# Parametric or non parametric test

I want to compare trends of R&D expenditures before and after a crisis. I was planning to use a paired T-test or a non-parametric alternative. But, before of that, I tested the data for normality. My findings are that the normality test shows one variable to be normal, and other to have a non-normal distribution. So, my question is should I use a paired T-test or an alternative. You can see results in the table.

               Kolm.Smirn Stat(p)   Shapiro-Wilk Stat(p)
Before crisis   0.131(0.200)            0.994(0.992)
After crisis    0.431(0.003)            0.697(0.009)


I would like to compare R&D expenditures before and after the crisis. So, I create the sample on this way: 2004 2005 2006 2007 2008 -> values of R&D expenditures and these values are arranged in a first column: In the second column I put values of R&D expenditures after the crisis, 2008, 2009,2009,2010,2011,2012. So my question is, can i use the rule which says if you have a greater median than mean, you should use non-parametric, and if you have a greater mean than the median, you use parametric test.Also, can I use the rules about small samples, which say that is better to use non-parametric test for samples which a number of observation is less than 30?

Thank you all for the answer. I have 10 countries and I would like to test if there is any significant difference in each of these countries in the level of R&D expenditures before and after the crisis. For example,

the first country is SERBIA and I create data on this waY: 2004 2005 2006 2007 2008 - amounts of R&D expenditures in these years will be before crisis values, and 2008 2009 2010 2011 2012 should be amounts of R&D expenditures after the crisis. So, my sample is small, so can I use the rule according to which we compare median and mean and according to this, we choose between parametric or non-parametric test. If mean greater tha n we use parametric, and if the median is higher than mean, we choose non-parametric. Second, can I refer to the rule on small samples where an abnormal distribution is assumed?

• Is this a cross sectional study? i.e. the expenditures are from different firms in the same time period – Aksakal May 17 '19 at 13:50
• No, i compare R&D expenditures in one country but before crisis 2004-2008(first pair), and after crisis 2008-2012 (second pair). – user248229 May 17 '19 at 14:07
• How many data points contribute to before and after crisis? – AdamO May 17 '19 at 15:24
• Normality of the pre-post sample $\ne$ normality of the paired differences. One would calculate the differences first then test for normality. – AdamO May 17 '19 at 15:26
• You can't arbitrarily pair data from a "pre" period and "post" period. You could pair time series from several government departments, like military, industry, aerospace, agriculture, etc. but not a handful of points in time. – AdamO May 17 '19 at 15:28

Suppose, that you think that the process is $$x_t=c+\phi_1x_{t-1}+\varepsilon_t$$ A simple way to test your hypothesis would be to define the dummy as: $$a_t=\begin{cases} 0, & \mbox{if } t<2007 \\ 1, & \mbox{if } t\ge 2007 \end{cases}$$ then the process becomes $$x_t=c+\alpha a_t+\phi_1x_{t-1}+\varepsilon_t$$ If there was an impact of recession then $$\alpha$$ is significant, and the long term mean $$E[x_t]$$ is shifted by $$\frac \alpha {1-\phi_1}$$ after 2007