An Explanation of Chi-Squared Distributions
Level Type I Error
The level of Type I error (a)
is decided by the scientist. The degrees of freedom is used
to determine the critical value of the X2 that
determines the rejection region. In our example there are
two classes which are B_ and bb. If we know the total number
of progeny and the number in one class, then we can subtract
to find the number in the second class. This means that 2-1
= df = 1.
| phenotype
(class) |
observed
number |
expected
number |
deviation
from expected |
X |
| wild
type |
99 |
108 |
-9 |
0.75 |
| mutant |
45 |
36 |
+9 |
2.25 |
| total |
144 |
144 |
0 |
3.00 |
The critical X
value with 1df and a = 0.05 is
3.84 and the calculated X
= 3.0. The calculated X
is smaller than the critical value, so we accept Ho. If the
calculated X
was 5.0, we would reject Ho at the a
= 0.05 level because a deviation from expected that is this
large would only occur 3 out of 100 times. Because this result
would occur only 3/100 when Ho is true, the correctness of
the genetic hypothesis would be doubtful.
For a X
= 3.0, the observed numbers in each class would occur 8 out
of 100 trials and this is sufficiently likely to accept Ho.
Degrees of freedom - If the total number of phenotypes
is known, then we can determine the number of individuals
in one of the two classes. n = 144 and there are two phenotypic
classes. If we determine the number of individuals in one
variable class, then the number in the other class is fixed.
