asbio (version 1.9-2)

MS.test: Mack-Skillings test

Description

Runs a Mack-Skillings test for situations applicable to rank-based permutation procedures with blocking and more than one replicate for treatments in a block.

Usage

MS.test(Y, X, reps)

Value

Returns a dataframe summarizing the degrees of freedom, test statistic and p-value.

Arguments

Y

A matrix of response data. The MS.test function requires that response data are organized in columns (see example below).

X

A vector of treatments. The length of the vector should be equal to the number of rows in the response matrix.

reps

The number of replicates in each treatment (unbalanced designs cannot be analyzed).

Author

Ken Aho

Details

When we have more than one replication within a block, and the number of replications is equal for all treatments, we can use the Mack-Skillings test (Mack and Skillings 1980) as a rank based permutation procedure to test for main effect differences. If ties occur the value of the significance level is only approximate. Hollander and Wolfe (1996) provide a method for finding exact P-values by deriving a test statistic distribution allowing ties.

References

Campbell, J. A., and O. Pelletier (1962) Determination of niacin (niacinamide) in cereal products. J. Assoc. Offic. Anal. Chem. 45: 449-453.

Hollander, M., and D. A. Wolfe (1999) Nonparametric Statistical Methods. New York: John Wiley & Sons.

Mack, G. A., and J. H. Skillings (1980) A Friedman-type rank test for main effects in a two-factor ANOVA. Journal of the American Statistical Association. 75: 947-951.

See Also

friedman.test

Examples

#data from Campbell and Pelletier (1962) 
Niacin0<-c(7.58,7.87,7.71,8.00,8.27,8,7.6,7.3,7.82,8.03,7.35,7.66)
Niacin4<-c(11.63,11.87,11.40,12.20,11.70,11.80,11.04,11.50,11.49,11.50,10.10,11.70)
Niacin8<-c(15.00,15.92,15.58,16.60,16.40,15.90,15.87,15.91,16.28,15.10,14.80,15.70)
Niacin<-cbind(Niacin0,Niacin4,Niacin8)
lab<-c(rep(1,3),rep(2,3),rep(3,3),rep(4,3))
MS.test(Niacin, lab, reps=3)