Multiple Comparisons

Analysis of variance models are typically used to compare the effects of several treatments upon some response. After an analysis of variance model has been fit, it is often of interest to determine whether any significant differences exist between the responses for the various treatment groups and, if so, to estimate the size of the differences. Multiple Comparisons provides tests for equality of effects and estimates of treatment effects.

The Multiple Comparisons dialog calculates simultaneous or nonsimultaneous confidence intervals or bounds for any number of estimable linear combinations of the parameters of a fixed-effects linear model. It requires the name of an Analysis of Variance (aov) model or Linear Model (lm) and specification of which effects are of interest.

To perform multiple comparisons

Choose Statistics __image\arrow5.gif Analysis of Variance __image\arrow5.gif Multiple Comparisons. The dialog shown below appears.

__image\multcomp.gif

The Multiple Comparisons dialog has the following options:

Model Object

Select the model object on which to perform multiple comparisons.

Name String Match

Enter a pattern used to restrict the list shown in the Model Object dropdown list. The symbol "*" matches any character. For example, to view all objects that begin with "last", enter last*. Use "[ ]" to denote a list of character options. For example, "model1", "model2", and "model3" match model[123], but "model4" does not.

Variable

Levels Of

Select the term in the model to which comparisons will be made. This list is empty until a selection has been made in Model Object.

Comparison Type

Select the type of comparisons to be made among the adjusted means.

mca all pairwise differences

mcc all pairwise differences between all adjusted means and the adjusted means for the factor level specified in Compare To Level

none if the adjusted means themselves are of interest without further differencing.

Compare To Level

Select the factor level to which all other levels will be compared. This field is available only when Comparisons is set to mcc.

Results

Save As

Enter the name for the object in which to save the results of the analysis.

Print Results

Select this to print out the results of the analysis in the designated output window.

Plot Intervals

Select this for a graphical representation of the intervals.

Options

Method

Choose either maximum likelihood (mle) or principal factor estimation (principal). The default is maximum likelihood estimation.

Confidence Level

Enter the confidence level to use when computing confidence intervals. This value should be less than 1 and greater than 0.

Bounds

Select upper.and.lower for confidence intervals. For one-sided confidence bounds, select either upper or lower.

Error Type

Select the error rate type. If family-wise is selected, the probability that all bounds hold is the level specified in Confidence Level. If comparison-wise is selected, the probability that any one pre-selected bound holds is the level specified in the Confidence Level.

Adjust For

Specify a list of other factors and/or covariates in the model, and specified adjustment values for these.

Contrast Matrix

Enter the name of a contrast matrix. Each column specifies a linear combination to be estimated under the textbook parameterization of the linear model. See the online Help for multicomp or the chapter Multiple Comparisons in the Guide to Statistics for more

Critical Point

Enter a value for the critical point used in the confidence intervals/bounds. Use this if none of the methods are suitable.

Simulation Size

Enter the size of the simulation to use. This is available when Method is Simulation or Best. The default value provides intervals or bounds whose actual family-wise error rate is within 10% of the requested rate.

Scheffe Rank

Enter the rank of the design matrix. For example, in a model consisting solely of a sum of continuous predictors, this would be the number of coefficients. This is used by the methods Scheffe, best, and best.fast for computing the Scheffe estimates.

Validity Check

Select this to check the validity of the specified critical point calculation method for the desired comparisons. If the validity check fails, processing stops with an error message.

Estimability Check

Select this to check estimability of the desired linear combinations. If the estimability condition fails, processing stops with an error message.

S-Plus language functions related to Multiple Comparisons

multicomp, multicomp.default,
multicomp.lm, print.multicomp, plot. multicomp

Other related S-Plus language functions

aov, lm