Presentation on theme: "The Chi Square Test A statistical method used to determine goodness of fit Goodness of fit refers to how close the observed data are to those predicted."— Presentation transcript:
1 The Chi Square TestA statistical method used to determine goodness of fitGoodness of fit refers to how close the observed data are to those predicted from a hypothesisNote:The chi square test does not prove that a hypothesis is correctIt evaluates to what extent the data and the hypothesis have a good fit
2 The Chi Square Test (we will cover this in lab; the following slides will be useful to review after that lab)The general formula is(O – E)2c2 = SEwhereO = observed data in each categoryE = observed data in each category based on the experimenter’s hypothesisS = Sum of the calculations for each category
3 Consider the following example in Drosophila melanogaster Gene affecting wing shapec+ = Normal wingc = Curved wingGene affecting body colore+ = Normal (gray)e = ebonyNote:The wild-type allele is designated with a + signRecessive mutant alleles are designated with lowercase lettersThe Cross:A cross is made between two true-breeding flies (c+c+e+e+ and ccee). The flies of the F1 generation are then allowed to mate with each other to produce an F2 generation.
4 Applying the chi square test The outcomeF1 generationAll offspring have straight wings and gray bodiesF2 generation193 straight wings, gray bodies69 straight wings, ebony bodies64 curved wings, gray bodies26 curved wings, ebony bodies352 total fliesApplying the chi square testStep 1: Propose a null hypothesis (Ho) that allows us to calculate the expected values based on Mendel’s lawsThe two traits are independently assorting
5 Step 2: Calculate the expected values of the four phenotypes, based on the hypothesis According to our hypothesis, there should be a 9:3:3:1 ratio on the F2 generationPhenotypeExpected probabilityExpected numberObserved numberstraight wings, gray bodies9/169/16 X 352 = 198193straight wings, ebony bodies3/163/16 X 352 = 6664curved wings, gray bodies62curved wings, ebony bodies1/161/16 X 352 = 2224
7 Step 4: Interpret the chi square value The calculated chi square value can be used to obtain probabilities, or P values, from a chi square tableThese probabilities allow us to determine the likelihood that the observed deviations are due to random chance aloneLow chi square values indicate a high probability that the observed deviations could be due to random chance aloneHigh chi square values indicate a low probability that the observed deviations are due to random chance aloneIf the chi square value results in a probability that is less than 0.05 (ie: less than 5%) it is considered statistically significantThe hypothesis is rejected
8 Step 4: Interpret the chi square value Before we can use the chi square table, we have to determine the degrees of freedom (df)The df is a measure of the number of categories that are independent of each otherIf you know the 3 of the 4 categories you can deduce the 4th (total number of progeny – categories 1-3)df = n – 1where n = total number of categoriesIn our experiment, there are four phenotypes/categoriesTherefore, df = 4 – 1 = 3Refer to Table 2.1
10 Step 4: Interpret the chi square value With df = 3, the chi square value of 1.06 is slightly greater than (which corresponds to P-value = 0.80)P-value = 0.80 means that Chi-square values equal to or greater than are expected to occur 80% of the time due to random chance alone; that is, when the null hypothesis is true.Therefore, it is quite probable that the deviations between the observed and expected values in this experiment can be explained by random sampling error and the null hypothesis is not rejected. What was the null hypothesis?