1. The Chi-Square Test
The chi-square test is a statistical test commonly used to compare the observed results of a genetic cross with the expected results from genetics ratios
Measures whether any deviation from the predicted norm that occurs in the results of a genetic cross exceeds the deviation that might occur by chance
X2 = Σ(d2/e)
d – deviation from expected value
e – expected value
Σ – “sum of”

2. Example #1 Expected phenotypic ratio 1:1
Sample size of 100 would yield expected ratio of 50/50
Actual results are 45 and 55
Can the deviation be reasonably attributed to chance or is there some other explanation?
1st phenotype 2nd phenotype
observed values
expected values (e)
deviation (d)
deviation squared (d2)
d2/e /50= /50=0.5
X2 = Σ(d2/e) = = 1.0

3. X2 = 1.0 next step is to consult a table of chi-square values
table gives the probability (p) that an amount of deviation as great or greater than that represented by the chi-square value would occur simply by chance
must take into account the number of classes (phenotypes)
# of independent classes is termed degree of freedom
degree of freedom = # of classes (phenotypes) minus 1
in our example: 2 phenotypes – 1 = 1 degree of freedom
X2 = 1.0

4. Example #2 Phenotypic ratio expected 1:1
sample size of 20 would yield expected ratio of 10/10
actual results are 5 and 15
1st phenotype 2nd phenotype
observed values
expected values (e)
deviation (d)
deviation squared (d2)
d2/e /10 = /10 = 2/5
X2 = Σ(d2/e) = = 5.0
degree of freedom = 1

5. Chi-square test is very sensitive to sample size
X2 = Σ(d2/e) = = 5.0
degree of freedom = 1
Chi-square test is very sensitive to sample size