1. Did Mendel fake is data? Do a quick internet search and can you find opinions that support or reject this point of view. Does it matter? Should it matter?

2. Does the data fit? Problem: Does experimentally determined data fits the results expected from theory (i.e. Mendel ’ s laws as expressed in the Punnett square). Example: –Expected 75% to 25% ratio –Does an observed result of 78 to 22 fit?? 85 to 15?

3. The Chi Square Test A “ Goodness of fit ” test A statistical way to “ Reject the Null Hypothesis ”

4. Null Hypothesis A way to state expected outcome Example 1: Hybrid parents will produce a 3:1 genotypic ration (predicted values based on punnett square analysis) Example 2: Flipping a coin should land on heads 50% of the time. **Chi-square is used to REJECT a hypothesis not to PROVE it.

5. Coin Data If this coin is fair…then we would expect the chi-square analysis to show us the results are due only to chance and not due to some other hypothesis. Let ’ s look how coin data either: –Rejects a hypothesis that a coin is fair or –Suggests that the hypothesis that a coin is fair is likely.

6. The Formula

7. Example Expected results of a coin toss (the Null Hypothesis): 50 heads, 50 tails Observed results: 55 heads, 45 tails Now it's just a matter of plugging into the formula:  2 = (55 - 50) 2 / 50 + (45 - 50 2 / 50 = (5) 2 /50 + (-5) 2 / 100 = 25 / 50 + 25 / 50 = 0.50 + 0.50 = 1.0 This is our chi-square value: now we need to see what it means and how to use it.

8. Chi-Square Table

9. Using the Table In our example of 55 heads to 45 tails, we calculated a chi-square value of 1.0, with 1 degree of freedom. Looking at the table, 1 d.f. is the first row, and p = 0.05 is the sixth column. Here we find the critical chi-square value, 3.841. Since our calculated chi-square, 1.0, is less than the critical value, 3.841, we “ fail to reject ” the null hypothesis. Thus, an observed ratio of 55 heads to 45 tails is a good fit to 50:50 ratio.

10. Degrees of Freedom A critical factor in using the chi-square test is the “ degrees of freedom ”, which is essentially the number of independent random variables involved. Degrees of freedom is simply the number of classes of offspring minus 1. For our example, there are 2 classes of offspring: heads and tails. Thus, degrees of freedom (d.f.) = 2 -1 = 1.

11. Critical Chi-Square Critical values for chi-square are found on tables, sorted by degrees of freedom and probability levels. Science uses p = 0.05. If your calculated chi-square value is greater than the critical value from the table, you “ reject the null hypothesis ”. If your chi-square value is less than the critical value, you “ fail to reject ” the null hypothesis (that is, you accept that your genetic theory about the expected ratio is correct).

12. Corn and Chi-Square for Real Question: Is this corn the result of the following dihybrid cross: PpSs X PpSs -First do the Punnett Square -Find the expected outcomes -Compare actual to expected by doing chi square. Share your results with a nearby group.

13. Lab Notebook Expectations Introduction: How does the dihybrid cross show Mendel ’ s Law of Independent Assortment? Identify the traits you will be looking at in the corn. Hypothesis: What do you expect from crossing two heterozygotes—may show a Punnett Square. Methods: How did you count a random sample of the corn? What does each kernel on the corn represent?

14. Data and analysis: -Chi-square analysis for your data. -Chi-square analysis for another group ’ s data. -Trend related to each chi-square analysis. Conclusion: -Explain how the chi-square analysis can confirm Mendel ’ s Law of Independent Assortment. -Discuss what genetic linkage is and why this would cause you to reject the null hypothesis shown in a dihybrid cross.

15. Practice How can Chi- square be used to analyze these results?

16. Back to problem set #21 Go back to the genetic recombination problem…do a chi- square analysis as if it was not linkage. What does your analysis tell you?

17. Do Mendel ’ s laws always apply? Dominance Segregation Independent Assortment

18. Questioning Mendel ’ s Peas If all his data made sense, what can we say about the genes he looked at: were they on the same chromosome or on different chromosomes?

19. A quick review of genetic material…. Chromosome Chromatin DNA Gene Nucleotide Nuclear proteins? Does the location of a gene affect inheritance patterns?

20. Genes are linked to chromosomes

21. Crossing-over Cross-overs occur when tetrads form during meiosis Recombination frequencies allow for the creation of chromosome maps

22. Recombination due to cross-overs

23. Recombination frequencies

24. Chromosome map

25. Sex-link chromosomes Genes located on the X or Y chromosomes are linked to gender What observation provide hints that a gene is sex linked?

26. Example: Eye Color in Fruit Flies