# Goodness-of-fit for contingency tables

I have a question on testing mortality table. Suppose I am given a simple mortality table:

age  | prob of dying  | prob of surviving
---------------------------------------
20   |  0.01          |   0.99
21   |  0.02          |   0.98
22   |  0.03          |   0.97
23   |  0.04          |   0.96
...


I want to test whether the table fit my observed data, i.e., whether the Observed values

age  | actual dead    | actual survivors
---------------------------------------
20   | 0              |  397
21   | 1              |  189
22   | 0              |  136
23   | 2              |  100
...


fit the expected values

age  | actaul dead       | actual survivors
---------------------------------------
20   | 3.97 (397*0,01)   |  393.03
21   | 3.8   (190*0.02)  |  186.2
22   | 4.08  (136*0.03)  |  131.92
23   | 4.08 (102*0.04)   |  97.92
...


How do I do that? What method should I use? Should I use Chi-Square, although my expected data is quite small? or there is another method?

• Thank you very much for the answer. I alreeady used Chi Square and G test. I am not sure if that is the right apporach, since I already have predetermined probabilities, so my expectations are calculated by the formula $$E(X_{20})=p_{20}*n_{20}$$ and not by the formula used in exact tests for contingcency tables (row*column/total_number) $$E(X_{20})=\frac{n_{20}*d}{n}$$ $p_{20}$ -prob a 20 year old to die $n_{20}$ -total number of 20 year olds $d$- total number of dead \$Could I still use a test of independence, like Fisher's or chi square, or should I consider a different approach? – naninko Apr 16 '13 at 13:04