Question

View the example chi square calculated for a monohybrid cross between two heterozygous flies

Phenotype	Observed	Expected	Deviation (observed - expected)^2/Expected
Brown Body Color	580	600
Black body Color	220	200
Total Flies = 800			Chi Square =?

What is the chi square value and the Deviation?

Answer this based on the values:

The Chi square value is ____ (more or less) than the critical value _______. The variation between the observed and expected is ______(due or not due) to chance. The observed data are _______ (consistent or inconsistant) with the expected data. We (reject or fail to reject) the hypotheis.

Answer 1

The deviation is the difference between an observed value and the expected value. To calculate deviation for each phenotype, we will find out the difference between the observed value and expected value for each phenotype.

Deviation for the brown body color phenotype will be calculated as shown below.

Deviation for the black body color phenotype will be calculated as follows.

We have calculated that deviation (d) for the brown body color phenotype is -20 and deviation (d) for the black body color phenotype is 20. Now, we will divide the square of the deviation for each phenotype by expected value for that phenotype as shown below. This will help us in calculating the Chi-square value as shown in the following table.

Phenotype	Observed	Expected	Deviation (observed - expected)	(Deviation)2 (observed - expected)2	(Deviation)2 /Expected (observed - expected)2/Expected
Brown Body Color	580	600	580-600 = -20	(-20)2 = 400	400/600 = 0.66 or 0.7
Black body Color	220	200	220-200 = 20	(20)2 = 400	400/200 = 2
Total Flies = 800					Chi-square = 2 + 0.7 Chi-square = 2.7

As we have found Chi-square value and deviation, we will fill blanks based on the values.

It is a statistical convention to take the Chi-square value at 0.05 probability label in the Chi-square table as a critical value. The degree of freedom for the table will be calculated by using n-1, where n is 2. So, the degree of freedom for the table is 1.

In the Chi-square table, the critical value at 0.05 probability label with a degree of freedom one is 3.84. So, the Chi-square value is less than the critical value of 3.84.

As the Chi-square value is less than the critical value, variation between the observed and expected is due to chance.

As the Chi-square value is less than the critical value, we will conclude that the observed data are consistent with the expected data.

As the Chi-square value is less than the critical value, we fail to reject the hypothesis.