I am conducting an experiment where I will measure the strength of a material used for roads. Ideally, I would like to use a large surface area to measure this but this takes too long and is really expensive. I therefore will scale it down to one area which is $50cm^2$ and one which is $12cm^2$. I then want to compare the data I get from both these samples and see how (if) they differ. For the smaller sample, I'll also be doing less observations, i.e I'll get around 30 values for the $50cm^2$ one and only like 3 or 4 for the $12cm^2$ due to how much it costs.

I was going to use the Normal Distribution, but as I won't have a lot of data, I can't justify using the Normal Distribution through the Central Limit Theorem.

Would I be able to use a non-parametric test like the Sign test? Or, would it actually be something like the Wilcoxon signed rank test as the data is paired isn't it? How would I compare the data from there?

  • $\begingroup$ Of possible interest: link1, link2. Note also that you do not need a large sample to assume normallity. $\endgroup$ – user10525 Nov 19 '12 at 11:51
  • $\begingroup$ Can I justify normallity in this case then? $\endgroup$ – Kaish Nov 19 '12 at 13:41
  • $\begingroup$ In order to answer this we would need to see the data or at least a more detailed description. Have you plotted a histogram, qq-plot or summary statistics of them? $\endgroup$ – user10525 Nov 19 '12 at 13:44
  • $\begingroup$ Not yet, I've not actually done the experiment, so I can't necesarrily justify normallity. Also, I will only have like 3 values, so I can't really justify it on just 3 values can I? $\endgroup$ – Kaish Nov 19 '12 at 14:30
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    $\begingroup$ Indeed, justifying normallity or any other model is going to be difficult with only 3 observations. Nonparametric methods are not safe in this case either, given that their convergence is typically slower. I would check several methods and see if the resulting conclusions agree. $\endgroup$ – user10525 Nov 19 '12 at 15:06

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