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# One-sample or two-sample t-test for testing for significant chance between percentages

I've located 15,000 random points within a study area and have classified the land cover for each point by overlaying the points on an aerial image. I've classified the same 15,300 points twice using aerial photos from two different years (1998 and 2014). From this I've calculated the percent cover of each land cover type within my study area in each year. If for example I found that there was 29% building cover in 1998 and 32% building cover in 2014, would I use a two sample or one sample t-test to determine if the change in cover was significant? I think 2 sample even though it's the same points spatially being classified, the different time periods assessed makes it two different samples, correct?

### 1 Answer by Expert Tutors

Kidane G. | Effective Statistics, Biostatistics and Probability TutoringEffective Statistics, Biostatistics and ...
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Hi Jenni,

It is not clear to me what is the question or objective that you are trying to address. In any case,  you will need a method beyond the standard one or two-sample t-test. The reason is that even though the 15, 000 random points were randomly selected, they are not random at all because they are spatially auto-correlated due to the fact that points closer to each other are more similar to each other than points further apart. Their randomness, however, helps you to obtain an unbiased estimate of the quantity (say mean change in land cover or use) you are trying to estimate in your study area. Your main problem is (related also to why I said you need a more sophisticated method beyond a simple t-test) how to estimate the variability of your estimator so that you can construct a confidence interval or conduct an (approximate)  hypothesis test.

Having said so, you can do a t-test using the change in percentage over time at each point if the spatial auto correlation is either found to be insignificant (this requires some statistical justification) or if you are willing to make the strong assumption that there is no spatial auto correlation.

I hope this helps.