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Math & Genetics

Math & Genetics. AP Biology. Laws of Probability. Segregation of the alleles into gametes is like a coin toss (heads or tails = equal probability ) Rule of Multiplication Probability that independent events will occur simultaneously is the product of their individual probabilities.

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Math & Genetics

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  1. Math & Genetics AP Biology

  2. Laws of Probability • Segregation of the alleles into gametes is like a coin toss (heads or tails = equal probability) • Rule of Multiplication • Probability that independent events will occur simultaneously is the product of their individual probabilities

  3. Example #1 • You have 2 coins. What is the probability that you will flip two heads? • Coin #1 = 1 in 2 chance heads = ½ • Coin #2 = 1 in 2 chance heads = ½ • ½ x ½ = ¼ • Answer = 1 in 4 (or, 25%) chance

  4. Example #2 • What is the probability that offspring of an F1 generation cross will be homozygous recessive? (Pp x Pppp) • Mom (Pp) = 1 in 2 chance for p = ½ • Dad (Pp) = 1 in 2 chance for p = ½ • ½ x ½ = ¼ • Answer = 1 in 4 (or, 25%) chance

  5. Laws of Probability, cont. • Rule of Addition • The probability of an event that can occur in two or more independent ways is the sum of the separate probabilities of the different ways.

  6. Example #1 • You have 2 coins. What is the probability that you will flip a heads and a tails?

  7. Example #2 • What is the probability that two heterozygous parents will produce heterozygous offspring? (Pp x PpPp)

  8. Example #3 • What is the probability that two parents heterozygous for both height and flower color will produce tall offspring with purple flowers? • Probability of Tt: • Probability of Pp = ½ (previous example) • Answer = ½ Tt x ½ Pp = ¼ chance of TtPp

  9. Chi Square Analysis • Statistics can be used to determine if differences among groups are significant or simply the result of predictable error • Chi-square test is used to determine if differences in experimental data (what is observed) and expected results is due to chance or some other circumstance

  10. Example • A Punnett square of the F1 cross Gg x Gg would predict the expected portion of green: albino seedlings would be 3:1 • Complete the Expected (e) column and the (o-e) column

  11. There is a small difference between the observed and expected results • Are these data close enough that the difference can be explained by random chance or variation in the sample? • To determine if the observed data fall within acceptable limits, a chi-square analysis is performed

  12. Hypothesis • Null hypothesis • There is no statistically significant difference between the observed and expected data • Alternative hypothesis • Accepted if the chi-square test indicates that the data vary too much from the expected value (in this case, 3:1)

  13. Calculating Chi Square (X2) • Formula: • o = observed number of individuals • e = expected number of individuals • Σ = sum of the values (in this case, the difference between observed and expected, squared, divided by the number expected

  14. This statistical test will examine the null hypothesis, which predicts that the data from the experimental cross from the example will be expected to fit the 3:1 ratio • Complete the rest of your data table

  15. X2 = 5.14 is now compared to the critical values table to determine if it is an acceptable value

  16. Chi-Square Critical Values Table • The chi-square critical values table provides two values that you need to calculate chi-square: • Degrees of freedom. This number is one less than the total number variables (df = n -1, where n is the # of variables) • Example: In a monohybrid cross, such as our example, there are two classes of offspring (green or albino peas). Therefore, there is just one degree of freedom. • Probability. The probability value (p) is the probability that a deviation as great as or greater than each chi-square value would occur simply by chance. • Many biologists agree that deviations having a chance probability greater than 0.05 (5%) are not statistically significant. Therefore, when you calculate chi-square you should consult the table for the p value in the 0.05 row.

  17. If your chi-squared value is below the value for 0.05, you can accept the null hypothesis • If your chi-squared value is above the value for 0.05, you should reject the null hypothesis

  18. Conclusions • We reject our null hypothesis… what does this mean? • Chance alone cannot explain the deviations we observed and there is, therefore, reason to doubt our original hypothesis (or to question our data collection accuracy) • Probability p = 0.05 means that only 5% of the time would you expect to see similar data if the null hypothesis was correct • You are 95% sure the data do not fit a 3:1 ratio • Consider why… • Additional experiments necessary • Sample too small? Errors in data collection?

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