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