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LECTURE 9 The Chi-Square Test
Micky Vincent
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The Chi-Square Test - Introduction• Many models are useful for
illustrating basic Mendelian genetics.•
Whether you use the fruit fly, corn, sweet pea or some other
system, the basicprinciples are applicable to all diploid systems
including humans.
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The Chi-Square Test - Introduction• Many models are useful for
illustrating basic Mendelian genetics.•
Whether you use the fruit fly, corn, sweet pea or some other
system, the basicprinciples are applicable to all diploid systems
including humans.
DihybridA. Purple - Smooth
B. Yellow – SmoothC. Purple – WrinkleD. Yellow - Wrinkle
MonohybridA.PurpleB.Yellow
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The Chi-Square Test - Introduction
• Note – We are only interested in the number of
PHENOTYPES!!
• Possible dihybridcrosses:
1.RRSuSu X rrsusu2.RRSuSu X RRsusu3.RRSuSu X Rrsusu4.RRSuSu X
RRSusu5.RRSuSu X rrSusu
6.Rrsusu X Rrsusu7.RrSusu X RrSusu8.RRsusu X RRsusu
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The Chi-Square Test - Introduction• One of the advantages of the
Mendelian approach is that it is quantitative and
may be tested mathematically.• A hypothesis is presented as a
null hypothesis, proposing that the observed data
are the same as the predicted results.
- i.e For monohybrid – 3:1For dihybrid – 9:3:3:1
• Therefore, we perform the Chi-Square Test (a statistical
analysis) to see if datafits our hypothesis.
• Also called Goodness of Fit test or Null Hypothesis.• Two
values are involved, an observed value (O), which is the frequency
of a
category from a sample, and the expected frequency (E), which is
calculatedbased upon the claimed distribution.
• The formula for the Chi-Square test is
O = an observed valueE = the expected frequency
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The Chi-Square Test - ExampleIn one dihybrid experiment, this
data was recorded from a total of 381 seeds:
- 216 Round, Yellow Seed; 79 Round, Green Seed; 65 Wrinkled,
Yellow Seed21 Wrinkled, Green
What ratio is expected? Perform a Chi-Square test to validate
the prediction.
Your Tentative Hypothesis: This is a dihybrid cross (RrYy x
RrYy) involving two pairs ofheterozygous genes resulting in a
expected (theoretical) ratio of 9:3:3:1.
Next, find the degree offreedom,
df=n –1n = number of phenotypes
In this case, the degree offreedom,df = n – 1
= 4 – 1= 3
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1.80
The Chi-Square Test - Example
In this table, 1.85 is the closest number. Then go to the top of
the column and locate yourprobability value. In this case the
probability value that lines up with 1.85 is 0.60. Thisnumber means
that the probability that your hypothesis is correct is 0.60 or 60
percent.The probability that your hypothesis is incorrect is 0.40
or 40 percent.
If the calculated chi-square value is less than the 0.05 value,
we accept the hypothesis.If the chi-square value is greater than
the value in the table, we reject the hypothesis.
Threrefore, because the calculated chi-square value is smaller,
then we accept thehypothesis that the data fits a 9:3:3:1
ratio.
