I have collected data for 3 decades for 5 things. I want to see if there is a change in these five things over the period of three decades. For example if A was 20 out of 80 in decade1, 40 out of 120 in decade 2 and 50 out of 70 in decade 3. now i want to check if the change in A was statistically significant over the period of 3 decades. do i use chi square, annova or any thing else. i have already made trend analysis diagrams and equations, but dont have a statistical test ! :(
I believe you'd use a Pearson's chi-squared contingency table test (of independence) on your 3x5 table. In R the
chisq.test does what you want (put the data into a table).
I suspect that the collectively exhaustive part might affect the answer, though. Perhaps now that we know what you have, someone more knowledgeable than I can chime in.
EDIT 3: Upon clarification, it sounds like you want to look at the percentages of Type A over the three decades. This kind of regression is mentioned in another thread. And the bottom line is to do a GLM regression with a pro bit link function.
EDIT 2: I don't know what tests are more powerful than others, but if you did the independence test, above, and you cannot reject independence, that's a sign that there is not a significant trend. If you could reject independence, then the number of articles by type does change significantly through the decades: though that doesn't mean there is a trend to the changes.
Also, you say that you want to look at type A and see if it's trended over the decades. Do you actually want to work with just the count of A, or with the percentage of A type stories? That is, since your types cover all possible news, I'd assume all of the types would increase over time. The question might be, as a percentage of all news, is type A significantly less now than it was 30 years ago.
Last, do you need statistics at all? If you look at stories of type A and see 30, 70, 80, you can say that they have increased over time. Period. You only need statistical tests when uncertainty is involved.
EDIT: What I say above would indicate that the data count types are not independent of the decade. To actually show a trend, you'd use a linear regression. In the case of count data, I believe you'd want to use a generalized linear model (glm in R) with a Poisson link function. Look for the statistical significance (or not) of the slope coefficient.
Though with only 3 data points, a "trend" is going to be hard to prove unless it is very large. (That is, you have low power.)