Performs a parametric test of differences in means between two groups of censored data, either in original or in log units (the latter becomes a test for difference in geometric means).

cen2means(x1, x2, group, LOG = TRUE, printstat = TRUE)

## Arguments

x1 The column of data values plus detection limits 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. Grouping or factor variable. Can be either a text or numeric value indicating the group assignment. 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). Logical TRUE/FALSE option of whether to print the resulting statistics in the console window, or not. Default is TRUE.

## Value

Q-Q Plot with Shapiro-Francia test for normality W and p-values. Returns the Maximum Likelihood Estimation (MLE) test results including Chi-Squared value, degrees of freedom and p-value of the test.

## Details

Because this is an MLE procedure, when a normal distribution model is used (LOG=FALSE) values may be modeled as below zero. When this happens the means may be too low and the p-values may be unreal (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.

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

## Examples


data(PbHeron)
cen2means(PbHeron$Liver,PbHeron$LiverCen,PbHeron$DosageGroup) #> MLE 't-test' of mean natural logs of CensData: PbHeron$Liver by Factor: PbHeron\$DosageGroup
#>      Assuming lognormal distribution of residuals around group geometric means
#>      geometric mean of High = 0.7762     geometric mean of Low = 0.05753
#>      Chisq = 9.696  on 1 degrees of freedom     p = 0.00185
#>