Genetics WorkShop Number Three The Chi-Square Worksheet - STUDENT'S COPY by Dr Jamie Love 2002 - 2010

Mendel's data from one experiment was ...
P = smooth seeds crossed with wrinkled seeds
F₁ = all smooth seeds (so smooth is dominant and wrinkled is recessive)
F₂ = 5,474 smooth seeds and 1,850 wrinkled seeds

1. What ratio did he observe?

2. What ratio did he expect?

You should understand that the chi-square compares the NUMBER (not ratio) observed to the NUMBER (not ratio) expected.
You already know the number observed.
Smooth =
Wrinkled =

3. What is the total number of seeds?

4. What number of wrinkled is expected?

5. What number of smooth is expected?

6. What is the difference between observed and expected smooth?

7. What is the difference between observed and expected wrinkled?

8. What is the square of the difference between the observed and expected smooth?

9. What is the square of the difference between the observed and expected wrinkled?

10. What is the square of the difference between the observed and expected smooth, divided by the expected number of smooth?

11. What is the square of the difference between the observed and expected wrinkled, divided by the expected number of wrinkled?

12. What is the sum of the "squared differences per expected"?

A. Significance Level
Any chi-square larger than the value from the 5% Table indicates an experiment in which the ratios observed are so far off the ratios expected that we have to conclude that the ratios expected are !
B. Degrees of Freedom
The "degrees of freedom" are one less than the number of .

13. Name all the different classes in the experiment (earlier).

14. How many degrees of freedom were in that experiment?

Here's a portion of the Chi Square Significance Table. 15. Is the chi-square you calculated within the boundary of "the possible"?

Degrees of Freedom 5 % Significance Levels 1 3.84 2 5.99 3 7.81 4 9.49

When doing a Chi-square it helps to set it up as a table and (perhaps helps) to understand that all we have been doing is represented by the equation ² = [(O - E)²/E]

Consider these results among the F₂ = 4,400 yellow seeds and 1,624 green seeds.
Use the space below to work out this chi-square using a table (as explained in the workshop).
First, set up a table.
Second, enter the data. Remember, data is what is observed. So data goes in the "observed" (O) column.
Next fill in the "expected" (E) column.
Finally, fill in the rest of the table.

Phenotypes	O	E	O-E	(O-E)2	(O-E)2 E
Total

Is the chi-square you calculated here within the boundary of "the possible"? (Use the Table from earlier.)

Do we accept that these results are within acceptable range of a 3 : 1 ratio?

Consider these results from a dihybrid cross
30 red tall
65 white tall
83 red short
206 white short

Based upon these numbers, which phenotypes are dominant and recessive for the two loci?
The biggest group is the white shorts so they must be the doubly dominant class. - white shorts can be assigned the genotype .
The least represented group, would be the doubly recessive so the red talls are the "1" in the 9 : 3 : 3 :1 ratio and have the genotype .
The other two classes make up the "3" in the ratio. The white talls have the genotype and the red shorts are .

In the space below, arrange your computation table starting with the "observed".
Then determine the "expecteds".
Finally, fill in the rest of the table and calculate the chi-square.

Phenotypes	O	E	O-E	(O-E)2	(O-E)2 E
Total

How many "classes" (categories, groups) are in this experiment?

Now, how many degrees of freedom are in this experiment?

Does the 9 : 3 : 3 : 1 ratio fit the data?

Degrees of Freedom 5 % Significance Levels 1 3.84 2 5.99 3 7.81 4 9.49

What is the expected ratio of boys to girls?

What is the degrees of freedom in that example?

If a particular IVF clinic can, indeed, increase the odds, would you expect the chi-square to be above or below the value of 3.84 (which I got from the table above)?

Store A made $1,000,000
Store B made $3,000,000
Store C brought in $5,000,000.
How would you use the chi-square to test the idea that these stores are different - beyond luck? (Don't do the chi-square - just tell me how you would set it up.)

Store A serves a population that is only a quarter the size of the communities served by stores B and C. Can you redo the chi-square? How?

And finally, what is the degree of freedom for this three-store problem?