F
Statistical Summary
We can now summarize those statistics for each type
of F
family with p = 0.2967. We can calculate the X
= c/I.
| Family |
n |
i |
c |
I |
c2/I |
df |
| F2
repulsion |
1415 |
1.235 |
-76.26 |
1747.5 |
3.33 |
1 |
| F2
coupling |
1764 |
3.158 |
+123.22 |
5570.6 |
2.73 |
1 |
| Sum |
|
46.96 |
7318.1 |
6.06 |
2 |
| Total
X2 |
|
(46.96)2/7318.1
= |
0.30 |
1 |
| Heterogeneity
X2 |
|
5.76 |
1 |
We have a pooled X2 = 0.30 w/1df which is
not significant. We accept 
=
0.2967 as a good fit for the pooled data. The significant
heterogeneity X2 tells us that we cannot
find one value of that
uniformly fits both types of data.
Correction for =
49.96/7318.1 = 0.007
The new estimate of p is 0.2967 + 0.007 = 0.303. There
is little change in p and this new estimate is close
enough. Now to find the standard error of this combined
estimate of p.
| Repulsion
(p = 0.303) |
Coupling
(p = 1 - 0.303) |
i = 2(1+2(0.303))
(2+(0.303))(1-0.303))
|
i
= 2(1+2(0.697))
(2+(0.697))(1-0.697))
|
=
2.3670 = 1.2459
= 1.8999 |
=
3.9436 = 3.0858
= 1.2780 |
I
= Ni = 1415(1.2459)
I = Nlll= 1762.8 |
I
= Ni = 1764(3.0858)
I = Nlll= 5443.9 |
= 0.0118
=
+ s.e. = 0.303 +
0.0118
First we estimate p seperately for F2 repulsion
and coupling families using the product method.
| Source
of data |
|
i |
n |
I |
pI |
| F2
repulsion |
0.244 |
1.1555 |
1415 |
1635.0 |
398.94 |
| F2
coupling |
0.318 |
2.9279 |
1764 |
5164.8 |
1642.21 |
Combined value of p by weighting = 
= 398.94 + 1642.41 = 2041.35
= 1635.0 + 5164.81
= 6800
= 0.300
This method was much easier than Fisher's Scoring Method.
However, Fisher's scoring method did not permit us to
test the overall X2 for the combined estimate
of p or to test for heterogeneity.
For a discussion of progeny testing of F2
data see:
Kramer, H.H., and C.R. Burnham. 1947. Genetics 32:379-390
Immer, F.R. 1934. Genetics 19:119-136.
