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”

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 45 55 expected values (e) 50 50 deviation (d) -5 +5 deviation squared (d2) 25 25 d2/e 25/50=0.5 25/50=0.5 X2 = Σ(d2/e) = 0.5 + 0.5 = 1.0

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

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 5 15 expected values (e) 10 10 deviation (d) -5 +5 deviation squared (d2) 25 25 d2/e 25/10 = 2.5 25/10 = 2/5 X2 = Σ(d2/e) = 2.5 +2.5 = 5.0 degree of freedom = 1

Chi-square test is very sensitive to sample size X2 = Σ(d2/e) = 2.5 +2.5 = 5.0 degree of freedom = 1 Chi-square test is very sensitive to sample size