I recently undertook to analyze a relatively simple data set.

It includes estimates of tree species composition for several sites within a forest (for example Poplar 0.7, white ash 0.2, sugar maple 0.1)

And it includes ground surveyed data of these same areas of the forest.

The goal is to assess the accuracy of the original estimates.

I originally thought to use - forgive me I have little training in stats - a chi-squared test of goodness of fit. But I have my doubts about this, since that test seems to be designed for cases in which the expected values are frequencies. Now I understand that my data is dealing with frequencies (frequencies of species occurring), but to me each site represents a single case, and the areas are limited. It is senseless to say that an estimate for one species off by 15% has a high probability of approaching the 'limit' if enough trees were measured, and so the fit is still good.. If you expect there to be 80% of one species and there is only 65% your expectation was incorrect, and that seems significant. Also, the chi-squared tests, as far as I understand, can only be performed for one site at a time, and so don't capture any larger trends in accuracy or inaccuracy.

Are their any tests that better fit this problem? I did run an RDA using covariates to 'pair' the sites, and it gave me a p value of 0.0001, but I'm not sure if that's the most appropriate test.

Thank you very much for reading and considering. Forgive my eccentric use of terms.

hi,
unfortunately this is a bit late to check the measurement because by looking at the data only you can not distinguish between a sensible effect (i.e. some trees having a greater proportion in some environments) and simple measurement error. If you can re-evaluate the percentages, it would make sense IMO to repeat the percentage estimate at some sites and see how much they differ.

Unfortunately the original estimates are made by gov. using photographic interpretation and were not generated by some model so I cannot repeat the process.

I do understand what you're saying about measurement error. I guess it is measurement precision - or lack of precision - that I'm trying to establish. But you're saying this is chasing one's tail since the measurements I wanted to use to assess the precision are themselves subject to error. I guess that this would decrease with sample size? When I first tried the chi-square I was using an average of the stems counted across the plots rather than the sum... maybe using a bigger number would change the result?

hi,
maybe the government aésp has some numbers relating to the accuracy of the estimate? On the other hand, the impact of the accuracy depends on what you want measure with this sample - due to measure,emnt noise you will probably not see finer effects but still see an effect if it is stronger than the noise.

There is no 'margin of error' given by the government; these are the numbers used to plan forest management with.

I think I can show how it effected our specific task - i.e. was it precise enough for this one purpose that we were applying it for.

The redundancy analysis I ran provides support for this, however, given my lack of statistical knowledge I feel less than comfortable accounting for the difference between that test and the chi-square tests.

If I were to use chi-square tests for this data, would I be committing the error of pseudoreplication? Since expected proportions are not based on any replication, they are just estimates for the whole stand? And the chi-square is by each stand?

I've also been told that chi-square measures for correlation, and that I would be better off using paired t tests or wilcoxon paired tests.