An Explanation of Chi-Squared Distributions
Level Type I Error
The level of Type I error (α)
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 |
X2 |
| wild
type |
99 |
108 |
-9 |
0.75 |
| mutant |
45 |
36 |
+9 |
2.25 |
| total |
144 |
144 |
0 |
3.00 |
The critical X2 value with 1df and α
= 0.05 is 3.84 and the calculated X2 = 3.0.
The calculated X2 is smaller than the critical
value, so we accept Ho. If the calculated X2
was 5.0, we would reject Ho at the α
= 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 X2 = 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.
