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?