Suppose we have two data vectors in which the first vector contains exact values of one parameter and the second vector contains estimated values for that parameter. I want to compare these data vectors and find how close the estimated values are to exact values. Also data vectors aren't normally distributed. I want to use Wilcoxon-Mann-Whitney test and compare the p-value of the test with the significance level (0.05). The null hypothesis in this test states that the median of two data samples are the same. Can I use this test?
What types of values are these (integers, positive integers, reals, positive reals, fractions between 0.0 and 1.0, etc.)? In what way might they deviate from normality?
I'm asking because if the only reason you're using Wilcoxon is that the quantities are not normal, you might not have to.
How were the estimated vectors obtained? Could this just be a regression with one vectors the observed values, the second vector the fitted/predicted values, and the difference between them the residuals? Is your goal to assess the goodness-of-fit for the model that gave you these estimates?
But I hate it when people restructure someone's question instead of actually answering it. So, here is how you do it in R.
1. Install R if you haven't already (http://cran.r-project.org/) and launch a console.
2. Copy your data into R
e.g. copy your two columns from a spreadsheet and do this: data
You may compare their distance (Euclidean distance..) or Pearson Correlation or Spearman's rank correlation if the values are ranked... I hope this helps..
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