1. Will use Fruit Flies for our example
R = Red eyes Rr X Rr
r = White eyes

2. The Chi-Square Test
Used to confirm whether a set of data follows a specific probability distribution.
IE…how likely is it that deviations from expected results are due solely to chance?

3. Goodness-of-fit test
Uses a sample to test whether a frequency distribution fits the predicted distribution
Example: Used to answer the following ques
Can we conclude that the 3:1 ratio is true based on the observation of _____(#) of fruit flies.

4. Observed vs. Expected Frequencies
The chi-square test basically compares the observed (O) and the expected (E) frequencies to determine whether there is a statistically significant difference
Observed frequency is the # of flies seen for each phenotype
Expected frequency is the # of flies expected for each penotype
Example: if cross is a monohybrid one, you would expect a 3:1 phenotypic ratio. Therefore, if you observed 100 flies, 75 of them should have the dominant phenotype, while 25 of them should have the recessive phenotype

5. Chi-square statistic
Use the following equation:

6. Determining the Critical Chi-Square Score
Use an already constructed table to see where your Chi-square value falls.
Which row you look in depends on the number of degrees of freedom.
The number of degrees of freedom is equal to the number of phenotypic categories minus 1.
Monohybrid…
Dihybrid…
Sex-linked…

7. Chi-square Values and Probabilities
2 ways to analyze
if X2 is less than number in box, good fit…
If P value is greater than .05, than good fit
Means your data did not happen by chance.

8. Let’s do an example problem
A cross between two fruit flies that are heterozygous for red eyes produced the following offspring:
260 Red eyes
178 White eyes
Calculate X2 for this experiment