Chi Square (X2) Analysis
Calculating the significance of deviation in experimental results
Suppose we have 40 offspring from a particular mating..... and the expected segregation ratio is 3 : 1
are we going to obtain exactly 30 Normal and
10 Abnormal quail?
What if......
What if the segregation ratio obtained is 33 Normal and 7 Abnormal quail,
is this a 3: 1 ratio?
Needed! an objective means of evaluating the ratio obtained (observed) -- there was a deviation in the ratio obtained from our hypothetical ratio.
• We are dealing with chance.
• Is the ratio observed due to chance or is our experiment or data flawed?
___________________
2 = (Observed - Expected) 2
Expected
Chi Square or Goodness of Fit Test
• Observed (O) = actual number of individuals for that phenotype.
• Expected (E) = the calculated number of individuals that would be expected for that particular phenotype.
• df, degrees of freedom = number of phenotypic classes in your hypothesis minus one.
• Probability Level for testing = .05 or .01
(P ‘chance alone could produce the deviation between expected and observed values’ )
• Table or Graph of Chi Square values
Variations of the Chi Square Table
What if the segregation ratio obtained is 35 Normal and 5 Abnormal quail, is this supportive of a 3: 1 ratio?
Observed: 40 offspring
35 Normal and 5 Abnormal
Expected: 30 Normal and 10 Abnormal
(Why this ratio ?)
Observed: 40 offspring
35 Normal and 5 Abnormal
Expected: 30 Normal and 10 Abnormal (Why this ratio ?)
Is this deviation (from a hypothesized 3:1 ratio) possibly due to chance or is the hypothesis incorrect !
Perform a Chi-square / _____________ !
Total number of observed quail = 40
Observed 35 Normal, 5 Abnormal
Expect in a 3:1 ratio involving 40 observed quail,
30 Normal and 10 Abnormal -- Test the ratio
X2 = (35-30)2/30 + (5-10)2/10
= 25/30 + 25/10
= .83 + 2.5 = 3.33, calculated X2 value
Tabular X2 @P=.05 with 1 df = 3.84
Calculated X2 3.33 < 3.84, the observed deviation from the hypothesized 3:1 ratio most probably occurred by _______ and a ________ ratio is __________!
Tabular X2 @P=.05 with 1 df = 3.84
Calculated X2 3.33 < 3.84, the observed deviation from the hypothesized 3:1 ratio most probably occurred by _______ and a ________ ratio is __________!
X
Inheritance of Star Gazing in Japanese Quail
J. Heredity (1972) 63:87-90
Inheritance of Star Gazing…….Chi-square Analysis
Concluding Questions Regarding
Chi-square• How is the Expected Ratio determined ?
• How is the Observed Ratio determined ?
• How many degrees of freedom are there ?
• Is there a deviation?
• Is the deviation significant? What caused it?
What if the segregation ratio obtained is 33 Normal and 7 Abnormal quail, is this supportive of a 3: 1 ratio?
The End