Computes tests for each of the two factors and optionally for their interaction using likelihood ratio tests. p-values will not be identical to the usual method of moments ANOVA tests but will be similar.

cen2way(y1, y2, fac1, fac2, LOG = TRUE, interact = TRUE)

## Arguments

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.

fac1

The first grouping or factor variable. Can be either a text or numeric value indicating the group assignment.

fac2

The second grouping or factor variable. Can be either a text or numeric value indicating the group assignment.

LOG

A logical variable indicating whether natural logs are to be taken of the 'y1' column data. Default is TRUE.

interact

A logical variable indicating whether to compute an interaction term between the two variables. Default is TRUE. #' @keywords two-way two-factor factorial ANOVA analysis of variance censored

## Value

Q-Q plots of residuals. Likelihood ratio test statistics ("chisquare"), degrees of freedom ("df") and p-values (pval) for two factors and optionally the interaction. Data on the underlying models, including AIC and R2 are also provided.

## Details

Tests are 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 unless you are transforming the y values prior to running the function (such as taking cube roots to approximate a gamma distribution). The 'delta.lr0x2' stat output is the -2loglikehood for the test of the model versus an intercept-only model.

## References

Helsel, D.R., 2011. Statistics for Censored Environmental Data using Minitab and R, 2nd ed. John Wiley & Sons, USA, N.J. Millard, S.P., 2013. EnvStats: An R Package for Environmental Statistics. Springer-Verlag, New York.

## Examples

data(Gales_Creek)
Gales_Creek\$Period <- c(rep("early", 35), rep("middle", 12), rep("late", 16))
with(Gales_Creek,cen2way(TCr, CrND, Season, Period))

#> Two-way Fixed Effects ANOVA by MLE Likelihood Ratio Tests for Censored Data
#> ln(TCr) modeled by Factor 1: Season  and Factor 2: Period
#>        ANOVA Table with interaction
#>        FACTORS   chisquare   df        pval
#>         Season     21.5100    1   3.520e-06
#>         Period      5.5840    2   6.130e-02
#>    interaction      0.8491    2   6.541e-01
#>
#>                MODELS   loglikelihood   delta.lr0x2        AIC        BIC
#>           Season only       -68.20914        24.700   147.4183   157.2127
#>           Period only       -76.16994         8.783   165.3399   177.2932
#>          both factors       -65.84173        29.440   142.6835   152.4779
#>    both + interaction       -65.41720        30.290   145.8344   159.9466
#>    Rescaled_Loglik_R2
#>                0.3516
#>                0.1411
#>                0.4047
#>                0.4138