# ScheffeTest: Scheffe Test for Pairwise and Otherwise Comparisons In DescTools: Tools for Descriptive Statistics

## Description

Scheffe's method applies to the set of estimates of all possible contrasts among the factor level means, not just the pairwise differences considered by Tukey's method.

## Usage

 ```1 2 3 4 5 6 7 8``` ```ScheffeTest(x, ...) ## S3 method for class 'aov' ScheffeTest(x, which = NULL, contrasts = NULL, conf.level = 0.95, ...) ## Default S3 method: ScheffeTest(x, g = NULL, which = NULL, contrasts = NULL, conf.level = 0.95, ...) ```

## Arguments

 `x` either a fitted model object, usually an `aov` fit, when g is left to `NULL` or a response variable to be evalutated by g (which mustn't be `NULL` then). `g` the grouping variable. `which` character vector listing terms in the fitted model for which the intervals should be calculated. Defaults to all the terms. `contrasts` a r x c matrix containing the contrasts to be computed, while `r` is the number of factor levels and `c` the number of contrasts. Each column must contain a full contrast ("sum") adding up to 0. Note that the argument `which` must be defined, when non default contrasts are used. Default value of `contrasts` is `NULL`. In this case all pairwise contrasts will be reported. `conf.level` numeric value between zero and one giving the confidence level to use. If this is set to NA, just a matrix with the p-values will be returned. `...` further arguments, currently not used.

## Value

A list of classes `c("PostHocTest")`, with one component for each term requested in `which`. Each component is a matrix with columns `diff` giving the difference in the observed means, `lwr.ci` giving the lower end point of the interval, `upr.ci` giving the upper end point and `pval` giving the p-value after adjustment for the multiple comparisons.

There are print and plot methods for class `"PostHocTest"`. The plot method does not accept `xlab`, `ylab` or `main` arguments and creates its own values for each plot.

## Author(s)

Andri Signorell <[email protected]>

## References

Robert O. Kuehl, Steel R. (2000) Design of experiments. Duxbury

Steel R.G.D., Torrie J.H., Dickey, D.A. (1997) Principles and Procedures of Statistics, A Biometrical Approach. McGraw-Hill

`pairwise.t.test`, `TukeyHSD`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```fm1 <- aov(breaks ~ wool + tension, data = warpbreaks) ScheffeTest(x=fm1) ScheffeTest(x=fm1, which="tension") TukeyHSD(fm1) # some special contrasts y <- c(7,33,26,27,21,6,14,19,6,11,11,18,14,18,19,14,9,12,6, 24,7,10,1,10,42,25,8,28,30,22,17,32,28,6,1,15,9,15, 2,37,13,18,23,1,3,4,6,2) group <- factor(c(1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3, 3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6)) r.aov <- aov(y ~ group) ScheffeTest(r.aov, contrasts=matrix( c(1,-0.5,-0.5,0,0,0, 0,0,0,1,-0.5,-0.5), ncol=2) ) # just p-values: ScheffeTest(r.aov, conf.level=NA) ```

### Example output

```  Posthoc multiple comparisons of means : Scheffe Test
95% family-wise confidence level

\$wool
diff    lwr.ci   upr.ci   pval
B-A -5.777778 -14.92513 3.369576 0.3526

\$tension
diff    lwr.ci    upr.ci   pval
M-L -10.000000 -21.20317  1.203174 0.0970 .
H-L -14.722222 -25.92540 -3.519048 0.0050 **
H-M  -4.722222 -15.92540  6.480952 0.6869

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Posthoc multiple comparisons of means : Scheffe Test
95% family-wise confidence level

\$tension
diff    lwr.ci    upr.ci   pval
M-L -10.000000 -21.20317  1.203174 0.0970 .
H-L -14.722222 -25.92540 -3.519048 0.0050 **
H-M  -4.722222 -15.92540  6.480952 0.6869

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Tukey multiple comparisons of means
95% family-wise confidence level

Fit: aov(formula = breaks ~ wool + tension, data = warpbreaks)

\$wool
diff       lwr       upr     p adj
B-A -5.777778 -12.12841 0.5728505 0.0736137

\$tension
diff       lwr        upr     p adj
M-L -10.000000 -19.35342 -0.6465793 0.0336262
H-L -14.722222 -24.07564 -5.3688015 0.0011218
H-M  -4.722222 -14.07564  4.6311985 0.4474210

Posthoc multiple comparisons of means : Scheffe Test
95% family-wise confidence level

\$group
diff    lwr.ci   upr.ci   pval
1-2,3  7.2500 -6.417446 20.91745 0.6367
4-5,6 14.0625  0.395054 27.72995 0.0401 *

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Posthoc multiple comparisons of means : Scheffe Test

\$group
1     2     3     4     5
2 0.927 -     -     -     -
3 0.531 0.977 -     -     -
4 0.848 0.273 0.054 -     -
5 0.940 1.000 0.970 0.296 -
6 0.400 0.934 1.000 0.031 0.920
```

DescTools documentation built on Aug. 14, 2018, 5:05 p.m.