FrF2-package {FrF2}R Documentation

Package for analysing Fractional Factorial designs with 2-level factors

Description

This package analyses Fractional Factorial designs with 2-level factors; it is meant for completely aliased designs only, i.e. e.g. not for analysing Plackett- Burman designs with interactions.

The package enables convenient main effects and interaction plots for all factors simultaneously and offers a cube plot for looking at the simultaneous effects of three factors. An enhanced DanielPlot function (modified from BsMD) is provided. Furthermore, the alias structure for Fractional Factorial 2-level designs is output in a more readable format than with the built-in function alias.

Details

This package analyses Fractional Factorial designs with 2-level factors; it is meant for completely aliased designs only, i.e. e.g. not for analysing Plackett- Burman designs with interactions.

The package works on linear models and enables convenient main effects and interaction plots (functions MEPlot and IAPlot) similar to those offered by Minitab software for all factors simultaneously, even though especially the interactions are often aliased, i.e. the model is typically singular. For the (rare) case of suspected three-factor-interactions, function cubePlot displays a cube with corners labeled with the (modeled) means of three factors simultaneously. Furthermore, the function DanielPlot from package BsMD has been modified to automatically label effects significant according to the Lenth-criterion, and to provide more usage comfort to the analyst. Finally, the function aliases determines the alias structure of a Fractional Factorial 2-level design in a format more suitable for human readers than the output from the built-in function alias.

Author(s)

Ulrike Groemping

Maintainer: Ulrike Groemping <groemping@tfh-berlin.de>

References

Box G. E. P, Hunter, W. C. and Hunter, J. S. (2005) Statistics for Experimenters, 2nd edition. New York: Wiley.

Daniel, C. (1959) Use of Half Normal Plots in Interpreting Two Level Experiments. Technometrics, 1, 311-340.

Lenth, R.V. (1989) Quick and easy analysis of unreplicated factorials. Technometrics, 31, 469-473.

See Also

BsMD-package, MEPlot, IAPlot, cubePlot, DanielPlot, aliases

Examples

    ### Injection Molding Experiment. Box et al. 1978.
    data(BM93.e3.data)  #from BsMD
    iMdat <- BM93.e3.data[1:16,2:10]  #only original experiment
    # make data more user-friendly
    colnames(iMdat) <- c("MoldTemp","Moisture","HoldPress","CavityThick","BoostPress",
             "CycleTime","GateSize","ScrewSpeed", "y")
    # linear model with all main effects and 2-factor interactions
    iM.lm <- lm(y ~ (.)^2, data = iMdat)
    # determine aliases
    aliases(iM.lm)
    # coded version
    aliases(iM.lm, code=TRUE)
    # normal plot of effects, default is autolabel with alpha=0.05
    DanielPlot(iM.lm)  
    DanielPlot(iM.lm,code=TRUE)
    DanielPlot(iM.lm,code=TRUE,alpha=0.5)
    # half normal plot of effects
    DanielPlot(iM.lm,code=TRUE,alpha=0.5,half=TRUE)
    # main effects plots
    MEPlot(iM.lm)
    # interaction plots
    IAPlot(iM.lm)
    # interaction plots with attention drawn to aliases
    IAPlot(iM.lm, show.alias=TRUE)
    # alias groups corresponding to interaction plots
    aliases(iM.lm)$aliases[9:15]
    # cube plot of three factors
    # (not very useful for this model, for demonstration only)
      ## per default, modeled means are shown
      ## this does not make a difference here, since the main effect of 
      ## ScrewSpeed is confounded with the MoldTemp:HoldPress:BoostPress
      ## interaction, so that the three-factor-interaction is indirectly included 
      ## in the modeled means
      cubePlot(iM.lm, "MoldTemp", "HoldPress", "BoostPress")
      ## modeled means without a three-factor interaction
      cubePlot(lm(y ~ (MoldTemp+HoldPress+BoostPress)^2, data = iMdat), 
         "MoldTemp", "HoldPress", "BoostPress")
      ## modeled=FALSE reverts to showing the apparent three-factor interaction
      cubePlot(lm(y ~ (MoldTemp+HoldPress+BoostPress)^2, data = iMdat), 
         "MoldTemp", "HoldPress", "BoostPress", modeled=FALSE)
      ## cubePlot also works on raw data
      cubePlot(iMdat$y, iMdat$MoldTemp, iMdat$HoldPress, iMdat$BoostPress)

[Package FrF2 version 0.8 Index]