Homegeneity X Part I

An Explanation of Homegeneity

Strickberger, 1968. Genetics. pg. 136-138.

Contingency X is used when there is no prior knowledge of the expected ratios of each factor. Homogeneity X 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 X 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 X test is used to compare how well the sample fits the expected values.

X = S[Observed - Expected]
                  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 F d  99B_: 45bb observed
n = 99 + 45 = 144      3/4 (144): 1/4 (144) expected
                              108: 36 expected

X = (99 - 108) + (45 - 36) = 0.75 + 2.25 = 3.00
           108              36

The larger the calculated X value, the greater the deviation of observed from expected numbers. Significant deviations result in rejection of the null hypothesis.
genotHo:3:1 ratio
genotHA: not 3:1 ratio