# The Chi-Square Test - Madeira City Schools ```
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R = Red eyes
r = White eyes
Rr X Rr
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?
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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.
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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
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Use the following equation:
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Use an already constructed table to see where
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…
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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.
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A cross between two fruit flies that are
heterozygous for red eyes produced the
following offspring:
◦ 260 Red eyes
◦ 178 White eyes
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Calculate X2 for this experiment
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