Combined Estimate Of 
Using the Product Method
See - Immer, F. R., and M.T. Henderson 1943, Linkage
Studies in Barley, Genetics 28:419-440. We will shown
that coupling data has more value (or information) than
repulsion data. The amount of information is:
The variance of p is Vp. To find Vp
we square the standard error of p.
V
= f
1 = N
= I
N V f
Summarizing we have:
| Type |
 |
(s.e.) |
f |
N |
I |
F
Repulsion |
0.245 |
0.0247 |
0.9297 |
1415 |
16371 |
| F
Coupling |
0.318 |
0.0139 |
0.5841 |
1764 |
5170.4 |
The combined estimate of p from both types of families
is found by weighting based on the amount of information
from each family. A coupling family has more weight
because coupling data provides more information (greater
precision) than repulsion data.
weighted
value = SIp
SI
| Type |
 |
I |
Ip |
| Repulsion |
0.245 |
1637.1 |
400.5920 |
| Coupling |
0.318 |
5170.4 |
1643.1522 |
| Sum |
|
6807.5 |
2043.7442 |
SIp
= 2043.74 = 0.3002 =
combined
SI 6807.5
Now we want to find the associated s.e. We look up
the f value for
= 0.3002 for repulsion and coupling data.
The s.e. for the combined estimate of p is:
In conclusion, using the product method, we find the
combined estimate and s.e. is:
** Before we calculate
for each set of data we should first do a X2
test for each separate locus and for linkage. Then we
can estimate p for each type of data. Later we will
calculate a heterogeneity X2 for combined
data using Fisher's Scoring Method.
