Download Chi Square Analysis

Chi-Square Analysis
AP Biology
So in your P1 you bred a pure
bred tongue roller RR with a
pure bred non-tongue roller rr
and obtain 100% Rr tongue
rollers in the F1. Now you
breed to of the F1 and get
this….
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In the event we had 100 offspring we should
get what phenotypic ratio? (Based on the
data above?) 3:1 so that…..
75 tongue rollers and 25 non-tongue rollers
BUT, what if we don’t get that exactly? What
if I get 81 tongue rollers and 19 non-tongue
rollers….is that ok? Or is that a difference
that is a problem?
To review
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We expected a 3:1 ratio of tongue to nontongue rollers or 75 rollers : 25 non-rollers.
Is our data close enough? Can we say with
certainty that tongue rolling is Mendelian and
there is no other inheritance issues going on?
Are we confident that we can accept those
differences as due to “random chance
alone”?
Validity of genetic crosses
CHI SQUARE ANALYSIS:
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The chi square analysis allows you to use
statistics to determine if your data is “good” or
“non-biased” or if the data is “bad” or “biased”
If statistics show the data is biased this means
that the data is statistically to far from what you
expected and something is causing the difference
beyond just normal chance occurrences.
In genetics, we are using laws of probability to
determine possible outcomes for genetic crosses.
How do we know if our data is a “good fit” for what
we predicted?
WE PERFORM A CHI SQUARE ANALYSIS!
CHI SQUARE FORMULA:
NULL HYPOTHESIS:
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The hypothesis is termed the null
hypothesis which states
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That there is NO substantial
statistical deviation (difference)
between observed values and the
expected values.
In other words, the results or
differences that do exist between
observed and expected outcomes are
totally random and occurred by
chance alone. And so we can accept
our original idea that tongue rolling is
a Mendelian, dominant trait.
CHI SQUARE VALUE:
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If the null hypothesis is supported by analysis
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The assumption is that mating is random and normal gene
segregation and independent assortment occurred.
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Note: this is the assumption in all genetic crosses! This is
normal meiosis occurring and we would expect random
segregation and independent assortment.
If the null hypothesis is not supported by analysis
•
The deviation (difference) between what was observed and
what the expected values were is statistically too far
apart…something non-random must be occurring….
•
Possible explanations:??????
DF VALUE:
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In order to determine the probability using a chi
square chart you need to first determine the
degrees of freedom (DF)
DEGREE OF FREEDOM: is the number of
phenotypic possibilities in your cross minus one.
 DF = # of groups (phenotype classes) – 1
Using the DF value, determine the probability or
distribution using the Chi Square table (given)
If the level of significance read from a given table
is less than or equal to 0.05, it means that
data is 95% probable of being duplicated
and thus, we accept it.
Let’s try it!
Expected
Tongue
rollers
Non-rollers
χ2 = Sum of all: (O-E)2
E
75
Observed
(Actual)
81
25
19