Chi Squared Analysis

Here are the directions for your Chi Squared Analysis in your fly lab write up.

1. The purpose of doing a statistical test:
a. Data varies from expected results
b. We need to know if variation is expected
c. Conduct statistical analysis to know:
i. If data falls within random variation
ii. Suggests we should find an alternative hypothesis

2. The purpose of the Chi squared test is to determine if your results vary significantly from expected numbers.

3. Steps of the Chi Squared Test:
a. State your NULL HYPOTHESIS (the null hypothesis states that your data do not differ significantly from your expected results).
b. Figure out expected ratios for data
c. Compile your data
d. Find the difference between the observed and expected number of each phenotype.
e. Square the differences from step 4.
f. Divide the squared differences from step 5 by the expected number of each phenotype.
g. Add the resulting values to determine a Chi Squared Value




4. To complete the former steps:
a. Use a table like this:

Phenotype Observed (o) Expected (e) 0-e (o-e)^2
Red eyes 51 50 1 1
White eyes 49 50 -1 1

Then add the values in the (o-e)^2 column. This is your Chi Squared value.

5. Using a Chi Squared Table:
a. Determine a Chi Squared value as shown above.
b. Determine the Degrees of freedom (# of phenotypic classes -1)
c. Determine acceptable level of probability—for the fly lab, use p>0.05 (for a discussion of p value, see point 6)
d. Find your Critical Value (the number in the cell where your degrees of freedom and p value intersect). See the table below.
e. If your calculated Chi Squared value is less than the critical value, accept your null hypothesis (there is no significant difference between observed and expected results).
f. If your Chi Squared value is equal to or greater than the critical value, propose an alternative hypothesis.

6. Determining a p value
a. The p value is the probability that the difference between your observed and expected values is due to chance alone.
b. In biological research, we generally accept p > 0.05. A p value of 0.05 means that the results we observed would be due to due to chance 5% of the time.

7. Interpreting Your Results:
a. Check your calculated Chi Squared value.
b. Compare it to the Critical Value from the table.
c. If your calculated Chi Squared value is less than the critical value, accept your null hypothesis (there is no significant difference between observed and expected results). For your flies, this means that your data match your prediction about the F2 phenotypes.
d. If your Chi Squared value is equal to or greater than the critical value, propose an alternative hypothesis. In your paper, make a suggestion about how the data you collected occurred that is different from your original hypothesis.

8. Chi Squared Table:






9. A practice problem:

Thomas Morgan did the following dihybrid cross: grey X black bodies and normal X vestigial wings. Grey bodies and normal wings are dominant.
• The cross can be symbolized: b+b vg+vg X bb vgvg, where b+ is grey body, b is black body, vg+ is normal wings and vg is vestigial wings.

• For this cross, he observed the following phenotypic ratios:
Grey-Normal: 965
Grey-Vestigial: 206
Black-Normal: 185
Black-Vestigial: 944

Answer the following questions:

What are the expected phenotypic ratios for a normal dihybrid cross?
If these traits normally show 20% recombination, what are the expected phenotypic ratios?
What is your null hypothesis?
What is your Chi Squared value?
How many Degrees of Freedom are there?
If we accept 90% probability, what is the critical value?
Should we accept or reject you null hypothesis?