I'm trying to determine if I'm correctly testing for significance of the change in artifact type presence across several time periods.
In an archaeological survey, stone tool artifacts were cataloged (let's say n=1000) . Within the whole population, 25 were identified as belonging to a particular culture (called Pinto). The overall population was also determined to span 3 time periods (let's call them Ages A, B, and C). The division of artifacts is not equal across these ages. Across A, B, and C, let's say it is 500, 200, 300. The Pinto artifacts are distributed between A, B, and C as n = 7, 4, and 14, respectively (yes, small sample sizes, welcome to archaeology...).
I want to know if the changes in the amount of Pinto tools across the ages is significant. If I do a chi-squared goodness of fit test using O = (7,4,14) and E of 8.3, I get X2 = 6.35 and a p = 0.04. So, yes, significant with alpha = 0.05.
The bigger question is whether this is a valid test. Are the rest of the artifacts (n=975) relevant to the question? Should I be using (very small) proportions of that overall pop for my chi-sq test? I only care about the one class within the collection, not how it relates to other classes (there are about 20) within the overall pop.
I welcome your thoughts.
