**Clearly, for those ***with serious damage*, MOST
(about FIVE TIMES more) people wear NO hearing protection, whereas for those
with *NO hearing damage*, MOST (more than FIVE TIMES more) people wear
hearing protection! So there DOES seem to be a relationship!

**Could this "relationship" have occurred just by chance
(assuming there was NO benefit from wearing hearing protection)?**

**To do this we test the **__
Null Hypothesis__ of "NO RELATIONSHIP" between wearing protection, and hearing
damage...

**We now need to compare **__these__
numbers with the numbers we would expect if there was NO relationship between
protection and damage, the "EXPECTED" numbers... Here's how we get
the EXPECTED [E] numbers:

Degrees of freedom are [ROWS-1]x[COLUMNS-1] or here 2x1=2

**...One way is to collapse either rows or columns**

**But if a table already has only 2x2 cells, even ONE
cell is 25% so NO cell of a 2x2 table can have an [E] number <5 **

**.**

Fisher's Exact Test calculated P directly as

**
P = **__(A+C)! x (B+D)! x (A+B)! x (C+D)!__

**
A! x B! x C! x D! x (A+B+C+D)!**

**
A B
A+B**

**
C D
C+D**

**
(A+C) (B+D) (A+B+C+D)**