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Chi Square (X 2 ) Analysis

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.

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Chi Square (X 2 ) Analysis

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  1. Chi Square (X2) Analysis Calculating the significance of deviation in experimental results

  2. 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......

  3. What if the segregation ratio obtained is 33Normal and 7Abnormal quail, is this a 3: 1 ratio?

  4. 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? • ___________________

  5. Chi Square or Goodness of Fit Test (Observed - Expected) 2 Expected • 2=

  6. 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

  7. Variations of the Chi Square Table

  8. What if the segregation ratio obtained is 35 Normal and 5 Abnormal quail, is this supportive of a 3: 1 ratio?

  9. Observed: 40 offspring 35 Normal and 5 Abnormal Expected: 30 Normal and 10 Abnormal (Why this ratio ?)

  10. 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 / _____________ !

  11. 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 __________!

  12. X 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 __________!

  13. Inheritance of Star Gazing in Japanese Quail J. Heredity (1972) 63:87-90

  14. Inheritance of Star Gazing…….Chi-square Analysis

  15. 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?

  16. What if the segregation ratio obtained is 33 Normal and 7 Abnormal quail, is this supportive of a 3: 1 ratio?

  17. The End

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