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Function offering four methods to find the CI around an observed Spearman correlation

getCISpearman.Rd

Function offering four methods to find the CI around an observed Spearman correlation

Usage

getCISpearman(rs, n, ci = 0.95, Gaussian = FALSE, FHP = FALSE)

Arguments

rs

numeric: the observed Spearman correlation

n

numeric: the number of (paired) values for the correlation

ci

numeric: the confidence interval you want, default .95, i.e. 95%

Gaussian

logical: use the Gaussian lookup for the CI, defaults to FALSE

FHP

logical: use the Fieller, Hartley & Pearson (1957) method, defaults to FALSE

Value

A named vector LCL and UCL

Background

This is very simple function to return the confidence limits of the confidence interval around an observed Pearson correlation given the number of observations in the dataset (n) and the confidence interval required (ci, defaults to .95). There are four methods obtained by using either the Bonett & White (2000) approximation to the SE of the correlation or the the Fieller, Hartley & Pearson (1957) approximation and combining those with either looking up the value of the Gaussian to get the desired CI coverage or using the value of the t distribution with df = n - 2. It is known that none of the methods work well, i.e. give coverage matching that desired and without bias, when the n is below 25 and/or the absolute population Spearman correlation is above .95 so use with caution if n < 25 and observed correlation > .90.

The function just returns a named vector of the LCL and UCL which should help using it in tidyverse pipes. See examples.

There is more information about the function in my Rblog at Confidence interval around Spearman correlation coefficient.

There is also a shiny app using this function at https://shiny.psyctc.org/apps/CISpearman/

References/acknowledgements

  1. This started from finding the excellent answers from onestop https://stats.stackexchange.com/users/449/onestop and retodomax https://stats.stackexchange.com/users/237402/retodomax to the question on CrossValidated specifically How to calculate a confidence interval for Spearman's rank correlation? Also, as referenced in that page ...

  2. Bishara, A. J., & Hittner, J. B. (2017). Confidence intervals for correlations when data are not normal. Behavior Research Methods, 49(1), 294–309. https://doi.org/10.3758/s13428-016-0702-8 gives extensive simulation work covering much more than these CIs. I checked my code against the results from the R code given in Supplement A to that paper. Then ...

  3. Bonett, D. G., & Wright, T. A. (2000). Sample size requirements for estimating pearson, kendall and spearman correlations. Psychometrika, 65(1), 23–28. https://doi.org/10.1007/BF02294183 is a classic (interesting to see how typesetting of equations has improved since 2000!) and ...

  4. Ruscio, J. (2008). Constructing Confidence Intervals for Spearman’s Rank Correlation with Ordinal Data: A Simulation Study Comparing Analytic and Bootstrap Methods. Journal of Modern Applied Statistical Methods, 7(2), 416–434. https://doi.org/10.22237/jmasm/1225512360 was another excellent paper on the topic.

Thanks to all those authors.

History/development log

Version 1: 27.xi.23

See also

Other confidence interval functions: getCIPearson(), plotBinconf(), plotCIPearson()

Author

Chris Evans

Examples

if (FALSE) {
getCISpearman(.5, 50)
# LCL       UCL
# 0.2338274 0.6964523
getCISpearman(.5, 50, Gaussian = TRUE)
# LCL       UCL
# 0.2412245 0.6923933
getCISpearman(.5, 50, Gaussian = TRUE, FHP = TRUE)
# LCL       UCL
# 0.2495794 0.6877365
getCISpearman(.5, 50, Gaussian = FALSE, FHP = TRUE)
# LCL       UCL
# 0.2424304 0.6917259

### imaginary correlations of CORE-OM scores against number of children by parental gender
### create a tibble of the imaginary data
tribble(~pGender, ~rs, ~n,
        "M", .12, 643,
        "F", .57, 808) -> tibDat

### check it
tibDat

### use it
tibDat %>%
  rowwise() %>%
  ### need to use list() as we're getting a vector
  ### using the default arguments for getCISpearman()
  mutate(CISpearman = list(getCISpearman(rs, n))) %>%
  ### now get the values from the vectors
  unnest_wider(CISpearman)
# # A tibble: 2 × 5
# pGender    rs     n    LCL   UCL
# <chr>   <dbl> <dbl>  <dbl> <dbl>
# 1 M        0.12   643 0.0427 0.196
# 2 F        0.57   808 0.518  0.618
### pretty clear that the correlation for the women is very different
### from that for the men
}