of 1
Outline lecture 3
Testing statistical significance of the agreement between observed and theoretical
segregation ratio.
2
Goodness of fit test
2
=
(Observed number expected number)2/expected number
The expected number, e.g., for the 3:1 ratio:
The expected number for the class of 3 = Total number x 3/4
The expected number for the class of 1 = Total number x 1/4
Null hypothesis (H0):
Alternative hypothesis (HA):
Character
red
pink
white
Total
P
ratio is
ratio is not
Observed
182
61
77
320
1:2:1
1:2:1
Expected
160
80
80
320
=
Conclusion:
Chi-square table
(O-E)2
484
361
9
(O probability E)2/E
3.0
4.5
0.1
7.6
3
In this case, P of the difference between the observed numbers in each class and expected
numbers on the basis of the H0 hypothesis is below the 0.05 (5%) probability boundary.
We therefore conclude that the difference is not due to chance alone; there is a cause.
The cause is that the population segregates in a different ratio than we hypothesized. We
therefore reject the H0 hypothesis and accept the HA hypothesis.