Download Chi-Square Goodness of Fit

The Hypothesis
The Hypothesis is a simple statement of the Genetic Inheritance of the
trait(s) of interest.
Example:
Ÿ The trait is Simple Mendelian.
Ÿ The traits have Duplicate Dominant Epistasis
Ÿ The trait is Simple Mendelian with a Penetrance of 80%
Ideally,The Hypothesis is created before the experiment. Often, you
will conduct a preliminary experiment to determine The Hypothesis,
then do a final experiment to test it.
Hypothesis for the Experiment
This is a statement of what we expect the results of experiment to be
if The Hypothesis is correct. It will change, depending on the
experiment used to test The Hypothesis.
Examples:
Ÿ The dihybrid cross gives a 3:1 ratio of Blue to Red
Ÿ The monohybrid cross gives a 2:1 ratio of Agouti to Yellow
Ÿ The trihybrid cross gives a 28:16:15:6:2 ratio.
The Experiment
The experiment is designed to be able to distinguish The Hypothesis
from other possible alternatives. While the mono-, di-, tri-hybrid
crosses are often used, many crosses are possible. Depending on the
question, other experiments may be more powerful, e.g., the test
cross is used when testing for linkage.
The Data
For Chi-Square Goodness of Fit Tests, the data consist of observed
number of individuals with each of the traits. Which traits are
expected and their frequencies depend on the Experimental
Hypothesis. The data can be tabulated as:
Phenotype
Brown
Albino
Total
Observed
80
20
100
Chi-Square Goodness of Fit
Phenotype
Brown
Albino
Total
Expected
Frequency
3/4
1/4
1
Chi-Square Goodness of Fit
Phenotype
Brown
Albino
Total
Expected
Frequency
3/4
1/4
1
Observed
80
20
100
Chi-Square Goodness of Fit
Phenotype
Brown
Albino
Total
Expected
Frequency
3/4
1/4
1
Observed Expected
80
75
20
25
100
100
Chi-Square Goodness of Fit
Phenotype
Brown
Albino
Total
Expected
Frequency
3/4
1/4
1
Observed Expected
80
75
20
25
100
100
O-E
5
-5
0
Chi-Square Goodness of Fit
Phenotype
Brown
Albino
Total
Expected
Frequency
3/4
1/4
1
Observed Expected
80
75
20
25
100
100
O-E
5
-5
0
(O−E ) 2
E
0.33
1
1.33
Chi Square Table
Degrees of
Freedom (df)
Chi-Square (x 2 )
1
3.84
2
5.99
3
7.82
4
5
6
7
9.49 11.07 12.59 14.07
Results of the Chi-Square Test
Statistical Result:
Ÿ If the calculated Chi-Square is greater than the tabled value,
Reject the Hypothesis.
Ÿ If the calculated Chi-Square is smaller than the tabled value,
Fail to Reject the Hypothsis.
Genetic Conclusion
Relates back to The Hypothesis.
If Reject the Hypothesis
vThere is enough evidence from this experiment to conclude
that Brown vs Albino is not Simple Mendelian.
Genetic Conclusion
Relates back to The Hypothesis.
If Reject the Hypothesis
vThere is enough evidence from this experiment to conclude
that Brown vs Albino is not Simple Mendelian.
If Fail to Reject the Hypothesis
vSimple Mendelian Inheritance is consistent with this
experiment.
Example
Genetic Situation
Ÿ Flower Color in Snapdragons
3 colors: Purple Pink White
Ÿ Hypothesis (Partial Dominance)
Purple:
WW
Pink:
Ww
White:
ww
Example
Genetic Situation
Ÿ Flower Color in Snapdragons
3 colors: Purple Pink White
Ÿ Hypothesis (Partial Dominance)
Purple:
WW
Pink:
Ww
White:
ww
Experiment
Ÿ Monohybrid Cross
Expected Results: ¼ Purple ½ Pink ¼ White
Results
Phenotype
Purple
Pink
White
Total
Observed Expected Chi-Square
345
329.25
705
658.5
267
329.25
1,317
1,317 7.32
Example
Genetic Situation
Ÿ Flower Color in Snapdragons
3 colors: Purple Pink White
Ÿ Hypothesis (Partial Dominance)
Purple:
WW
Pink:
Ww
White:
ww
Experiment
Ÿ Monohybrid Cross
Expected Results: ¼ Purple ½ Pink ¼ White
Results
Phenotype
Purple
Pink
White
Total
Observed Expected Chi-Square
345
329.25
705
658.5
267
329.25
1,317
1,317 7.32
Conclusion
Ÿ Statistical Conclusion
7.32 > 5.99
Reject the Hypothesis
Ÿ Genetic Conclusion
There is enough evidence from this experiment to conclude
that purple flower color in snapdragons does not have Partial
Dominance Inheritance