Bio 121 - Mendelian Genetics
Chi square values - Remember that Chi square operates by comparing the actual, or observed, frequencies to the frequencies we might expect. In other words, chi square compares what actually happened to what hypothetically would have happened if "all other things were equal" (basically, this is our null hypothesis). If our actual results are sufficiently different from the predicted null hypothesis results, we can reject the null hypothesis and claim (in this instance) that no statistically significant relationship exists between our variables.

Our Null Hypothesis (Ho) - "There is no significant difference between our observed Blue/Yellow kernel ratio and the expected Blue/Yellow kernel ratio". In other words our ratio should be very close to the ratio predicted by our knowledge of Genetics.
Chi-square requires that you use numerical values, not percentages or ratios.

Three ears of the F2 generation corn with mostly blue kernels

Results from your Kernel count:

Kernel Color # of Kernels
Blue
Yellow

Your Blue to Yellow Kernel ratio was 0 (Blue): 1 (Yellow).

Although the predicted ratio for a Hybrid cross is 3(Blue):1(Yellow), you will rarely find that exactly 3/4 of the kernels are blue and exactly 1/4 are yellow. We will test that any variation from the predicted 3:1 ratio is due to chance, or something else, using Chi square analysis. We had a total of 68 kernels, so the predicted ratio would be 51(Blue):17(Yellow) [That is 68 total kernels X 3/4 for blue, and 68 total kernels X 1/4 for Yellow].

Calculating your Chi-Square: Fill in the table below. Do 1 column at a time. (example).
(You can find a calculator on a Windows computer by clicking Start -> Programs -> Accessories.)

  Blue Yellow
Observed (o)
Expected (e) 51 17
(o - e)
[subtract e from o in each column]
(o - e)2
[square the value in the column above this one]
(o - e)2/e
[divide the value in the column above this one above by e]
Χ2 = Σ of all (o - e)2/e or..

   Blue (o - e)2/e
+ Yellow (o - e)2/e

[add the (o - e)2/e value for Blue to the (o - e)2/e value for Yellow]. This is your Chi Square value. Its simple!

Interpreting Chi Square Values: We now need some criterion or yardstick against which to measure our chi square value, to tell us whether or not it is significant. What we need to know is the probability of getting a chi square value of a minimum given size even if our variables are not related at all. That is, we need to know how much larger than 0 (the absolute chi square value of the null hypothesis) our table's chi square value must be before we can confidently reject the null hypothesis. The probability we seek depends in part on the degrees of freedom of the table from which our chi square value is derived.

Determining degrees of freedom (df): Degrees of freedom can be calculated as the number of categories in the problem minus 1. In our example, there are two categories (blue and yellow); therefore, there is 1 degree of freedom in our example.

Chi-Square Distribution Table: Using the table below, find the chi square value corresponding to he correct number of degrees of freedom at a confidence probability of 95% (0.05). If our Chi square value is greater than the Chi square value at our desired confidence level, we must reject the null hypothesis and conclude that the difference between observed and expected values is real and not chance. In this case this means either our genetic hypothesis is wrong (we thought this was the result from a hybrid cross) or our sample size was too small.

Degrees of Freedom (df)


Probability (p)

  Not significant Significant
  0.95 0.90 0.80 0.70 0.50 0.30 0.20 0.10 0.05 0.01 0.001

1

0.004 0.02 0.06 0.15 0.46 1.07 1.64 2.71 3.84 6.64 10.83

2

0.10 0.21 0.45 0.71 1.39 2.41 3.22 4.60 5.99 9.21 13.82

3

0.35 0.58 1.01 1.42 2.37 3.66 4.64 6.25 7.82 11.34 16.27

4

0.71 1.06 1.65 2.20 3.36 4.88 5.99 7.78 9.49 13.28 18.47

5

1.14 1.61 2.34 3.00 4.35 6.06 7.29 9.24 11.07 15.09 20.52

6

1.63 2.20 3.07 3.83 5.35 7.23 8.56 10.64 12.59 16.81 22.46

7

2.17 2.83 3.82 4.67 6.35 8.38 9.80 12.02 14.07 18.48 24.32

8

2.73 3.49 4.59 5.53 7.34 9.52 11.03 13.36 15.51 20.09 26.12

9

3.32 4.17 5.38 6.39 8.34 10.66 12.24 14.68 16.92 21.67 27.88

10

3.94 4.86 6.18 7.27 9.34 11.78 13.44 15.99 18.31 23.21 29.59

Questions:

1. Was your chi square value greater or less than that of a probability of (0.05) with 1 degree of freedom? (The above number in Green).

Greater than
Less than

2. Do you accept or reject the null hypothesis?

Accept
Reject

3. How confident are you that the trait for yellow/blue kernel color is controlled by a single pair of alleles?

95% sure
0.05% sure
10% sure
No way, I rejected the null hypothesis

4. In Chi Square analysis, higher chi square values correlate with:

Lower p (higher confidence) values
Higher p (lower confidence) values
Neither
Both

5. At a probability level of 0.01, one could expect variation between observed and expected results to occur due to chance:

1% of the time
5% of the time
10% of the time
99% of the time

Name:
Section - Please select your section from this list