Performs a permutation test of differences in means between two groups of censored data.

`cenperm2(y1, y2, grp, R = 9999, alternative = "two.sided", printstat = TRUE)`

- y1
The column of data values plus detection limits

- y2
The column of indicators, where 1 (or

`TRUE`

) indicates a detection limit in the`y1`

column, and 0 (or`FALSE`

) indicates a detected value in`y1`

.- grp
Grouping or factor variable. Can be either a text or numeric value indicating the group assignment.

- R
The number of permutations used. Default is 9999

- alternative
indicates the alternative hypothesis and must be one of "

`two.sided`

", "`greater`

" or "`less`

". You may also specify just the initial letter. Default is "`two.sided`

".- printstat
Logical

`TRUE`

/`FALSE`

option of whether to print the resulting statistics in the console window, or not. Default is`TRUE.`

Permutation test results with the number of permutations, range in group means and their difference, and range in `p-value`

.

Because this is a permutation test it avoids the problem with MLE tests (`cen2means`

) that assume a normal distribution. No values are modeled as below zero and `p-values`

are trustworthy. Ranges in means and p-values are due to interval-censoring of censored data means.

Good, P., 2000. Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses, 2nd ed, Springer Series in Statistics. Springer-Verlag, New York, NY. doi: 10.1007/978-1-4757-3235-1

Helsel, D.R., 2011. Statistics for Censored Environmental Data using Minitab and R, 2nd ed. John Wiley & Sons, USA, N.J.

Shapiro, S.S., Francia, R.S., 1972. An approximate analysis of variance test for normality. Journal of the American Statistical Association 67, 215–216.

```
data(PbHeron)
cenperm2(PbHeron$Liver,PbHeron$LiverCen,PbHeron$DosageGroup,alternative="t")
#> Permutation test of mean CensData: PbHeron$Liver by Factor: PbHeron$DosageGroup
#> 9999 Permutations alternative = two.sided
#> mean of High = 9.288 to 9.288 mean of Low = 0.1093 to 0.1207
#> Mean (High - Low) = 9.179 to 9.167 p = 0.0016 to 0.0018
#>
```