pvrank (version 1.0)

qrank: Calculation of quantiles of rank correlations

Description

For a given value of the test statistic, this routine computes approximated or exact conservative and liberal critical values under the hypothesis of no association.

Usage

qrank(prob, n, index="spearman", approx="vggfr", print = FALSE, lower.tail = TRUE)

Arguments

prob

the nominal level of significance.

n

the number of ranks.

index

a character string that specifies the rank correlation used in the test. Acceptable values are: "spearman","kendall","gini","r4". Only enough of the string to be unique is required.

approx

a character string that specifies the type of approximation to the null distribution: "vggfr", "exact","gaussian","student".

print

FALSE suppresses partial output.

lower.tail

logical; if TRUE (default), probability $P [X\leq x]$ is computed, otherwise $P[X>x]$.

Value

• a list containing the following components:
• n
  number of ranks.
• Statistic
  coefficient of rank order association
• Level
  nominal level
• Cq
  conservative quantile
• Cv
  conservative p-value
• Lq
  liberal quantile
• Lv
  liberal p-value

Details

This routine provides two exact quantiles corresponding to a conservative level (next smaller exact size) and a liberal level (next larger exact size). However, in the case of $n>26$ (Spearman) or $n>60$ (Kendall) or $n>24$ (Gini) or $n>15$ (r4), approximated quantiles are provided according to approx. The default option is "vggfr".

Exact computations use frequencies obtained by complete enumeration for Spearman's rho, Gini's gamma, and r4. A recursive formula is employed in the case of Kendall's tau.

Examples

qrank(0.10,61,"K","St")
qrank(0.01,25,"S","Ga")
qrank(0.05,27,"G","Vg",TRUE,FALSE)
qrank(0.03,11,"r4","Ex",TRUE,FALSE)