Genetics WorkShop Number Three
by Dr Jamie Love
2002  2010

Mendel's data from one experiment was ...
P = smooth seeds crossed with wrinkled seeds
F_{1} = all smooth seeds (so smooth is dominant and wrinkled is recessive)
F_{2} = 5,474 smooth seeds and 1,850 wrinkled seeds
1. What ratio did he observe?
5474 / 1850 = 2.9589189 : 1 = 2.96 : 1
2. What ratio did he expect?
3 : 1
You should understand that the chisquare compares the NUMBER (not ratio) observed to the NUMBER (not ratio) expected.
You already know the number observed.
Smooth = 5474
Wrinkled = 1850
3. What is the total number of seeds?
7324
4. What number of wrinkled is expected?
7324 / 4 = 183
5. What number of smooth is expected?
1831 X 3 = 5493 or 7324 X 3/4 = 5493
6. What is the difference between observed and expected smooth?
5474  5493 = 19
7. What is the difference between observed and expected wrinkled?
1850  1831 = 19
8. What is the square of the difference between the observed and expected smooth?
19^{2} = 361 or 19 X 19 = 361
9. What is the square of the difference between the observed and expected wrinkled?
19^{2} = 361 or 19 X 19 = 361
10. What is the square of the difference between the observed and expected smooth, divided by the expected number of smooth?
361 / 5493 = 0.06572 = 0.066
11. What is the square of the difference between the observed and expected wrinkled, divided by the expected number of wrinkled?
361 / 1831 = 0.19716 = 0.197
12. What is the sum of the "squared differences per expected"?
0.066 + 0.197 = 0.263 the ^{2} = 0.263
Therefore, the chisquare for this experiment is ^{2} = 0.263.
A. Significance Level
Any chisquare 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 wrong!
B. Degrees of Freedom
The "degrees of freedom" are one less than the number of classes.
13. Name all the different classes in the experiment (earlier).
Smooth and Wrinkled
14. How many degrees of freedom were in that experiment?
2  1 = 1
Here's a portion of the Chi Square Significance Table.
15. Is the chisquare you calculated within the boundary of "the possible"?


When doing a Chisquare 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 F_{2} = 4,400 yellow seeds and 1,624 green seeds.
Use the space below to work out this chisquare 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.
E 

4518 
118 
13,924 
3.08 

1506 
118 
13,924 
9.24 

Is the chisquare you calculated here within the boundary of "the possible"? (Use the Table from earlier.)
NO! ^{2} = 12.32 but, with one degree of freedom we cannot accept any ratio that gives us a chisquare larger than 3.84.
Do we accept that these results are within acceptable range of a 3 : 1 ratio?
No! We must reject the 3 : 1 ratio. This data is far off the 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 WS.
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 wwss.
The other two classes make up the "3" in the ratio. The white talls have the genotype Wss and the red shorts are wwS.
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 chisquare.
E 

(WS) 
216 
10 
100 
0.463 

(wwS) 
72 
11 
121 
1.681 

(Wss) 
72 
7 
49 
0.681 

(wwss) 
24 
6 
36 
1.500 

How many "classes" (categories, groups) are in this experiment?
Four (Red and tall, White and tall, Red and short, White and short)
Now, how many degrees of freedom are in this experiment?
Three (4 1 )
Does the 9 : 3 : 3 : 1 ratio fit the data?
Yes!


What is the expected ratio of boys to girls?
1 : 1
What is the degrees of freedom in that example?
There are two categories (classes) so there is one degree of freedom.
If a particular IVF clinic can, indeed, increase the odds, would you expect the chisquare to be above or below the value of 3.84 (which I got from the table above)?
If the IVF clinic can change the ratio from the expected 1 : 1 then the chisquare, calculated on the number of daughters (or sons) born, would be greater than 3.84.
Store A made $1,000,000
Store B made $3,000,000
Store C brought in $5,000,000.
How would you use the chisquare to test the idea that these stores are different  beyond luck? (Don't do the chisquare  just tell me how you would set it up.)
You would "expect" a 1 : 1 : 1 ratio in the revenues if they were all the same. You would expect
Store A = $3,000,000
Store B = $3,000,000
Store C = $3,000,000
You could now find, for each store, the difference between expected and observed revenues, square the difference, divide that by the expected and then add all three together to get a chisquare value.
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 chisquare? How?
The information about the populations tells you that there are four times as many likely customers for stores B and C as A. You can express that as a ratio of 1 : 4 : 4.
And finally, what is the degree of freedom for this threestore problem?
There are three categories (Stores, A, B and C) so there are two degrees of freedom.