# Which statistical method of anlysis should I use?

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?

• Of possible interest: link1, link2. Note also that you do not need a large sample to assume normallity. – user10525 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? – user10525 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
• 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. – user10525 Nov 19 '12 at 15:06