LAB ____: THE CHI-SQUARE TEST

Name __________________________________ Period _________
AP Biology Date ______________________
1. What is the chi-square test used for?
LAB ____: THE CHI-SQUARE TEST
The chi-square test is a statistical test that makes a comparison between the data
collected in an experiment versus the data you expected to find. The chi-square test is a
way to evaluate this variability to get an idea if the difference between real and expected
results are due to normal random chance, or if there is some other factor involved (like
an unbalanced coin or a different inheritance scheme than the one you predicted).
2. Why is probability important in genetics?
Most eukaryotic organisms are diploid. In preparation for sexual reproduction, the two
copies of each chromosome first separate are randomly sorted into the gametes during
meiosis. When gametes from two different parents combine in fertilization, new
combinations of alleles are created. Thus chance plays a major role in determining which
alleles, and therefore which combinations of traits end up in each new individual, so the
inheritance of characteristics is the result of random chance and can be calculated by
using the laws of probability.
3. Briefly describe how the chi-square analysis may be used in genetics.
In classical genetics research where you are trying to determine the inheritance pattern
of a phenotype, you establish your predicted genetic explanation and the expected
phenotype ratios in the offspring (from your Punnett square) as your null hypothesis.
After you make your crosses, you would then compare your observed results (phenotype
counts) against your expected results and complete a chi-square analysis. If the p value is
determined to be greater than .05 then you would accept your null hypothesis (differences
are due to random chance alone) and your genetic explanation for this trait is supported.
If the p value is determined to be .05 or less then you would reject your null hypothesis—
random chance alone can only explain this level of difference fewer than 1 time out of
every 20 times—and your genetic explanation for this trait is unsupported. You therefore
have to consider alternative inheritance patterns for the trait you are researching.
4. Suppose you were to obtain a chi-square value of 7.82 or greater in your data analysis (with
2 degrees of freedom). What would this indicate?
Since 7.82 is between 5.99 (p=.05) and 9.21 (p=.01), I would reject my null hypothesis. If
it were in coin flips, then I would have to say that there was something wrong with my
coin. If it were in a genetics experiment, then I would have to say that my inheritance
pattern model is not supported and I would have to suggest another model.
5. Suppose you were to obtain a chi-square value of 4.60 or lower in your data analysis (with 2
degrees of freedom). What would this indicate?
Since 4.60 is at p=.0.10, I would accept my null hypothesis. If it were in coin flips, then I
would be allowed to say that my coin was a “fair” coin. If it were in a genetics
experiment, then I would be allowed to say that my inheritance pattern model is
supported.
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Adapted by Kim B. Foglia • www.ExploreBiology.com • 2005-2006

Name __________________________________ AP Biology
6. A heterozygous white-fruited squash plant is crossed with a yellow-fruited plant, yielding 200
seeds. Of these, 110 produce white-fruited plants while only 90 produce yellow-fruited
plants. Are these results statistically significant? Explain using chi-square analysis.
Expected: 1 yellow : 1 white ratio
w w
W Ww Ww
w ww ww
A B C D E
Obs Exp Obs - Exp (Obs – Exp) 2 (Obs – Exp) 2
Exp
white-fruit 110 100 10 100 1
yellow-fruit 90 100 -10 100 1
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X 2 Total 2
Degrees of Freedom 1
At x 2 = 2 (df 1), you would get a p value > 0.30 and therefore you would accept your null
hypothesis and you could say that your proposed inheritance pattern was supported.
7. What if there were 2000 seeds and 1100 produced white-fruited plants & 900 yellow-fruited?
Are these results statistically significant? Explain using chi-square analysis.
Expected: 1 yellow : 1 white ratio
w w
W Ww Ww
w ww ww
A B C D E
Obs Exp Obs - Exp (Obs – Exp) 2 (Obs – Exp) 2
Exp
white-fruit 1100 1000 100 10,000 10
yellow-fruit 900 1000 -100 10,000 10
X 2 Total 20
Degrees of Freedom 1
At x 2 = 20 (df 1), you would get a p value

Name __________________________________ AP Biology
8. TEAM DATA: What was your hypothesis (expected values) for your individual team coin
toss?
Exp
H/H 25
H/T 50
T/T 25
What was your calculated chi-square value for your individual team data? _______________
Answers will vary
What p value does this chi-square correspond to? __________________________________
Answers will vary
Was your hypothesis supported by your results? Explain using your chi-square analysis.
___________________________________________________________________________
Answers will vary
___________________________________________________________________________
___________________________________________________________________________
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9. CLASS DATA: What was your hypothesis (expected values) for the class coin toss?
___________________________________________________________________________
Answers will vary
___________________________________________________________________________
What was your calculated chi-square value for the class data? ________________________
Answers will vary
What p value does this chi-square correspond to? __________________________________
Answers will vary
Was your hypothesis supported by the results? Explain using your chi-square analysis.
___________________________________________________________________________
Answers will vary
___________________________________________________________________________
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Adapted by Kim B. Foglia • www.ExploreBiology.com • 2005-2006

Name __________________________________ AP Biology
10. When scientists design research studies they purposely choose large sample sizes. Work
through these scenarios to see why:
a. Just as in your experiment, you flipped 2 coins, but you only did it 10 times. You
collected these data below. Use the chart to calculate the chi-square value:
Obs Exp Obs - Exp (Obs – Exp) 2 (Obs – Exp) 2
Exp
H/H 1 2.5 -1.5 2.25 .9
H/T 8 5 3 9 1.8
T/T 1 2.5 -1.5 2.25 .9
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X 2 Total 3.6
Would you accept or reject the null hypothesis? Explain using your chi-square analysis.
With X 2 =3.6 and df=2, would accept null hypothesis with p>0.10
b. Now you flipped your 2 coins again, but you did it 100 times. You collected these data
below. Use the chart to calculate the chi-square value:
Obs Exp Obs - Exp (Obs – Exp) 2 (Obs – Exp) 2
Exp
H/H 10 25 -15 225 9
H/T 80 50 30 900 18
T/T 10 25 -15 225 9
X 2 Total 36
Would you accept or reject the null hypothesis? Explain using your chi-square analysis.
With X 2 =36 and df=2, would reject null hypothesis with p

Name __________________________________ AP Biology
d. Now, using your understanding of the chi-square test, explain why scientists purposely
choose large sample sizes when they design research studies.
With a small sample size, random chance is “allowed” to play a larger role in the
variation of the data (the difference between observed and expected). In other words, the
probability of getting a ratio of 1:8:1 in 10 flips by random chance is high enough that
the chi-square analysis would allow you to conclude that there is nothing wrong with
your coins. But with a larger sample size, random chance is not “allowed” to play a such
a role. The probability of getting a ratio of 1:8:1 in 100 or 1000 flips by random chance
is so low that the chi-square analysis would force you to conclude that there is something
wrong with your model—you did not use fair coins or you are not a fair flipper. Another
way to look a this is if they are testing the efficacy of a drug, do you want them to test it
on 10 subjects or 10,000 subjects?
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Adapted by Kim B. Foglia • www.ExploreBiology.com • 2005-2006