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Scheffé's Method for Planned Contrasts

Source: R/Scheffe_test.R
Scheffe_test.Rd

Performs Scheffé's multiple-comparison procedure for testing planned contrasts among group means following an analysis of variance (ANOVA). By default, all pairwise comparisons are performed (NOT recommended, please use other tests to conduct pairwise comparison). Users can also specify custom contrasts through the planned_contrasts argument.

Usage

Scheffe_test(
  data,
  formula = NULL,
  alpha = 0.05,
  rounding = 4,
  verbose = TRUE,
  planned_contrasts = NULL
)

Arguments

data

A data frame, a list, or an object returned by oneway_anova(), from which the response and grouping variables are obtained.

formula

A two-sided formula specifying the response and grouping variables in the form response ~ group. Ignored if data is a list or an "oneway_aov" object.

alpha

A numeric value between 0 and 1 (default: 0.05) specifying the significance level.

rounding

An integer (default: 4). The number of decimal places to display in the output.

verbose

Logical (default: TRUE). Show warnings and messages.

planned_contrasts

An optional contrast matrix. For example, see pairwise_contrasts(). Each row represents a contrast, and each column corresponds to a group. If NULL, all pairwise contrasts are generated automatically. Custom contrasts should have coefficients that define the intended linear comparisons among group means.

Value

An object containing the results of the Scheffé planned-contrast analysis, including the underlying ANOVA results, group summaries, post-hoc comparison results, and contrast matrix. The object is returned invisibly.

References

Heckert, N.A., Filliben, J.J., Croarkin, C.M., Hembree, B., Guthrie, W.F., Tobias, P., & Prinz, J. (2002). Handbook 151: Nist/sematech e-handbook of statistical methods. Section 7.4.6.2: Scheffe's method https://doi.org/10.18434/M32189

Howell, D.C. (2010). Statistical Methods for Psychology (7th ed.). Cengage Learning. Chapter 12: Multiple comparisons among treatment means, Section 12.3: A Priori Comparisons, pg. 374.

Montgomery, D.C. (2017). Design and analysis of experiments (9th ed.). John Wiley & Sons. pg. 89-95.

Scheffé, H. (1953). A method for judging all contrasts in the analysis of variance. Biometrika, 40, 87–104. https://doi.org/10.1093/biomet/40.1-2.87

See also

oneway_anova(), pairwise_contrasts()

Examples

# Compare all pairwise group means using Scheffé's method
out <- Scheffe_test(morphine, tolerance ~ grp)
#> 
#> -----------------------------------
#> Scheffe's planned contrasts method
#> -----------------------------------
#> Data: morphine ; Formula: tolerance ~ grp
#> 
#>     x1  x2 [x1 - x2] Pvalue signif     [x1 - x2] 95% CI      F  Fcrit StdErr
#> 1   MM  MS         6 0.0049     **   [-3.1939, 15.1939]  4.500 3.2505 2.8284
#> 2   MM McM       -19 0.0000    ***  [-28.1939, -9.8061] 45.125 3.2505 2.8284
#> 3   MM  SM       -14 0.0000    ***  [-23.1939, -4.8061] 24.500 3.2505 2.8284
#> 4   MM  SS        -1 0.9725     ns   [-10.1939, 8.1939]  0.125 3.2505 2.8284
#> 5   MS McM       -25 0.0000    *** [-34.1939, -15.8061] 78.125 3.2505 2.8284
#> 6   MS  SM       -20 0.0000    *** [-29.1939, -10.8061] 50.000 3.2505 2.8284
#> 7   MS  SS        -7 0.0008    ***   [-16.1939, 2.1939]  6.125 3.2505 2.8284
#> 8  McM  SM         5 0.0268      *   [-4.1939, 14.1939]  3.125 3.2505 2.8284
#> 9  McM  SS        18 0.0000    ***    [8.8061, 27.1939] 40.500 3.2505 2.8284
#> 10  SM  SS        13 0.0000    ***    [3.8061, 22.1939] 21.125 3.2505 2.8284
#> 

# Specify custom contrasts
grp_names <- c("MS", "MM", "SS", "SM", "McM")
ca <- c(-1, -1, -1, 1.5, 1.5)
cb <- c(0, -1, 0, 0, 1)
cc <- c(-1, 0, 1, 0, 0)
cd <- c(0, 1, -1, 0, 0)
contr <- matrix(c(ca, cb, cc, cd), ncol = length(grp_names), byrow = TRUE)
colnames(contr) <- grp_names
out <- Scheffe_test(morphine, tolerance ~ grp, planned_contrasts = contr)
#> 
#> -----------------------------------
#> Scheffe's planned contrasts method
#> -----------------------------------
#> Data: morphine ; Formula: tolerance ~ grp
#> 
#>         x1           x2 [x1 - x2] Pvalue signif   [x1 - x2] 95% CI       F
#> 1 McM + SM MM + MS + SS   18.1667 0.0000    *** [12.2321, 24.1013] 99.0083
#> 2      McM           MM   19.0000 0.0000    ***  [9.8061, 28.1939] 45.1250
#> 3       SS           MS    7.0000 0.0008    *** [-2.1939, 16.1939]  6.1250
#> 4       MM           SS   -1.0000 0.9725     ns [-10.1939, 8.1939]  0.1250
#>    Fcrit StdErr
#> 1 3.2505 1.8257
#> 2 3.2505 2.8284
#> 3 3.2505 2.8284
#> 4 3.2505 2.8284
#>