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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 X 2 = Σ(d 2 /e) d – deviation from expected value e – expected value Σ – sum of

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Example #1 Expected phenotypic ratio1:1 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? 1 st phenotype 2 nd phenotype observed values4555 expected values (e)5050 deviation (d)-5+5 deviation squared (d 2 )2525 d 2 /e 25/50=0.5 25/50=0.5 X 2 = Σ(d 2 /e) = 0.5 + 0.5 = 1.0

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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 X 2 = 1.0

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Example #2 Phenotypic ratio expected1:1 sample size of 20 would yield expected ratio of 10/10 actual results are 5 and 15 1 st phenotype2 nd phenotype observed values515 expected values (e)1010 deviation (d)-5+5 deviation squared (d 2 )2525 d 2 /e 25/10 = 2.5 25/10 = 2.5 X 2 = Σ(d 2 /e) = 2.5 +2.5 = 5.0 degree of freedom = 1

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X 2 = Σ(d 2 /e) = 2.5 +2.5 = 5.0 degree of freedom = 1 Chi-square test is very sensitive to sample size

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