goreTest function

Gore Test

Performs Gore's test. The null hypothesis H$_0: \theta_i = \theta_j~~(i \ne j)$ is tested against the alternative H$_{\mathrm{A}}: \theta_i \ne \theta_j$, with at least one inequality beeing strict.

goreTest(y, groups, blocks)

Arguments

• y: a numeric vector of data values.
• groups: a vector or factor object giving the group for the corresponding elements of "y".
• blocks: a vector or factor object giving the group for the corresponding elements of "y".

Returns

A list with class "htest" containing the following components:

• method: a character string indicating what type of test was performed.
• data.name: a character string giving the name(s) of the data.
• statistic: the estimated quantile of the test statistic.
• p.value: the p-value for the test.
• parameter: the parameters of the test statistic, if any.
• alternative: a character string describing the alternative hypothesis.
• estimates: the estimates, if any.
• null.value: the estimate under the null hypothesis, if any.

Details

The function has implemented Gore's test for testing main effects in unbalanced CRB designs, i.e. there are one ore more observations per cell. The statistic is assymptotically chi-squared distributed.

Examples

## Crop Yield of 3 varieties on two
## soil classes
X <-c("130,A,Light
115,A,Light
123,A,Light
142,A,Light
117,A,Heavy
125,A,Heavy
139,A,Heavy
108,B,Light
114,B,Light
124,B,Light
106,B,Light
91,B,Heavy
111,B,Heavy
110,B,Heavy
155,C,Light
146,C,Light
151,C,Light
165,C,Light
97,C,Heavy
108,C,Heavy")
con <- textConnection(X)
x <- read.table(con, header=FALSE, sep=",")
close(con)
colnames(x) <- c("Yield", "Variety", "SoilType")
goreTest(y = x$Yield, groups = x$Variety, blocks = x$SoilType)

References

Gore, A. P. (1975) Some nonparametric tests and selection procedures for main effects in two-way layouts. Ann. Inst. Stat. Math. 27 , 487--500.

See Also

friedmanTest, skillingsMackTest, durbinTest