BIOL 310 1st Edition Lecture 4 Outline of Previous Lecture- MendelismI. A re-examination of Mendel’s Observations and ConclusionsII. Alternative method for Dihybrid CrossesIII. Mixed CrossesIV. 4 trait mixed crossOutline of Current Lecture:I. Testing agreement of hypotheses and dataa. Chi-Squaresb. What is a P-ValueII. Mendels tests: F2’s of round, yellow X wrinkled, greeni. A re-examination of Mendel’s Observations and ConclusionsCHI-SQUARE (GOODNESS-OF-FIT) TEST- For example: IF YOU FLIP A COIN 100 TIMES YOU “EXPECT”:o 50 heads and 50 tails- Do you really expect to see those results?o No, but expect something close to it- Why not? = random/chance deviation- If flip 10 times versus 100 times, does proportional deviation remain constant?o No, you get a 6:4 vs a 51:49, so as you increase the number of times you flip the coin, the proportion gets closer -Impact of absolute deviation decreases with larger sample sizeMany statistical tests attempt to determine whether observed deviation from theoretical expectation can be explained by random chance aloneHow?1. DEVELOP NULL HYPOTHESIS- observed = expectedOr, No real difference between expected and observedThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.2. USE STATISTICAL METHODS-e.g. CHI-SQUARE TEST, t-Test, and many othersa. CHI-SQUARE TEST :  [(Observed - Expected)2/Expected] for each/all classes- Value compared to table to interpretFOR EXAMPLE:MENDEL'S F2 FLOWER COLOR DATAObserved Expected Expected DEVNumber Proportion Number (O-E) (O-E)2/E705 purple ¾ 697 8 64/697=0.09224 white ¼ 232 -8 64/232=0.28929 total 4/4 929 0 2= 0.37Expected Number= total * proportionDEV = Observed # - Expected #- What is the null hypothesis? o No real difference between E and O- What is the working hypothesis? o ¾ purple: ¼ white- To assess the 2 value, take into account the number of degree's of freedomo Degrees of Freedom (d.f.)= number of classes – 1o In this case, d.f. = 2 classes (purple and white) – 1 = 1 df- By inspection of table: Use top line in table b/c 1 df. Our chi-squared value (0.37) is between 0.016 and 0.455 on 1 df line. - Values at top of the table (P-values): Go to top of table and by inspection, corresponding P value = 0.9 > P > 0.5b. What is a P-Value?So what does this P-value mean? Basically…. If 100 friends of Mendel's independently repeatedthe same test, between 50 and 90 of them would expect to observe as much or more deviation as you did due to random chance aloneIn science, if P ≤ 0.05 (5%): reject the null hypothesis and reject working hypothesis: too muchdeviation to easily be explained by random chance alone. Observed data is NOT consistent withprediction of hypothesis (expected data). Does NOT disprove hypothesisIf P > 0.05: Fail to reject (ACCEPT) null hypothesis and working hypothesis. Observed deviation easily explained by chance alone. Oberved results ARE consistent with predictions of hypothesis (expected data). Does NOT prove hypothesis is correct/right.- In reality, P values around 0.05 are iffy either way and tests often are repeatedIII. Mendels tests: F2's of round, yellow X wrinkled, green- What is the working hypothesis? o 9:3:3:1 ratio of yellow/round to yellow/wrinkled to green/round to green/wrinkled - What is the null hypothesis? o No real difference between E and OF2 Progeny:Obs. Exp Exp Num. Prop # O-E (O-E)2/Eround, yellow 315round, green 108wrinkled, yellow 101wrinkled, green 32556YOU SHOULD KNOW HOW TO FILL OUT THE BOLDED PORTIONS OF THIS CHART! It IS going to be on the