How to Perform Pairwise Comparisons with Limited Data?

[amalak]

Hi there,

If I have 5 numbers that represent the area of a forest from 5 separate years, is it possible to yield 4 pairwise comparisons? I would like to know if the change in area is significant from year to year, but cannot figure out which statistical test to use since I only have one measurement (the area) in each treatment (the year).

(Note: I've tried to justify using the z-test, t-test, and ANOVA, but I either cannot assume normality or have too few observations within each group.)

Any guidance would be much appreciated. Thank you in advance.

p.s. This is for my job, not for homework.

 

[chiro]

Hey amalak and welcome to the forums.

Have you considered a transformation of your data so that you can meet the normality requirements? This is a typical strategy to use when things don't meet the assumptions and you need to think about how you can take your data and transform it so that you can specific piece of statistical machinery.

In terms of statistical theory, the generalized form of inference is the Bayesian Inference and this is often used when the frequentist methods just don't cut it (especially good for small samples with some kind of expert or prior information).

I would firstly try to transform your data and if you absolutely need something for this, then you should read the Bayesian Inference and how you can extend the paired t-test to the Bayesian situation.

There is a program called WinBUGS which will take a model, simulate it using MCMC and you can use those distributions to get the mean and variance of the simulated distribution to use for hypothesis testing, but it's pretty complicated because of it's general nature.