Using `cor.test()` on ranked data - r

Question

I would like to do a Spearman correlation test using rank data. How can I do this with cor.test()? I don't want the function to rerank the data.
Additionally, what form does the data need to be in? From the help, it seems to be the raw data as compared to a correlation matrix.
Consider this example
## Hollander & Wolfe (1973), p. 187f.
## Assessment of tuna quality. We compare the Hunter L measure of
## lightness to the averages of consumer panel scores (recoded as
## integer values from 1 to 6 and averaged over 80 such values) in
## 9 lots of canned tuna.
library(tidyverse)
A <- tibble(
x = c(44.4, 45.9, 41.9, 53.3, 44.7, 44.1, 50.7, 45.2, 60.1),
y = c( 2.6, 3.1, 2.5, 5.0, 3.6, 4.0, 5.2, 2.8, 3.8)
) %>%
mutate(rank_x = rank(x),
rank_y = rank(y)
)
Spearman's correlation coefficient is defined as Pearson's correlation between ranked variables
cor(A$x, A$y, method = "spearman")
#[1] 0.6
cor(A$rank_x, A$rank_y, method = "pearson")
#[1] 0.6
what about cor.test()? Can I use the rank data as its input?
x1 <- cor.test(A$x, A$y, method = "spearman")
x1
# Spearman's rank correlation rho
#
# data: A$x and A$y
# S = 48, p-value = 0.1
# alternative hypothesis: true rho is not equal to 0
# sample estimates:
# rho
# 0.6
x2 <- cor.test(A$rank_x, A$rank_y, method = "pearson")
x2
# Pearson's product-moment correlation
# data: A$rank_x and A$rank_y
# t = 2, df = 7, p-value = 0.09
# alternative hypothesis: true correlation is not equal to 0
# 95 percent confidence interval:
# -0.11 0.90
# sample estimates:
# cor
# 0.6
x3 <- cor.test(A$rank_x, A$rank_y, method = "spearman")
# Spearman's rank correlation rho
#
# data: A$rank_x and A$rank_y
# S = 48, p-value = 0.1
# alternative hypothesis: true rho is not equal to 0
# sample estimates:
# rho
# 0.6

Answer 1

Yes, you should use method = Spearman for ranked or original data. If rank data is used, the data is not reranked in the function.
As the help file implies, using method=Pearson with rank data conducts a Pearson's correlation test on the ranks, which would follow a t-distribution. However, since the ranks are not continuous variables, this approach is not correct.
getAnywhere(cor.test.default)
A single object matching ‘cor.test.default’ was found
It was found in the following places
registered S3 method for cor.test from namespace stats
namespace:stats
with value
function (x, y, alternative = c("two.sided", "less",
"greater"), method = c("pearson", "kendall",
"spearman"), exact = NULL, conf.level = 0.95, continuity = FALSE,
...)
{
alternative <- match.arg(alternative)
method <- match.arg(method)
DNAME <- paste(deparse1(substitute(x)), "and", deparse1(substitute(y)))
if (!is.numeric(x))
stop("'x' must be a numeric vector")
if (!is.numeric(y))
stop("'y' must be a numeric vector")
if (length(x) != length(y))
stop("'x' and 'y' must have the same length")
OK <- complete.cases(x, y)
x <- x[OK]
y <- y[OK]
n <- length(x)
NVAL <- 0
conf.int <- FALSE
if (method == "pearson") {
if (n < 3L)
stop("not enough finite observations")
method <- "Pearson's product-moment correlation"
names(NVAL) <- "correlation"
r <- cor(x, y)
df <- n - 2L
ESTIMATE <- c(cor = r)
PARAMETER <- c(df = df)
STATISTIC <- c(t = sqrt(df) * r/sqrt(1 - r^2))
if (n > 3) {
if (!missing(conf.level) && (length(conf.level) !=
1 || !is.finite(conf.level) || conf.level < 0 ||
conf.level > 1))
stop("'conf.level' must be a single number between 0 and 1")
conf.int <- TRUE
z <- atanh(r)
sigma <- 1/sqrt(n - 3)
cint <- switch(alternative, less = c(-Inf, z + sigma *
qnorm(conf.level)), greater = c(z - sigma * qnorm(conf.level),
Inf), two.sided = z + c(-1, 1) * sigma * qnorm((1 +
conf.level)/2))
cint <- tanh(cint)
attr(cint, "conf.level") <- conf.level
}
PVAL <- switch(alternative, less = pt(STATISTIC, df),
greater = pt(STATISTIC, df, lower.tail = FALSE),
two.sided = 2 * min(pt(STATISTIC, df), pt(STATISTIC,
df, lower.tail = FALSE)))
}
else {
if (n < 2)
stop("not enough finite observations")
PARAMETER <- NULL
TIES <- (min(length(unique(x)), length(unique(y))) <
n)
if (method == "kendall") {
method <- "Kendall's rank correlation tau"
names(NVAL) <- "tau"
r <- cor(x, y, method = "kendall")
ESTIMATE <- c(tau = r)
if (!is.finite(ESTIMATE)) {
ESTIMATE[] <- NA
STATISTIC <- c(T = NA)
PVAL <- NA
}
else {
if (is.null(exact))
exact <- (n < 50)
if (exact && !TIES) {
q <- round((r + 1) * n * (n - 1)/4)
STATISTIC <- c(T = q)
pkendall <- function(q, n) .Call(C_pKendall,
q, n)
PVAL <- switch(alternative, two.sided = {
if (q > n * (n - 1)/4) p <- 1 - pkendall(q -
1, n) else p <- pkendall(q, n)
min(2 * p, 1)
}, greater = 1 - pkendall(q - 1, n), less = pkendall(q,
n))
}
else {
xties <- table(x[duplicated(x)]) + 1
yties <- table(y[duplicated(y)]) + 1
T0 <- n * (n - 1)/2
T1 <- sum(xties * (xties - 1))/2
T2 <- sum(yties * (yties - 1))/2
S <- r * sqrt((T0 - T1) * (T0 - T2))
v0 <- n * (n - 1) * (2 * n + 5)
vt <- sum(xties * (xties - 1) * (2 * xties +
5))
vu <- sum(yties * (yties - 1) * (2 * yties +
5))
v1 <- sum(xties * (xties - 1)) * sum(yties *
(yties - 1))
v2 <- sum(xties * (xties - 1) * (xties - 2)) *
sum(yties * (yties - 1) * (yties - 2))
var_S <- (v0 - vt - vu)/18 + v1/(2 * n * (n -
1)) + v2/(9 * n * (n - 1) * (n - 2))
if (exact && TIES)
warning("Cannot compute exact p-value with ties")
if (continuity)
S <- sign(S) * (abs(S) - 1)
STATISTIC <- c(z = S/sqrt(var_S))
PVAL <- switch(alternative, less = pnorm(STATISTIC),
greater = pnorm(STATISTIC, lower.tail = FALSE),
two.sided = 2 * min(pnorm(STATISTIC), pnorm(STATISTIC,
lower.tail = FALSE)))
}
}
}
else {
method <- "Spearman's rank correlation rho"
if (is.null(exact))
exact <- TRUE
names(NVAL) <- "rho"
r <- cor(rank(x), rank(y))
ESTIMATE <- c(rho = r)
if (!is.finite(ESTIMATE)) {
ESTIMATE[] <- NA
STATISTIC <- c(S = NA)
PVAL <- NA
}
else {
pspearman <- function(q, n, lower.tail = TRUE) {
if (n <= 1290 && exact)
.Call(C_pRho, round(q) + 2 * lower.tail,
n, lower.tail)
else {
den <- (n * (n^2 - 1))/6
if (continuity)
den <- den + 1
r <- 1 - q/den
pt(r/sqrt((1 - r^2)/(n - 2)), df = n - 2,
lower.tail = !lower.tail)
}
}
q <- (n^3 - n) * (1 - r)/6
STATISTIC <- c(S = q)
if (TIES && exact) {
exact <- FALSE
warning("Cannot compute exact p-value with ties")
}
PVAL <- switch(alternative, two.sided = {
p <- if (q > (n^3 - n)/6) pspearman(q, n, lower.tail = FALSE) else pspearman(q,
n, lower.tail = TRUE)
min(2 * p, 1)
}, greater = pspearman(q, n, lower.tail = TRUE),
less = pspearman(q, n, lower.tail = FALSE))
}
}
}
RVAL <- list(statistic = STATISTIC, parameter = PARAMETER,
p.value = as.numeric(PVAL), estimate = ESTIMATE, null.value = NVAL,
alternative = alternative, method = method, data.name = DNAME)
if (conf.int)
RVAL <- c(RVAL, list(conf.int = cint))
class(RVAL) <- "htest"
RVAL
}
<bytecode: 0x0000018603fa9418>
<environment: namespace:stats>