Contingency Tables

Contingency Tables:
l In many situations, enumeration data collected simultaneously for two
variables, and it is desired to test the hypothesis that the frequencies of
occurrence categories of one variable are independent of frequencies in
the second variable.
l The 2X2 Contingency table: It is commonly encountered in biological
research. For such tables, the computing formula:
l Note: If , will increase , rather than
decrease it.
l Equation (1) should be used.
First criteria of Total
Classification
1 2
Second criteria of
classification
1 a b a+b
2 c d c+d
Total a+c b+d n
( )
( )( )( )( )
( )
( )( )( )( ) - - - - - - - - - - - - (2) Yate s Correction
a c b d a b c d
n ad bc - 0.5n
- - - - - - - - - - - - (1)
a c b d a b c d
n ad bc
,
2
2
2
2
+ + + +
-
=
+ + + +
-
=
c
c
ad - bc £ n/2 Yate,s correction c 2
PDF created
Note:
1- Yarnold (1970), suggested that the minimum cell expectation should be
greater than 5s/r c, where s is the number of cell expectation less than
5.
2- Fisher mentioned that, some times we have data that can be
summarized in a 2X2 contingency table, but these are derived from
very small samples. For example, n less than 20 or if n is between 20
and 40 and one of expected frequencies is less than 5 the Chi-square
test is avoided.