Chi Square (X 2 ) Analysis Calculating the significance of deviation in experimental results.

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Presentation transcript:

Chi Square (X 2 ) 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 =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 X 2 = (35-30) 2 /30 + (5-10) 2 /10 = 25/ /10 = = 3.33, calculated X 2 value Tabular X with 1 df = 3.84 Calculated X < 3.84, the observed deviation from the hypothesized 3:1 ratio most probably occurred by _______ and a ________ ratio is __________!

Tabular X with 1 df = 3.84 Calculated X < 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