Yate's Correction Term
Yate’s correction term - When n is 50 or less and there are
only two classes, Yate’s correction term is used to improve
the accuracy of the X
test. The binomial distribution is used for an exact test
of discrete classes. The X
test is an approximate test used when class sizes are large.
Yate’s correction is used for small class sizes such that
the X test
more closely approximates the true significance level found
from the binomial distribution.
Example 1
Strickberger, M.W. 1968. Genetics. The Macmillan Co., New
genotYork. pg. 132.
With 1df Ho:3:1 ratio, n = 50
observed - 30 tall plants : 20 short plants
expected - 37.5 tall : 12.5 short
X = [|
observed - expected |- 1/2]
X
= [l obseexpected number
The Yate’s correction term is to subtract 1/2 from the absolute
value of observed number minus expected.
Example 2
| |
Tall |
Short |
Totals |
| observed |
30 |
20 |
50 |
| expected |
37.5 |
12.5 |
50 |
| observed-expected |
-7.5 |
+7.5 |
|
| |observed-expected| |
7.5 |
7.5 |
|
| |observed-expected
-1/2|
|
49.0 |
49.0 |
|
(| observed - expected |- 1/2)
(| observedexpected
49.0 = 1.31 49.0
= 3.92
37.5 12.5
X = 1.31
+ 3.92 = 5.23
The critical X
value for 1df, a = 0.05 is
3.84. 5.23 is too large, because it is larger than 3.84.
Reject Ho:3:1 ratio because calculated X2 is too
large.
(Tt x Tt mating rejected)
Now test Ho:1:1 ratio.
| |
Tall |
Short |
Totals |
| observed |
30 |
20 |
50 |
| expected |
25=1/2(50) |
25=1/2(50) |
50 |
| observed-expected |
5 |
-5 |
|
| |observed-expected|
-1/2 |
5-1/2=4.5 |
5-1/2=4.5 |
|
| |observed-expected|
-1/2
|
20.25 |
20.25 |
|
| {|
observed - expected | - 1/2}2
|
20.25 |
=
.81 |
20.25 |
=
.81 |
| expected
number |
25 |
25 |
X = 0.81
+ 0.81, a = 0.05, df = 1.
X
= 1.62
1.62 is the calculated X
which is less than the critical
X2 = 3.84, so fail to reject Ho. The evidence supports
a 1:1 ratio of a Tt x tt mating.
** A hypothesis can never be proven, but the observed data
may result in a failure to reject the null hypothesis.
