland) ||
 * Black || Green |||||| Orange, Red & Yellow ||  ||
 * 64.00002 || 36 |||||| 196 ||  ||
 * (O - E)2 / E || Total ||
 * 5.333335 || 3 |||||| 5.444444444 || 13.77777911 ||
 * 5.333335 || 3 |||||| 5.444444444 || 13.77777911 ||


 * H o - There will be no significant differences in the frequency of jellybaby polymorphisms in the Bush Habitat**

A //p// value of 0 was obtained. This does not exceed the critical threshold. The null hypothesis must be accepted. There is no significant difference in the frequency of polymorphisms in the Bush habitat.
 * |||||||||| O - E ||  ||
 * || Black || Green |||||| Orange, Red & Yellow || Total ||
 * Bush 1 || -1 || -2 |||||| 3 || 0 ||
 * Bush 2 || 1 || 0 |||||| -1 || 0 ||
 * Bush 3 || 0 || 2 |||||| -2 || 0 ||
 * Total || 0 || 0 |||||| 0 || 0 ||
 * = (O - E)2 (Bush) ||  ||
 * Black || Green |||||| Orange, Red & Yellow ||  ||   ||
 * 0 || 0 |||||| 0 ||  ||   ||
 * (O - E)2 / E ||  ||   ||
 * 0 ||  ||||||   ||   ||   ||
 * 0 ||  ||||||   ||   ||   ||


 * H o - There will be no significant differences in the frequency of jellybaby polymorphisms between the Woodland & Bush Habitats **


 * ||||||= O-E ||
 * || Black || Green || Orange, Red & Yellow ||
 * Wood (Total) || 8.000001 || 6 || -14 ||
 * Bush (Total) || 0 || 0 || 0 ||
 * Total || 8 || 6 || -14 ||
 * = (O - E)2 ||
 * Black || Green |||||| Orange, Red & Yellow ||  ||
 * 64.00002 || 36 |||||| 196 ||  ||
 * (O - E)2 / E ||  ||
 * 5.333335 || 3 |||||| 5.444444444 || 13.77777911 ||

A p value of 13.77777911 was obtained. There are 2 degrees of freedom, the table of chi sqared results sets a critical value of 10.60 for p<0.05. As results exceed this value we can reject the null hypothesis. A significant difference in the jellybaby polymorphisms was observed & it is very unlikly that the results obtained were due to sampling error.