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I have a sample of 197 responses. 8.6% (17)are from Group A, the remainder from Group B. (The groups are mutually exclusive, and not independent). (If it helps visualize the issue, Group A is under 10's, Group B respondents aged 11+.)

The responses are then sorted in to groups by type. Type 1 is "head injuries", and there are 3 members of this group. 2 are from Group B, 1 is from Group A.

I would expect the results for head injuries to be under 10 (Group A) & head injury: 0.3 Under 10 & no head injury: 16.7 Over 10 (Group B) & head injury: 2.7 Over 10 & no head injury: 179.3

I have asked a few friends how to test if the expected value being so much lower than the observed value is significant. So far responses seem to favour a Z test, or a chi squared test with a correction for very small numbers. I'm innumerate in the extreme, but can manage either well enough -- just not sure what is the appropriate test here?

chl
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user31717
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    You want the Fisher-Irwin test. See Ian Campbell's [website](http://www.iancampbell.co.uk/twobytwo/twobytwo.htm) for the details and data to support the recommendation. – Ray Koopman Oct 20 '13 at 19:41
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    Of possible interest (in line with @Ray's comment): [Chi-square test for equality of distributions: how many zeroes does it tolerate?](http://stats.stackexchange.com/q/4023/930), [Yates continuity correction for 2 x 2 contingency tables](http://stats.stackexchange.com/q/4569/930). – chl Oct 20 '13 at 22:27

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