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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?

kjetil b halvorsen
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Kaish
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  • Of possible interest: [link1](http://stats.stackexchange.com/questions/30141/determine-if-a-heavy-tailed-distributed-process-has-improved-significantly/30148#30148), [link2](http://stats.stackexchange.com/questions/31755/what-to-do-when-the-means-of-two-samples-are-significantly-different-but-the-dif/31761#31761). Note also that you do not need a large sample to assume normallity. –  Nov 19 '12 at 11:51
  • Can I justify normallity in this case then? – Kaish Nov 19 '12 at 13:41
  • 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? –  Nov 19 '12 at 13:44
  • 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? – Kaish Nov 19 '12 at 14:30
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    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. –  Nov 19 '12 at 15:06
  • Several methods using parametric tests? Not non parametric tests? – Kaish Nov 19 '12 at 15:49
  • Both, parametric and nonparametric. The goal of this is to conduct a [sensitivity analysis](http://en.wikipedia.org/wiki/Sensitivity_analysis). –  Nov 19 '12 at 15:52

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