Package 'confintr' reference manual

Title:	Confidence Intervals
Description:	Calculates classic and/or bootstrap confidence intervals for many parameters such as the population mean, variance, interquartile range (IQR), median absolute deviation (MAD), skewness, kurtosis, Cramer's V, odds ratio, R-squared, quantiles (incl. median), proportions, different types of correlation measures, difference in means, quantiles and medians. Many of the classic confidence intervals are described in Smithson, M. (2003, ISBN: 978-0761924999). Bootstrap confidence intervals are calculated with the R package 'boot'. Both one- and two-sided intervals are supported.
Authors:	Michael Mayer [aut, cre]
Maintainer:	Michael Mayer <[email protected]>
License:	GPL (>= 2)
Version:	1.0.3
Built:	2024-08-23 05:32:53 UTC
Source:	https://github.com/mayer79/confintr

CI for the NCP of the Chi-Squared Distribution

Description

This function calculates CIs for the non-centrality parameter (NCP) of the $\chi^2$ -distribution. A positive lower $(1 - \alpha) \cdot 100\%$ -confidence limit for the NCP goes hand-in-hand with a significant association test at level $\alpha$ .

Usage

ci_chisq_ncp(
  x,
  probs = c(0.025, 0.975),
  correct = TRUE,
  type = c("chi-squared", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_chisq_ncp(
  x,
  probs = c(0.025, 0.975),
  correct = TRUE,
  type = c("chi-squared", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	The result of `stats::chisq.test()`, a matrix/table of counts, or a `data.frame` with exactly two columns representing the two variables.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`correct`	Should Yates continuity correction be applied to the 2x2 case? The default is `TRUE` (also used in the bootstrap), which differs from `ci_cramersv()`.
`type`	Type of CI. One of "chi-squared" (default) or "bootstrap".
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Details

By default, CIs are computed by Chi-squared test inversion. This can be unreliable for very large test statistics. The default bootstrap type is "bca".

Value

An object of class "cint", see ci_mean() for details.

References

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.

Examples

ci_chisq_ncp(mtcars[c("am", "vs")])
ci_chisq_ncp(mtcars[c("am", "vs")], type = "bootstrap", R = 999)  # Use larger R
ci_chisq_ncp(mtcars[c("am", "vs")])
ci_chisq_ncp(mtcars[c("am", "vs")], type = "bootstrap", R = 999)  # Use larger R

CI for Correlation Coefficients

Description

This function calculates CIs for a population correlation coefficient. For Pearson correlation, "normal" CIs are available (by stats::cor.test()). Also bootstrap CIs are supported (by default "bca", and the only option for rank correlations).

Usage

ci_cor(
  x,
  y = NULL,
  probs = c(0.025, 0.975),
  method = c("pearson", "kendall", "spearman"),
  type = c("normal", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_cor(
  x,
  y = NULL,
  probs = c(0.025, 0.975),
  method = c("pearson", "kendall", "spearman"),
  type = c("normal", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector or a `matrix`/`data.frame` with exactly two numeric columns.
`y`	A numeric vector (only used if `x` is a vector).
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`method`	Type of correlation coefficient, one of "pearson" (default), "kendall", or "spearman". For the latter two, only bootstrap CIs are supported.
`type`	Type of CI. One of "normal" (the default) or "bootstrap" (the only option for rank-correlations).
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Value

An object of class "cint", see ci_mean() for details.

Examples

ci_cor(iris[1:2])
ci_cor(iris[1:2], type = "bootstrap", R = 999)  # Use larger R
ci_cor(iris[1:2], method = "spearman", type = "bootstrap", R = 999)  # Use larger R
ci_cor(iris[1:2])
ci_cor(iris[1:2], type = "bootstrap", R = 999)  # Use larger R
ci_cor(iris[1:2], method = "spearman", type = "bootstrap", R = 999)  # Use larger R

CI for the Population Cramer's V

Description

This function calculates CIs for the population Cramer's V. By default, a parametric approach based on the non-centrality parameter (NCP) of the chi-squared distribution is utilized. Alternatively, bootstrap CIs are available (default "bca"), also by boostrapping CIs for the NCP and then mapping the result back to Cramer's V.

Usage

ci_cramersv(
  x,
  probs = c(0.025, 0.975),
  type = c("chi-squared", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  test_adjustment = TRUE,
  ...
)
ci_cramersv(
  x,
  probs = c(0.025, 0.975),
  type = c("chi-squared", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  test_adjustment = TRUE,
  ...
)

Arguments

`x`	The result of `stats::chisq.test()`, a matrix/table of counts, or a `data.frame` with exactly two columns representing the two variables.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. One of "chi-squared" (default) or "bootstrap".
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`test_adjustment`	Adjustment to allow for test of association, see Details. The default is `TRUE`.
`...`	Further arguments passed to `boot::boot()`.

Details

A positive lower $(1 - \alpha) \cdot 100\%$ -confidence limit for the NCP goes hand-in-hand with a significant association test at level $\alpha$ . In order to allow such test approach also with Cramer's V, if the lower bound for the NCP is 0, we round down to 0 the lower bound for Cramer's V as well. Without this slightly conservative adjustment, the lower limit for V would always be positive since the CI for V is found by $\sqrt{(\textrm{CI for NCP} + \textrm{df})/(n \cdot (k - 1))}$ , where $k$ is the smaller number of levels in the two variables (see Smithson, p.40). Use test_adjustment = FALSE to switch off this behaviour. Note that this is also a reason to bootstrap V via NCP instead of directly bootstrapping V.

Further note that no continuity correction is applied for 2x2 tables, and that large chi-squared test statistics might provide unreliable results with method "chi-squared", see stats::pchisq().

Value

An object of class "cint", see ci_mean() for details.

References

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.

Examples

# Example from Smithson, M., page 41
test_scores <- as.table(
  rbind(
    Private = c(6, 14, 17, 9),
    Public = c(30, 32, 17, 3)
  )
)
suppressWarnings(X2 <- stats::chisq.test(test_scores))
ci_cramersv(X2)
# Example from Smithson, M., page 41
test_scores <- as.table(
  rbind(
    Private = c(6, 14, 17, 9),
    Public = c(30, 32, 17, 3)
  )
)
suppressWarnings(X2 <- stats::chisq.test(test_scores))
ci_cramersv(X2)

CI for the Non-Centrality Parameter of the F Distribution

Description

Based on the inversion principle, parametric CIs for the non-centrality parameter (NCP) Delta of the F distribution are calculated. To keep the input interface simple, we do not provide bootstrap CIs here.

Usage

ci_f_ncp(x, df1 = NULL, df2 = NULL, probs = c(0.025, 0.975))
ci_f_ncp(x, df1 = NULL, df2 = NULL, probs = c(0.025, 0.975))

Arguments

`x`	The result of `stats::lm()` or the F test statistic.
`df1`	The numerator df. Only used if `x` is a test statistic.
`df2`	The denominator df. Only used if `x` is a test statistic.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.

Details

A positive lower $(1 - \alpha) \cdot 100\%$ -confidence limit for the NCP goes hand-in-hand with a significant F test at level $\alpha$ . According to stats::pf(), the results might be unreliable for very large F values.

Value

An object of class "cint", see ci_mean() for details.

References

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.

Examples

fit <- lm(Sepal.Length ~ ., data = iris)
ci_f_ncp(fit)
ci_f_ncp(fit, probs = c(0.05, 1))
fit <- lm(Sepal.Length ~ ., data = iris)
ci_f_ncp(fit)
ci_f_ncp(fit, probs = c(0.05, 1))

CI for the IQR

Description

This function calculates bootstrap CIs (by default "bca") for the population interquartile range (IQR), i.e., the difference between first and third quartile.

Usage

ci_IQR(
  x,
  probs = c(0.025, 0.975),
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_IQR(
  x,
  probs = c(0.025, 0.975),
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. Currently not used as the only type is `"bootstrap"`.
`boot_type`	Type of bootstrap CI c("bca", "perc", "norm", "basic").
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Value

An object of class "cint", see ci_mean() for details.

Examples

x <- rnorm(100)
ci_IQR(x, R = 999)  # Use larger R
x <- rnorm(100)
ci_IQR(x, R = 999)  # Use larger R

CI for the Kurtosis

Description

This function calculates bootstrap CIs for the population kurtosis. Note that we use the version of the kurtosis that equals 3 under a normal distribution, i.e., we are not calculating the excess kurtosis. By default, bootstrap type "bca" is used.

Usage

ci_kurtosis(
  x,
  probs = c(0.025, 0.975),
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_kurtosis(
  x,
  probs = c(0.025, 0.975),
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. Currently not used as the only type is `"bootstrap"`.
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Value

An object of class "cint", see ci_mean() for details.

Examples

x <- 1:20
ci_kurtosis(x, R = 999)  # Use larger R
x <- 1:20
ci_kurtosis(x, R = 999)  # Use larger R

CI for the MAD

Description

This function calculates bootstrap CIs (default: "bca") for the population median absolute deviation (MAD), see stats::mad() for more information.

Usage

ci_mad(
  x,
  probs = c(0.025, 0.975),
  constant = 1.4826,
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_mad(
  x,
  probs = c(0.025, 0.975),
  constant = 1.4826,
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`constant`	Scaling factor applied. The default (1.4826) ensures that the MAD equals the standard deviation for a theoretical normal distribution.
`type`	Type of CI. Currently not used as the only type is `"bootstrap"`.
`boot_type`	Type of bootstrap CI c("bca", "perc", "norm", "basic").
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Value

An object of class "cint", see ci_mean() for details.

Examples

x <- rnorm(100)
ci_mad(x, R = 999)  # Use larger R
x <- rnorm(100)
ci_mad(x, R = 999)  # Use larger R

CI for the Population Mean

Description

This function calculates CIs for the population mean. By default, Student's t method is used. Alternatively, Wald and bootstrap CIs are available.

Usage

ci_mean(
  x,
  probs = c(0.025, 0.975),
  type = c("t", "Wald", "bootstrap"),
  boot_type = c("stud", "bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_mean(
  x,
  probs = c(0.025, 0.975),
  type = c("t", "Wald", "bootstrap"),
  boot_type = c("stud", "bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. One of "t" (default), "Wald", or "bootstrap".
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Details

The default bootstrap type for the mean is "stud" (bootstrap t) as it enjoys the property of being second order accurate and has a stable variance estimator (see Efron, p. 188).

Value

An object of class "cint" containing these components:

parameter: Parameter specification.
interval: CI for the parameter.
estimate: Parameter estimate.
probs: Lower and upper probabilities.
type: Type of interval.
info: Additional description.

References

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.
Efron, B. and Tibshirani R. J. (1994). An Introduction to the Bootstrap. Chapman & Hall/CRC.

Examples

x <- 1:100
ci_mean(x)
ci_mean(x, type = "bootstrap", R = 999, seed = 1)  # Use larger R
x <- 1:100
ci_mean(x)
ci_mean(x, type = "bootstrap", R = 999, seed = 1)  # Use larger R

CI for the Population Mean Difference

Description

This function calculates CIs for the population value of mean(x) - mean(y). The default is Student's method with Welch's correction for unequal variances, but also bootstrap CIs are available.

Usage

ci_mean_diff(
  x,
  y,
  probs = c(0.025, 0.975),
  var.equal = FALSE,
  type = c("t", "bootstrap"),
  boot_type = c("stud", "bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_mean_diff(
  x,
  y,
  probs = c(0.025, 0.975),
  var.equal = FALSE,
  type = c("t", "bootstrap"),
  boot_type = c("stud", "bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`y`	A numeric vector.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`var.equal`	Should the two variances be treated as being equal? The default is `FALSE`. If `TRUE`, the pooled variance is used to estimate the variance of the mean difference. Otherweise, Welch's approach is used. This also applies to the "stud" bootstrap.
`type`	Type of CI. One of "t" (default), or "bootstrap".
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Details

The default bootstrap type is "stud" (bootstrap t) as it has a stable variance estimator (see Efron, p. 188). Resampling is done within sample. When boot_type = "stud", the standard error is estimated by Welch's method if var.equal = FALSE (the default), and by pooling otherwise. Thus, var.equal not only has an effect for the classic Student approach (type = "t") but also for boot_type = "stud".

Value

An object of class "cint", see ci_mean() for details.

References

Efron, B. and Tibshirani R. J. (1994). An Introduction to the Bootstrap. Chapman & Hall/CRC.

Examples

x <- 10:30
y <- 1:30
ci_mean_diff(x, y)
t.test(x, y)$conf.int
ci_mean_diff(x, y, type = "bootstrap", R = 999)  # Use larger R
x <- 10:30
y <- 1:30
ci_mean_diff(x, y)
t.test(x, y)$conf.int
ci_mean_diff(x, y, type = "bootstrap", R = 999)  # Use larger R

CI for the Population Median

Description

This function calculates CIs for the population median by calling ci_quantile().

Usage

ci_median(
  x,
  probs = c(0.025, 0.975),
  type = c("binomial", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_median(
  x,
  probs = c(0.025, 0.975),
  type = c("binomial", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. One of "binomial" (default), or "bootstrap".
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Value

An object of class "cint", see ci_mean() for details.

Examples

ci_median(1:100)
ci_median(1:100)

CI for the Population Median Difference of two Samples

Description

This function calculates bootstrap CIs for the population value of median(x) - median(y) by calling ci_quantile_diff().

Usage

ci_median_diff(
  x,
  y,
  probs = c(0.025, 0.975),
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_median_diff(
  x,
  y,
  probs = c(0.025, 0.975),
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`y`	A numeric vector.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. Currently, "bootstrap" is the only option.
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Value

An object of class "cint", see ci_mean() for details.

Examples

x <- 10:30
y <- 1:30
ci_median_diff(x, y, R = 999)  # Use larger value for R
x <- 10:30
y <- 1:30
ci_median_diff(x, y, R = 999)  # Use larger value for R

CI for the Odds Ratio

Description

This function calculates a CI for the odds ratio in a 2x2 table/matrix or a data frame with two columns. The CI is obtained through stats::fisher.test(). Bootstrap CIs are not available.

Usage

ci_oddsratio(x, probs = c(0.025, 0.975))
ci_oddsratio(x, probs = c(0.025, 0.975))

Arguments

`x`	A 2x2 matrix/table of counts, or a `data.frame` with exactly two columns representing the two binary variables.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.

Value

An object of class "cint", see ci_mean() for details.

Examples

x <- cbind(c(10, 5), c(4, 4))
ci_oddsratio(x)
x <- cbind(c(10, 5), c(4, 4))
ci_oddsratio(x)

CI for a Population Proportion

Description

This function calculates CIs for a population proportion. By default, "Clopper-Pearson" CIs are calculated (via stats::binom.test()). Further possibilities are "Wilson" (without continuity correction), "Agresti-Coull" (using normal quantile instead of +2 correction), and "bootstrap" (by default "bca").

Usage

ci_proportion(
  x,
  n = NULL,
  probs = c(0.025, 0.975),
  type = c("Clopper-Pearson", "Agresti-Coull", "Wilson", "bootstrap"),
  boot_type = c("bca", "perc", "stud", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_proportion(
  x,
  n = NULL,
  probs = c(0.025, 0.975),
  type = c("Clopper-Pearson", "Agresti-Coull", "Wilson", "bootstrap"),
  boot_type = c("bca", "perc", "stud", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector with one value (0/1) per observation, or the number of successes.
`n`	The sample size. Only needed if `x` is a vector of length 1.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. One of "Clopper-Pearson" (the default), "Agresti–Coull", "Wilson", "bootstrap".
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Details

Note that we use the formulas for the Wilson and Agresti-Coull intervals in https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval. They agree with binom::binom.confint(x, n, method = "ac"/"wilson").

Value

An object of class "cint", see ci_mean() for details.

References

Clopper, C. and Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika. 26 (4).
Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22 (158).
Agresti, A. and Coull, B. A. (1998). Approximate is better than 'exact' for interval estimation of binomial proportions. The American Statistician, 52 (2).

Examples

x <- rep(0:1, times = c(50, 100))
ci_proportion(x)
ci_proportion(x, type = "Wilson")
ci_proportion(x, type = "Agresti-Coull")
x <- rep(0:1, times = c(50, 100))
ci_proportion(x)
ci_proportion(x, type = "Wilson")
ci_proportion(x, type = "Agresti-Coull")

CI for a Population Quantile

Description

This function calculates CIs for a population quantile. By default, distribution-free CIs based on the binomial distribution are calculated, see Hahn and Meeker. Alternatively, bootstrap CIs are available (default "bca").

Usage

ci_quantile(
  x,
  q = 0.5,
  probs = c(0.025, 0.975),
  type = c("binomial", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_quantile(
  x,
  q = 0.5,
  probs = c(0.025, 0.975),
  type = c("binomial", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`q`	A single probability value determining the quantile (0.5 for median).
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. One of "binomial" (default), or "bootstrap".
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Value

An object of class "cint", see ci_mean() for details.

References

Hahn, G. and Meeker, W. (1991). Statistical Intervals. Wiley 1991.

Examples

x <- 1:100
ci_quantile(x, q = 0.25)
x <- 1:100
ci_quantile(x, q = 0.25)

CI for the Population Quantile Difference of two Samples

Description

This function calculates bootstrap CIs for the population value of q-quantile(x) - q-quantile(y), by default using "bca" bootstrap. Resampling is done within sample.

Usage

ci_quantile_diff(
  x,
  y,
  q = 0.5,
  probs = c(0.025, 0.975),
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_quantile_diff(
  x,
  y,
  q = 0.5,
  probs = c(0.025, 0.975),
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`y`	A numeric vector.
`q`	A single probability value determining the quantile (0.5 for median).
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. Currently, "bootstrap" is the only option.
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Value

An object of class "cint", see ci_mean() for details.

Examples

x <- 10:30
y <- 1:30
ci_quantile_diff(x, y, R = 999)  # Use larger R
x <- 10:30
y <- 1:30
ci_quantile_diff(x, y, R = 999)  # Use larger R

CI for the Population R-Squared

Description

This function calculates parametric CIs for the population $R^2$ . It is based on CIs for the non-centrality parameter $\Delta$ of the F distribution found by test inversion. Values of $\Delta$ are mapped to $R^2$ by $R^2 = \Delta / (\Delta + \textrm{df}_1 + \textrm{df}_2 + 1)$ , where the $\textrm{df}_j$ are the degrees of freedom of the F test statistic. A positive lower $(1 - \alpha) \cdot 100\%$ -confidence limit for the $R^2$ goes hand-in-hand with a significant F test at level $\alpha$ .

Usage

ci_rsquared(x, df1 = NULL, df2 = NULL, probs = c(0.025, 0.975))
ci_rsquared(x, df1 = NULL, df2 = NULL, probs = c(0.025, 0.975))

Arguments

`x`	The result of `stats::lm()` or the F test statistic.
`df1`	The numerator df. Only used if `x` is a test statistic.
`df2`	The denominator df. Only used if `x` is a test statistic.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.

Details

According to stats::pf(), the results might be unreliable for very large F values. Note that we do not provide bootstrap CIs here to keep the input interface simple.

Value

An object of class "cint", see ci_mean() for details.

References

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.

Examples

fit <- lm(Sepal.Length ~ ., data = iris)
summary(fit)$r.squared
ci_rsquared(fit)
ci_rsquared(fit, probs = c(0.05, 1))
fit <- lm(Sepal.Length ~ ., data = iris)
summary(fit)$r.squared
ci_rsquared(fit)
ci_rsquared(fit, probs = c(0.05, 1))

CI for the Population Std

Description

This function calculates CIs for the population standard deviation. They are derived from CIs for the variance by taking the square-root, see ci_var().

Usage

ci_sd(
  x,
  probs = c(0.025, 0.975),
  type = c("chi-squared", "bootstrap"),
  boot_type = c("bca", "perc", "stud", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_sd(
  x,
  probs = c(0.025, 0.975),
  type = c("chi-squared", "bootstrap"),
  boot_type = c("bca", "perc", "stud", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. One of `"chi-squared"` (default) or `"bootstrap"`.
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Value

An object of class "cint", see ci_mean() for details.

Examples

x <- 1:100
ci_sd(x)
ci_sd(x, type = "bootstrap", R = 999)  # Use larger R
x <- 1:100
ci_sd(x)
ci_sd(x, type = "bootstrap", R = 999)  # Use larger R

CI for the Skewness

Description

This function calculates bootstrap CIs for the population skewness. By default, bootstrap type "bca" is used.

Usage

ci_skewness(
  x,
  probs = c(0.025, 0.975),
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_skewness(
  x,
  probs = c(0.025, 0.975),
  type = "bootstrap",
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. Currently not used as the only type is `"bootstrap"`.
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Value

An object of class "cint", see ci_mean() for details.

Examples

x <- 1:20
ci_skewness(x, R = 999)  # Use larger R
x <- 1:20
ci_skewness(x, R = 999)  # Use larger R

CI for the Population Variance

Description

This function calculates CIs for the population variance.

Usage

ci_var(
  x,
  probs = c(0.025, 0.975),
  type = c("chi-squared", "bootstrap"),
  boot_type = c("bca", "perc", "stud", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)
ci_var(
  x,
  probs = c(0.025, 0.975),
  type = c("chi-squared", "bootstrap"),
  boot_type = c("bca", "perc", "stud", "norm", "basic"),
  R = 9999L,
  seed = NULL,
  ...
)

Arguments

`x`	A numeric vector.
`probs`	Lower and upper probabilities, by default `c(0.025, 0.975)`.
`type`	Type of CI. One of `"chi-squared"` (default) or `"bootstrap"`.
`boot_type`	Type of bootstrap CI. Only used for `type = "bootstrap"`.
`R`	The number of bootstrap resamples. Only used for `type = "bootstrap"`.
`seed`	An integer random seed. Only used for `type = "bootstrap"`.
`...`	Further arguments passed to `boot::boot()`.

Details

By default, classic CIs are calculated based on the chi-squared distribution, assuming normal distribution (see Smithson). Bootstrap CIs are also available (default: "bca"). We recommend them for the non-normal case.

The stud (bootstrap t) bootstrap uses the standard error of the sample variance given in Wilks.

Value

An object of class "cint", see ci_mean() for details.

References

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.
S.S. Wilks (1962), Mathematical Statistics, Wiley & Sons.

Examples

x <- 1:100
ci_var(x)
ci_var(x, type = "bootstrap", R = 999)  # Use larger R
x <- 1:100
ci_var(x)
ci_var(x, type = "bootstrap", R = 999)  # Use larger R

Cramer's V

Description

This function calculates Cramer's V, a measure of association between two categorical variables.

Usage

cramersv(x)
cramersv(x)

Arguments

`x`	The result of `stats::chisq.test()`, a matrix/table of counts, or a `data.frame` with exactly two columns representing the two variables.

Details

Cramer's V is a scaled version of the chi-squared test statistic $\chi^2$ and takes values in $[0, 1]$ . It is calculated as $\sqrt{\chi^2 / (n \cdot (k - 1))}$ , where $n$ is the number of observations, and $k$ is the smaller of the number of levels of the two variables.

Yates continuity correction is never applied. So in the 2x2 case, if x is the result of stats::chisq.test(), make sure no continuity correction was applied. Otherwise, results can be inconsistent.

Value

A numeric vector of length one.

References

Cramer, Harald. 1946. Mathematical Methods of Statistics. Princeton: Princeton University Press, page 282 (Chapter 21. The two-dimensional case).

Examples

cramersv(mtcars[c("am", "vs")])
cramersv(mtcars[c("am", "vs")])

Type Check

Description

Checks if an object inherits class "cint".

Usage

is.cint(x)
is.cint(x)

Arguments

`x`	Any object.

Value

A logical vector of length one.

Examples

is.cint(ci_proportion(5, 20))
is.cint(c(1, 2))
is.cint(ci_proportion(5, 20))
is.cint(c(1, 2))

Pearson's Measure of Kurtosis

Description

Defined as the ratio of the 4th central moment and the squared second central moment. Under perfect normality, the kurtosis equals 3. Put differently, we do not show "excess kurtosis" but rather kurtosis.

Usage

kurtosis(z, na.rm = TRUE)
kurtosis(z, na.rm = TRUE)

Arguments

`z`	A numeric vector.
`na.rm`	Logical flag indicating whether to remove missing values or not. Default is `TRUE`.

Value

Numeric vector of length 1.

Examples

kurtosis(1:10)
kurtosis(rnorm(1000))
kurtosis(1:10)
kurtosis(rnorm(1000))

Sample Moments

Description

Calculates central or non-central sample moments.

Usage

moment(z, p = 1, central = TRUE, na.rm = TRUE)
moment(z, p = 1, central = TRUE, na.rm = TRUE)

Arguments

`z`	A numeric vector.
`p`	Order of moment.
`central`	Should central moment be calculated? Default is `TRUE`.
`na.rm`	Logical flag indicating whether to remove missing values or not. Default is `TRUE`.

Value

Numeric vector of length 1.

Examples

moment(1:10, p = 1)
moment(1:10, p = 1, central = FALSE)
moment(1:10, p = 2) / stats::var(1:10)
moment(1:10, p = 1)
moment(1:10, p = 1, central = FALSE)
moment(1:10, p = 2) / stats::var(1:10)

Odds Ratio

Description

This function calculates the odds ratio of a 2x2 table/matrix, or a data frame with two columns.

Usage

oddsratio(x)
oddsratio(x)

Arguments

`x`	A 2x2 matrix/table of counts, or a `data.frame` with exactly two columns representing the two binary variables.

Details

The numerator equals the ratio of the top left entry and the bottom left entry of the 2x2 table, while the denominator equals the ratio of the top right entry and the bottom right entry. The result is usually slightly different from the one of stats::fisher.test(), which is based on the ML estimate of the odds ratio.

Value

A numeric vector of length one.

Examples

tab <- cbind(c(10, 5), c(4, 4))
oddsratio(tab)
tab <- cbind(c(10, 5), c(4, 4))
oddsratio(tab)

Print "cint" Object

Description

Print method for an object of class "cint".

Usage

## S3 method for class 'cint'
print(x, digits = getOption("digits"), ...)
## S3 method for class 'cint'
print(x, digits = getOption("digits"), ...)

Arguments

`x`	A on object of class "cint".
`digits`	Number of digits used to format numbers.
`...`	Further arguments passed from other methods.

Value

Invisibly, the input is returned.

Examples

ci_mean(1:100)
ci_mean(1:100)

Standard errors

Description

Functions to calculate standard errors of different statistics. The availability of a standard error (or statistic proportional to it) allows to apply "stud" (bootstrap t) bootstrap.

Usage

se_mean(z, na.rm = TRUE, ...)

se_mean_diff(z, y, na.rm = TRUE, var.equal = FALSE, ...)

se_var(z, na.rm = TRUE, ...)

se_proportion(z, na.rm = TRUE, ...)
se_mean(z, na.rm = TRUE, ...)

se_mean_diff(z, y, na.rm = TRUE, var.equal = FALSE, ...)

se_var(z, na.rm = TRUE, ...)

se_proportion(z, na.rm = TRUE, ...)

Arguments

`z`	Numeric vector.
`na.rm`	Should missing values be removed before calculation? Default is `TRUE`.
`...`	Further arguments to be passed from other methods.
`y`	Numeric vector.
`var.equal`	Should the variances be treated as being equal? Default is `FALSE`.

Value

A numeric vector of length one.

Examples

se_mean(1:100)
se_mean(1:100)

Sample Skewness

Description

Calculates sample skewness. A value of 0 refers to a perfectly symmetric distribution.

Usage

skewness(z, na.rm = TRUE)
skewness(z, na.rm = TRUE)

Arguments

`z`	A numeric vector.
`na.rm`	Logical flag indicating whether to remove missing values or not. Default is `TRUE`.

Value

Numeric vector of length 1.

Examples

skewness(1:10)
skewness(rexp(100))
skewness(1:10)
skewness(rexp(100))

Package 'confintr'

Help Index

CI for the NCP of the Chi-Squared Distribution

Description

Usage

Arguments

Details

Value

References

See Also

Examples

CI for Correlation Coefficients

Description

Usage

Arguments

Value

Examples

CI for the Population Cramer's V

Description

Usage

Arguments

Details

Value

References

See Also

Examples

CI for the Non-Centrality Parameter of the F Distribution

Description

Usage

Arguments

Details

Value

References

See Also

Examples

CI for the IQR

Description

Usage

Arguments

Value

Examples

CI for the Kurtosis

Description

Usage

Arguments

Value

See Also

Examples

CI for the MAD

Description

Usage

Arguments

Value

Examples

CI for the Population Mean

Description

Usage

Arguments

Details

Value

References

Examples

CI for the Population Mean Difference

Description

Usage

Arguments

Details

Value

References

Examples

CI for the Population Median

Description

Usage

Arguments

Value

See Also

Examples

CI for the Population Median Difference of two Samples

Description

Usage