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Did Mendel fake is data?

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- Do a quick internet search and can you find opinions that support or reject this point of view.
- Does it matter? Should it matter?

- 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?

- A “Goodness of fit” test
- A statistical way to “Reject the 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.

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.

- 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 - 502 / 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.

Chi-Square 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.

- 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.

- 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).

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.

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?

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.

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

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

- Dominance
- Segregation
- Independent Assortment

- 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?

- A quick review of genetic material….
- Chromosome
- Chromatin
- DNA
- Gene
- Nucleotide
- Nuclear proteins?

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

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