Homegeneity X2
Part I
An Explanation of Homegeneity
Strickberger, 1968. Genetics. pg. 136-138.
Contingency X2 is used when there is no
prior knowledge of the expected ratios of each factor.
Homogeneity X2 is a more powerful test to
evaluate the relative differences between different
experiments or samples when we have prior knowledge
of the expected values. If the homogeneity X2
is significant, this indicates that there is heterogeneity
among experiments. Heterogeneity is an indication that
there was some unknown source of variability between
experiments. The experimental technique may be flawed
or phenotypes may have been mis-classified in some experiments.
Chi-square distribution is used for sample sizes of
50 or more phenotypes. Due to sampling variation the
observed numbers may not equal the expected numbers.
The X2 test is used to compare how well the
sample fits the expected values.
| X2 = |
S[Observed - Expected]2 |
| Expected |
with summation across each class. Numbers are used
rather than the frequencies of each class. Expected
numbers are calculated by multiplying the total number
by the probability of a given phenotype.
Example
Hartl, Daniel L. 1994. Genetics
3rd ed. Jones and Bartlett. genotBoston
pg. 48
Bb x Bb cross 
F2 99B_: 45bb observed
n = 99 + 45 = 144 3/4
(144): 1/4 (144) expected
108: 36 expected
| X2 = |
(99 - 108)2 |
+ |
(45 - 36)2 |
= 0.75 + 2.25 = 3.00 |
| 108 |
36 |
The larger the calculated X2 value, the
greater the deviation of observed from expected numbers.
Significant deviations result in rejection of the null
hypothesis.
Ho:3:1 ratio
HA: not 3:1 ratio
