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c2-test is frequently used in biology
to find out whether observed data is different from expected results.
For example in a cross of flies, we found that 23 progenies are female
and 47 are male.
| Observed | Expected | Total |
| Male | 23 | 35 | 58 |
| Female | 47 | 35 | 82 |
| Total | 70 | 70 | 140 |
For this simple example, there are only 2 columns (observed and expected) and 2 rows (male and female), thus
the degree of freedom
df = (number of columns - 1) * (number of rows - 1) = 1.
c2 is calculated using the following formula:
c2 = S
(Observed Value - Expected Value)2 / (Expected Value).
Note in this version of c2-test the expected value is calculated
from a hypothesis (i.e., the frequency of male or female progenies should be 0.5).
For the above example, c2 = (23-35)2/35 + (45-35)2/35
= 7.11.
Checking the c2 table
| |
Probability |
Degrees of
Freedom |
0.9 |
0.5 |
0.1 |
0.05 |
0.01 |
| 1 |
0.02 |
0.46 |
2.71 |
3.84 |
6.64 |
| 2 |
0.21 |
1.39 |
4.61 |
5.99 |
9.21 |
| 3 |
0.58 |
2.37 |
6.25 |
7.82 |
11.35 |
| 4 |
1.06 |
3.36 |
7.78 |
9.49 |
13.28 |
| 5 |
1.61 |
4.35 |
9.24 |
11.07 |
15.09 |
we find p < 0.01.
Web
c2 calculator
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