Performs a parametric test of differences in means between groups of censored data, followed by a parametric Tukey's multiple comparison test.

`cenanova(x1, x2, group, LOG = TRUE, printstat = TRUE)`

## Arguments

- x1
The column of data values plus detection limits

- x2
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`

.

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

- LOG
Indicator of whether to compute tests in the original units, or on their logarithms. The default is to use the logarithms (`LOG = TRUE`

). To compute in original units, specify the option `LOG = FALSE`

(or `LOG = 0`

).

- printstat
Logical `TRUE`

/`FALSE`

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

## Value

Returns the Maximum Likelihood Estimation (MLE) comparison results including Chi-Squared value, degrees of freedom and `p-value`

of the test. Test assumes log-normal(`LOG=TRUE`

) or normal(`LOG=FALSE`

) distribution of residuals from group means.

Tukey's multiple comparison p-values of pairwise differences in group means are also printed.

Group Names of groups (NOTE: `== 0`

indicates null hypothesis of "equals zero").

`Estimate`

Estimated difference between group means.

`Std. Error`

Standard error of estimate.

`z value`

Test statistic.

`Pr(>|z|)`

P-values for test that difference in means equals zero.

## Details

Test is computed using Maximum Likelihood Estimation. When a gaussian distribution model is used (LOG=FALSE) modeled values may fall below zero, producing unreal p-values (often lower than they should be). Because of this, testing in log units is preferable and is the default.

## References

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

#' @examples
data(PbHeron)
cenanova(PbHeron$Liver,PbHeron$LiverCen,PbHeron$DosageGroup)

cenanova(PbHeron$Liver,PbHeron$LiverCen,PbHeron$DosageGroup,LOG=FALSE)