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?
