In a prospective study, we draw a sample of size 100 where two sttributes A
and B
were present.
Our goal is to assess whether there is any association between these two attributes. The data looks like following:
Table 1.
A
Present Absent|
Present x1 x2 |
B |
Absent x3 x4 |
----------------------------|---
100
Attribute A
can be divided into two parts, pathogenic A
and non-pathogenic A
. Now, with the same sample of 100, we test whether there is any association between attribute B
and pathogenic A
.
Table 2.
PATHOGENIC A
Present Absent|
Present y1 y2 |
B |
Absent y3 y4 |
----------------------------|---
100
Since in both tables, we have used the same sample of size 100 and the attribute B
is common, hence
$$(x1+x2)=(y1+y2), \quad\text{and}\quad (x3+x4)=(y3+y4),$$ that is, the corresponding row totals are same.
In the first table, the number of sample where B
is present or absent was not known, that is, the row totals were not fixed. A data analyst didn't saw table 2, before conducting the test of table 1. But after conducting the test of table 1, if the analyst comes to table 2, will he consider the row totals fixed?
But if he would see table 2 before table 1, then he would consider the row totals of table 2 not fixed.