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The denominator \eqn{n - 1} is used which gives an unbiased estimator
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The denominator \eqn{n - 1} is used which gives an unbiased estimator
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of the (co)variance for i.i.d. observations. These functions return
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of the (co)variance for i.i.d. observations. These functions return
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\code{\link{NA}} when there is only one observation.
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\code{\link{NA}} when there is only one observation.
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For \code{cor()}, if \code{method} is \code{"kendall"} or
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For \code{cor()}, if \code{method} is \code{"kendall"} or
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\code{"spearman"}, Kendall's \eqn{\tau}{tau} or Spearman's
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\code{"spearman"}, Kendall's \eqn{\tau} or Spearman's
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\eqn{\rho}{rho} statistic is used to estimate a rank-based measure of
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\eqn{\rho} statistic is used to estimate a rank-based measure of
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association. These are more robust and have been recommended if the
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association. These are more robust and have been recommended if the
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data do not necessarily come from a bivariate normal distribution.\cr
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data do not necessarily come from a bivariate normal distribution.\cr
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For \code{cov()}, a non-Pearson method is unusual but available for
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For \code{cov()}, a non-Pearson method is unusual but available for
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the sake of completeness. Note that \code{"spearman"} basically
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the sake of completeness. Note that \code{"spearman"} basically
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computes \code{cor(R(x), R(y))} (or \code{cov(., .)}) where \code{R(u)
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103 |
computes \code{cor(R(x), R(y))} (or \code{cov(., .)}) where \code{R(u)
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:= rank(u, na.last = "keep")}. In the case of missing values, the
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:= rank(u, na.last = "keep")}. In the case of missing values, the
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ranks are calculated depending on the value of \code{use}, either
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ranks are calculated depending on the value of \code{use}, either
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based on complete observations, or based on pairwise completeness with
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based on complete observations, or based on pairwise completeness with
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reranking for each pair.
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reranking for each pair.
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When there are ties, Kendall's \eqn{\tau_b}{tau_b} is computed, as
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When there are ties, Kendall's \eqn{\tau_b} is computed, as
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proposed by \bibcitet{R:Kendall:1945}.
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proposed by \bibcitet{R:Kendall:1945}.
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Scaling a covariance matrix into a correlation one can be achieved in
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Scaling a covariance matrix into a correlation one can be achieved in
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many ways, mathematically most appealing by multiplication with a
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many ways, mathematically most appealing by multiplication with a
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diagonal matrix from left and right, or more efficiently by using
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diagonal matrix from left and right, or more efficiently by using
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