How to handle the zero deviation with Wilcoxon test and t-test(with zero standard deviation data) I am a newbie of statistics
I am looking for a statistical test for zero standard deviation data VS a distributed data
Here is the example:
ddd2

      name   srmse_avg           method
459  arone 8.587927  ARMA    1 proposed
468  arone 8.952136  ARMA    2 proposed
477  arone 8.443238  ARMA    3 proposed
486  arone 8.096387  ARMA    4 proposed
495  arone 8.644613  ARMA    5 proposed

1359 arone 9.515574  ARMA    1 baseline
1368 arone 9.515574  ARMA    2 baseline
1377 arone 9.515574  ARMA    3 baseline
1386 arone 9.515574  ARMA    4 baseline
1395 arone 9.515574  ARMA    5 baseline

Actually, I did the Wilcoxon test in r, and Here is the result
> test <- wilcox.test(ddd2$srmse_avg ~ ddd2$method, alternative = "greater")
Warning message:
In wilcox.test.default(x = c(9.51557350975475, 9.51557350975475,  :
  cannot compute exact p-value with ties
> test

    Wilcoxon rank sum test with continuity correction

data:  ddd2$rmse_avg by ddd2$method
W = 100, p-value = 3.193e-05
alternative hypothesis: true location shift is greater than 0

So I am not sure that I can trust this result

*

*Did I do this correctly? because the baseline method has zero standard deviation

*Is there any statistical test method for this kind of dataset?

*Is there any way for avoiding the warning message?

Thank you so much!!

I just realized that this is a problem of non-parametric problem for one sample t-test
like Wilcoxon signed rank sum test or sign test...
Please let me know if this is wrong..
 A: *

*The warning from the wilcox.test() function just means what it says:  the function cannot compute the exact p-value when there are ties.  So it computes an asymptotic p-value using an approximation.  This is fine.  By default, the function applies a continuity correction, which is helpful with the smaller sample size.


*It does appear that you are right that what you really want is a one-sample test.  As you mention, the one-sample Wilcoxon signed rank test or one-sample sign test would be options. You could also use a permutation test.  The choice of test depends on the exact hypothesis you wish to test.
A: Let $H_0$ be the null hypothesis that the (population) standard deviation is zero
You can have a test that rejects this null when the observations are not all the same. This has zero Type I error rate: if the population standard deviation is zero, the observations are all the same with probability 1.  It has 100% power against any continuous distribution with non-zero standard deviation and pretty good power against discrete distributions.
You do need a criterion for when two observations are the same, which will depend on your measurement methods.
