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Theil-Sen estimate and confidence interval for slope

Source: R/statpsych2.R
ci.theil.Rd

Computes a Theil-Sen estimate and distribution-free confidence interval for the population slope in a simple linear regression model. An approximate standard error is recovered from the confidence interval.

For more details, see Section 1.32 of Bonett (2021, Volume 2)

Usage

ci.theil(alpha, y, x)

Arguments

alpha

alpha level for 1-alpha confidence

y

vector of response variable scores

x

vector of predictor variable scores (paired with y)

Value

Returns a 1-row matrix. The columns are:

  • Estimate - Theil-Sen estimate of population slope

  • SE - recovered standard error

  • LL - lower limit of confidence interval

  • UL - upper limit of confidence interval

References

Hollander M, Wolf DA (1999). Nonparametric Statistical Methods. Wiley.

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

y <- c(21, 4, 9, 12, 35, 18, 10, 22, 24, 1, 6, 8, 13, 16, 19)
x <- c(67, 28, 30, 28, 52, 40, 25, 37, 44, 10, 14, 20, 28, 40, 51)
ci.theil(.05, y, x)
#>  Estimate        SE        LL   UL
#>       0.5 0.1085927 0.3243243 0.75

# Should return:
# Estimate        SE        LL   UL
#      0.5 0.1085927 0.3243243 0.75