[R] how to test difference in my case?

[Xu Yuan]

hello all,

I wonder if anyone could give me a hint on which statistical technique
I should use and how to carry it out in R in my case. Thanks in
advance.

My data is composed of two columns, the same numerical variable
(continuous) from actual measurement and model prediction. My
objective is to compare the data agreement (if there is significant
difference) and make conclusions about the model efficiency. Since the
measured and predicted variable was based on the same unit, the first
test came into my mind was paired t-test. However, the paired
difference is not normal (p-value = 0.0048 from SAS proc univariate).
In this case, I can either do a wilcoxon signed-rank test or do
transformations about the data. I was told that wilcoxon signed-rank
test is not as widely recognized as paired t-test in the literature,
so I prefer to do transformation. My question is: do I need to do
transformations on both columns of original data, or just the paired
difference? What transformation is appropriate? I thought about log
transformation, but if I find significant (or no significant)
difference between the logged data (measured and predicted), can I say
there is significant (or no significant) difference between the
original data?


After this step of analysis, I will convert the continuous numerical
data into qualitative categorical ranking (value=1, 2, 3 and 4). Which
statistical test and R command should I use to compare the ranking
agreement between the actual measurement and prediction?

Thank you very much for helping me out. I haven't slept since a long
time ago and this is kind of emergency. If there is any confusion
about my description, please let me know.

Regards,
XY