R/meta_se.R
In dgbonett/vcmeta: Varying Coefficient Meta-Analysis
Defines functions
se.bscor
se.cohen
se.biphi
se.tetra
se.ave.cor.nonover
se.ave.cor.over
se.ave.mean2.dep
se.prop.ps
se.prop2
se.slope
se.meanratio.ps
se.meanratio2
se.odds
se.pbcor
se.semipartial
se.spear
se.cor
se.stdmean.ps
se.stdmean2
se.mean.ps
se.mean2
Documented in
se.ave.cor.nonover
se.ave.cor.over
se.ave.mean2.dep
se.biphi
se.bscor
se.cohen
se.cor
se.mean2
se.mean.ps
se.meanratio2
se.meanratio.ps
se.odds
se.pbcor
se.prop2
se.prop.ps
se.semipartial
se.slope
se.spear
se.stdmean2
se.stdmean.ps
se.tetra
# se.mean2 =================================================================
#' Computes the standard error for a 2-group mean difference
#'
#'
#' @description
#' This function computes the standard error of a
#' 2-group mean difference using the estimated means, estimated
#' standard deviations, and sample sizes. The effect size estimate
#' and standard error output from this function can be used as input
#' in the \link[vcmeta]{meta.ave.gen}, \link[vcmeta]{meta.lc.gen},
#' and \link[vcmeta]{meta.lm.gen} functions in applications where
#' compatible mean differences from a combination of 2-group
#' and paired-samples experiments are used in the meta-analysis.
#' Equality of variances is not asumed.
#'
#'
#' @param m1 estimated mean for group 1
#' @param m2 estimated mean for group 2
#' @param sd1 estimated standard deviation for group 1
#' @param sd2 estimated standard deviation for group 2
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated mean difference
#' * SE - standard error
#'
#'
#' @examples
#' se.mean2(21.9, 16.1, 3.82, 3.21, 40, 40)
#'
# # Should return:
#' # Estimate SE
#' # Mean difference: 5.8 0.7889312
#'
#'
#' @references
#' \insertRef{Snedecor1980}{vcmeta}
#'
#'
#' @export
se.mean2 <- function(m1, m2, sd1, sd2, n1, n2) {
d <- m1 - m2
se <- sqrt(sd1^2/n1 + sd2^2/n2)
out <- t(c(d, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Mean difference: "
return(out)
}
# se.mean.ps =================================================================
#' Computes the standard error for a paired-samples mean difference
#'
#'
#' @description
#' This function computes the standard error of a
#' paired-samples mean difference using the estimated means,
#' estimated standard deviations, estimated Pearson correlation,
#' and sample size. The effect size estimate and standard error
#' output from this function can be used as input in the
#' \link[vcmeta]{meta.ave.gen}, \link[vcmeta]{meta.lc.gen},
#' and \link[vcmeta]{meta.lm.gen} functions in applications where
#' compatible mean differences from a combination of 2-group
#' and paired-samples experiments are used in the meta-analysis.
#' Equality of variances is not assumed.
#'
#'
#' @param m1 estimated mean for measurement 1
#' @param m2 estimated mean for measurement 2
#' @param sd1 estimated standard deviation for measurement 1
#' @param sd2 estimated standard deviation for measurement 2
#' @param cor estimated correlation for measurements 1 and 2
#' @param n sample size
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated mean difference
#' * SE - standard error
#'
#'
#' @examples
#' se.mean.ps(23.9, 25.1, 1.76, 2.01, .78, 25)
#'
#' # Should return:
#' # Estimate SE
#' # Mean difference: -1.2 0.2544833
#'
#' @references
#' \insertRef{Snedecor1980}{vcmeta}
#'
#'
#' @export
se.mean.ps <- function(m1, m2, sd1, sd2, cor, n) {
d <- m1 - m2
se <- sqrt((sd1^2 + sd2^2 - 2*cor*sd1*sd2)/n)
out <- t(c(d, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Mean difference: "
return(out)
}
# se.stdmean2 ================================================================
#' Computes the standard error for a 2-group standardized mean difference
#'
#'
#' @description
#' This function computes the standard error of a 2-group standardized
#' mean difference using the sample sizes and the estimated means
# and standard deviations. Use the square root average variance
#' standardizer (stdzr = 0) for 2-group experimental designs. Use the
#' square root weighted variance standardizer (stdzr = 3) for 2-group
#' nonexperimental designs with simple random sampling. The single-group
#' standardizers (stdzr = 1 and stdzr = 2) can be used with either
#' 2-group experimental or nonexperimental designs. The effect size
#' estimate and standard error output from this function can be used as
#' input in the \link[vcmeta]{meta.ave.gen}, \link[vcmeta]{meta.lc.gen},
#' and \link[vcmeta]{meta.lm.gen} functions in applications where compatible
#' standardized mean differences from a combination of 2-group and
#' paired-samples experiments are used in the meta-analysis. Equality
#' of variances is not assumed.
#'
#'
#' @param m1 estimated mean for group 1
#' @param m2 estimated mean for group 2
#' @param sd1 estimated standard deviation for group 1
#' @param sd2 estimated standard deviation for group 2
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#' @param stdzr
#' * set to 0 for square root average variance standardizer
#' * set to 1 for group 1 SD standardizer
#' * set to 2 for group 2 SD standardizer
#' * set to 3 for square root weighted variance standardizer
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated standardized mean difference
#' * SE - standard error
#'
#'
#' @examples
#' se.stdmean2(21.9, 16.1, 3.82, 3.21, 40, 40, 0)
#'
#' # Should return:
#' # Estimate SE
#' # Standardized mean difference: 1.643894 0.2629049
#'
#'
#' @references
#' \insertRef{Bonett2009a}{vcmeta}
#'
#'
#' @seealso \link[vcmeta]{se.cohen}
#'
#'
#' @export
se.stdmean2 <- function(m1, m2, sd1, sd2, n1, n2, stdzr) {
df1 <- n1 - 1
df2 <- n2 - 1
if (stdzr == 0) {
s <- sqrt((sd1^2 + sd2^2)/2)
d <- (m1 - m2)/s
se <- sqrt(d^2*(sd1^4/df1 + sd2^4/df2)/(8*s^4) + (sd1^2/df1 + sd2^2/df2)/s^2)
}
else if (stdzr == 1) {
s <- sd1
d <- (m1 - m2)/s
se <- sqrt(d^2/(2*df1) + 1/df1 + sd2^2/(df2*sd1^2))
}
else if (stdzr == 2) {
s <- sd2
d <- (m1 - m2)/s
se <- sqrt(d^2/(2*df2) + 1/df2 + sd1^2/(df1*sd2^2))
}
else {
s <- sqrt((df1*sd1^2 + df2*sd2^2)/(n1 + n2 - 2))
d <- (m1 - m2)/s
se <- sqrt(d^2*(1/df1 + 1/df2)/8 + (sd1^2/n1 + sd2^2/n2)/s^2)
}
out <- t(c(d, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Standardized mean difference: "
return(out)
}
# se.stdmean.ps ==============================================================
#' Computes the standard error for a paired-samples standardized mean
#' difference
#'
#'
#' @description
#' This function computes the standard error of a paired-samples standardized
#' mean difference using the sample size and estimated means, standard
#' deviations, and estimated correlation. The effect size estimate and standard error
#' output from this function can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions in
#' applications where compatible standardized mean differences from a combination
#' of 2-group and paired-samples experiments are used in the meta-analysis.
#' Equality of variances is not assumed.
#'
#'
#' @param m1 estimated mean for measurement 1
#' @param m2 estimated mean for measurement 2
#' @param sd1 estimated standard deviation for measurement 1
#' @param sd2 estimated standard deviation for measurement 2
#' @param cor estimated correlation for measurements 1 and 2
#' @param n sample size
#' @param stdzr
#' * set to 0 for square root average variance standardizer
#' * set to 1 for measurement 1 SD standardizer
#' * set to 2 for measurement 2 SD standardizer
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated standardized mean difference
#' * SE - standard error
#'
#'
#' @examples
#' se.stdmean.ps(23.9, 25.1, 1.76, 2.01, .78, 25, 0)
#'
#' # Should return:
#' # Estimate SE
#' # Standardizedd mean difference: -0.6352097 0.1602852
#'
#'
#' @references
#' \insertRef{Bonett2009a}{vcmeta}
#'
#'
#' @export
se.stdmean.ps <- function(m1, m2, sd1, sd2, cor, n, stdzr) {
df <- n - 1
v1 <- sd1^2
v2 <- sd2^2
vd <- v1 + v2 - 2*cor*sd1*sd2
if (stdzr == 0) {
s <- sqrt((sd1^2 + sd2^2)/2)
d <- (m1 - m2)/s
se <- sqrt(d^2*(v1^2 + v2^2 + 2*cor^2*v1*v2)/(8*df*s^4) + vd/(df*s^2))
}
else if (stdzr == 1) {
s <- sd1
d <- (m1 - m2)/s
se <- sqrt(d^2/(2*df) + vd/(df*v1))
}
else {
s <- sd2
d <- (m1 - m2)/s
se <- sqrt(d^2/(2*df) + vd/(df*v2))
}
out <- t(c(d, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Standardized mean difference: "
return(out)
}
# se.cor ==========================================================
#' Computes the standard error for a Pearson or partial correlation
#'
#'
#' @description
#' This function computes the standard error of a
#' Pearson or partial correlation using the estimated correlation,
#' sample size, and number of control variables. The correlation,
#' along with the standard error output from this function, can be used
#' as input in the \link[vcmeta]{meta.ave.cor.gen} function in applications
#' where a combination of different types of correlations are used in
#' the meta-analysis.
#'
#'
#' @param cor estimated Pearson or partial correlation
#' @param s number of control variables (set to 0 for Pearson)
#' @param n sample size
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - Pearson or partial correlation (from input)
#' * SE - standard error
#'
#'
#' @examples
#' se.cor(.40, 0, 55)
#'
#' # Should return:
#' # Estimate SE
#' # Correlation: 0.4 0.116487
#'
#'
#' @references
#' \insertRef{Bonett2008a}{vcmeta}
#'
#'
#' @export
se.cor <- function(cor, s, n) {
se.cor <- sqrt((1 - cor^2)^2/(n - 3 - s))
out <- t(c(cor, se.cor))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Correlation: "
return(out)
}
# se.spear ===================================================================
#' Computes the standard error for a Spearman correlation
#'
#'
#' @description
#' This function computes the Bonett-Wright standard
#' error of a Spearman correlation using the estimated correlation
#' and sample size. The standard error from this function can be used
#' as input in the \link[vcmeta]{meta.ave.cor.gen} function in applications
#' where a combination of different types of correlations are used in
#' the meta-analysis.
#'
#'
#' @param cor estimated Spearman correlation
#' @param n sample size
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - Spearman correlation (from input)
#' * SE - standard error
#'
#'
#' @examples
#' se.spear(.40, 55)
#'
#' # Should return:
#' # Estimate SE
#' # Spearman correlation: 0.4 0.1210569
#'
#'
#' @references
#' \insertRef{Bonett2000}{vcmeta}
#'
#'
#' @export
se.spear <- function(cor, n) {
se.cor <- sqrt((1 - cor^2)^2*(1 + cor^2/2)/(n - 3))
out <- t(c(cor, se.cor))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Spearman correlation: "
return(out)
}
# se.semipart ================================================================
#' Computes the standard error for a semipartial correlation
#'
#'
#' @description
#' This function computes the standard error of a
#' semipartial correlation using the estimated correlation, sample
#' size, and squared multiple correlation for the full model. The full
#' model includes the independent variable of interest and all control
#' variables. The effect size estimate and standard error output from this
#' function can be used as input in the \link[vcmeta]{meta.ave.cor.gen}
#' function in applications where a combination of different types
#' of correlations are used in the meta-analysis.
#'
#'
#' @param cor estimated semipartial correlation
#' @param r2 estimated squared multiple correlation for a model that
#' includes the IV and all control variables
#' @param n sample size
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - semipartial correlation (from input)
#' * SE - standard error
#'
#'
#' @examples
#' se.semipartial(.40, .25, 60)
#'
#' # Should return:
#' # Estimate SE
#' # Semipartial correlation: 0.4 0.1063262
#'
#'
#' @export
se.semipartial <- function(cor, r2, n) {
r0 <- r2 - cor^2
a <- r2^2 - 2*r2 + r0 - r0^2 + 1
se.cor <- sqrt(a/(n - 3))
out <- t(c(cor, se.cor))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Semipartial correlation: "
return(out)
}
# se.pbcor ==============================================================
#' Computes the standard error for a point-biserial correlation
#'
#'
#' @description
#' This function computes a point-biserial correlation and its standard
#' error for two types of point-biserial correlations in 2-group designs
#' using the estimated means, estimated standard deviations, and samples
#' sizes. Equality of variances is not assumed. One type of point-biserial
#' correlation uses an unweighted average of variances and is recommended
#' for 2-group experimental designs. The other type of point-biserial
#' correlation uses a weighted average of variances and is recommended for
#' 2-group nonexperimental designs with simple random sampling (but not
#' stratified random sampling). This function is useful in a meta-analysis
#' of compatible point-biserial correlations where some studies used a
#' 2-group experimental design and other studies used a 2-group
#' nonexperimental design. The effect size estimate and standard error
#' output from this function can be used as input in the
#' \link[vcmeta]{meta.ave.cor.gen} function.
#'
#'
#' @param m1 estimated mean for group 1
#' @param m2 estimated mean for group 2
#' @param sd1 estimated standard deviation for group 1
#' @param sd2 estimated standard deviation for group 2
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#' @param type
#' * set to 1 for weighted variance average
#' * set to 2 for unweighted variance average
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated point-biserial correlation
#' * SE - standard error
#'
#'
#' @examples
#' se.pbcor(21.9, 16.1, 3.82, 3.21, 40, 40, 1)
#'
#' # Should return:
#' # Estimate SE
#' # Point-biserial correlation: 0.6349786 0.05981325
#'
#'
#' @references
#' \insertRef{Bonett2020b}{vcmeta}
#'
#'
#' @export
se.pbcor <- function(m1, m2, sd1, sd2, n1, n2, type) {
df1 <- n1 - 1
df2 <- n2 - 1
if (type == 1) {
u <- n1/(n1 + n2)
s <- sqrt((df1*sd1^2 + df2*sd2^2)/(df1 + df2))
d <- (m1 - m2)/s
c <- 1/(u*(1 - u))
cor <- d/sqrt(d^2 + c)
se.d <- sqrt(d^2*(1/df1 + 1/df2)/8 + 1/n1 + 1/n2)
se.cor <- (c/(d^2 + c)^(3/2))*se.d
} else {
s <- sqrt((sd1^2 + sd2^2)/2)
d <- (m1 - m2)/s
cor <- d/sqrt(d^2 + 4)
se.d <- sqrt(d^2*(sd1^4/df1 + sd2^4/df2)/(8*s^4) + (sd1^2/df1 + sd2^2/df2)/s^2)
se.cor <- (4/(d^2 + 4)^(3/2))*se.d
}
out <- t(c(cor, se.cor))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Point-biserial correlation: "
return(out)
}
# se.odds ====================================================================
#' Computes the standard error for a log odds ratio
#'
#'
#' @description
#' This function computes a log odds ratio and its standard error using
#' the frequency counts and sample sizes in a 2-group design. These
#' frequency counts and sample sizes can be obtained from a 2x2
#' contingency table. This function is useful in a meta-analysis of
#' odds ratios where some studies report the sample odds ratio and its
#' standard error and other studies only report the frequency counts
#' or a 2x2 contingency table. The log odds ratio and standard error
#' output from this function can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions.
#'
#'
#' @param f1 number of participants who have the outcome in group 1
#' @param f2 number of participants who have the outcome in group 2
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated log odds ratio
#' * SE - standard error
#'
#'
#' @examples
#' se.odds(36, 50, 21, 50)
#'
#' # Should return:
#' # Estimate SE
#' # Log odds ratio: 1.239501 0.4204435
#'
#'
#' @references
#' \insertRef{Bonett2015}{vcmeta}
#'
#'
#' @export
se.odds <- function(f1, n1, f2, n2) {
log.OR <- log((f1 + .5)*(n2 - f2 + .5)/((f2 + .5)*(n1 - f1 + .5)))
se.log.OR <- sqrt(1/(f1 + .5) + 1/(f2 + .5) + 1/(n1 - f1 + .5) + 1/(n2 - f2 + .5))
out <- t(c(log.OR, se.log.OR))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Log odds ratio: "
return(out)
}
# se.meanratio2 =========================================================
#' Computes the standard error for a 2-group log mean ratio
#'
#'
#' @description
#' This function computes the standard error of a
#' 2-group log mean ratio using the estimated means, estimated standard
#' deviations, and sample sizes. The log mean estimate and standard
#' error output from this function can be used as input in the
#' \link[vcmeta]{meta.ave.gen}, \link[vcmeta]{meta.lc.gen}, and
#' \link[vcmeta]{meta.lm.gen} functions in application where compatible
#' mean ratios from a combination of 2-group and paired-samples experiments
#' are used in the meta-analysis. Equality of variances is not assumed.
#'
#'
#' @param m1 estimated mean for group 1
#' @param m2 estimated mean for group 2
#' @param sd1 estimated standard deviation for group 1
#' @param sd2 estimated standard deviation for group 2
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated log mean ratio
#' * SE - standard error
#'
#' @examples
#' se.meanratio2(21.9, 16.1, 3.82, 3.21, 40, 40)
#'
#' # Should return:
#' # Estimate SE
#' # Log mean ratio: 0.3076674 0.041886
#'
#'
#' @references
#' \insertRef{Bonett2020}{vcmeta}
#'
#'
#' @export
se.meanratio2 <- function(m1, m2, sd1, sd2, n1, n2) {
logratio <- log(m1/m2)
var1 <- sd1^2/(n1*m1^2)
var2 <- sd2^2/(n2*m2^2)
se <- sqrt(var1 + var2)
out <- t(c(logratio, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Log mean ratio: "
return(out)
}
# se.meanratio.ps =============================================================
#' Computes the standard error for a paired-samples log mean ratio
#'
#'
#' @description
#' This function computes the standard error of a
#' paired-samples log mean ratio using the estimated means, estimated
#' standard deviations, estimated Pearson correlation, and sample
#' size. The log-mean estimate and standard error output from
#' this function can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions in
#' applications where compatible mean ratios from a combination of 2-group
#' and paired-samples experiments are used in the meta-analysis.
#' Equality of variances is not assumed.
#'
#'
#' @param m1 estimated mean for measurement 1
#' @param m2 estimated mean for measurement 2
#' @param sd1 estimated standard deviation for measurement 1
#' @param sd2 estimated standard deviation for measurement 2
#' @param cor estimated correlation for measurements 1 and 2
#' @param n sample size
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated log mean ratio
#' * SE - standard error
#'
#' @examples
#' se.meanratio.ps(21.9, 16.1, 3.82, 3.21, .748, 40)
#'
#' # Should return:
#' # Estimate SE
#' # Log mean ratio: 0.3076674 0.02130161
#'
#'
#' @references
#' \insertRef{Bonett2020}{vcmeta}
#'
#'
#' @export
se.meanratio.ps <- function(m1, m2, sd1, sd2, cor, n) {
logratio <- log(m1/m2)
var1 <- sd1^2/(n*m1^2)
var2 <- sd2^2/(n*m2^2)
cov <- cor*sd1*sd2/(n*m1*m2)
se <- sqrt(var1 + var2 - 2*cov)
out <- t(c(logratio, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Log mean ratio: "
return(out)
}
# se.slope =================================================================
#' Computes a slope and standard error
#'
#'
#' @description
#' This function computes a slope and its standard error
#' for a simple linear regression model (random-x model) using the estimated
#' Pearson correlation and the estimated standard deviations of the response
#' variable and predictor variable. This function is useful in a meta-analysis
#' of slopes of a simple linear regression model where some studies report
#' the Pearson correlation but not the slope.
#'
#'
#' @param cor estimated Pearson correlation
#' @param sdy estimated standard deviation of the response variable
#' @param sdx estimated standard deviation of the predictor variable
#' @param n sample size
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated slope
#' * SE - standard error
#'
#'
#' @examples
#' se.slope(.392, 4.54, 2.89, 60)
#'
#' # Should return:
#' # Estimate SE
#' # Slope: 0.6158062 0.1897647
#'
#'
#' @references
#' \insertRef{Snedecor1980}{vcmeta}
#'
#'
#' @export
se.slope <- function(cor, sdy, sdx, n) {
slope <- cor*sdy/sdx
se.slope <- sqrt((sdy^2*(1 - cor^2)*(n - 1))/(sdx^2*(n - 1)*(n - 2)))
out <- t(c(slope, se.slope))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Slope: "
return(out)
}
# se.prop2 ===================================================================
#' Computes the estimate and standard error for a 2-group proportion
#' difference
#'
#'
#' @description
#' This function computes the Agresti-Caffo standard
#' error of a 2-group proportion difference using the frequency
#' counts and sample sizes. The effect size estimate and standard
#' error output from this function can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions in
#' applications where compatible proportion differences from a combination of
#' 2-group and paired-samples studies are used in the meta-analysis.
#'
#'
#' @param f1 number of participants in group 1 who have the outcome
#' @param f2 number of participants in group 2 who have the outcome
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated proportion difference
#' * SE - standard error
#'
#'
#' @examples
#' se.prop2(31, 16, 40, 40)
#'
#' # Should return:
#' # Estimate SE
#' # Proportion difference: 0.3571429 0.1002777
#'
#'
#' @references
#' \insertRef{Agresti2000}{vcmeta}
#'
#'
#' @export
se.prop2 <- function(f1, f2, n1, n2) {
p1 <- (f1 + 1)/(n1 + 2)
p2 <- (f2 + 1)/(n2 + 2)
est <- p1 - p2
se <- sqrt(p1*(1 - p1)/(n1 + 2) + p2*(1 - p2)/(n2 + 2))
out <- t(c(est, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Proportion difference: "
return(out)
}
# se.prop.ps ==============================================================
#' Computes the estimate and standard error for a paired-samples
#' proportion difference
#'
#'
#' @description
#' This function computes the Bonett-Price standard error
#' of a paired-samples proportion difference using the frequency counts
#' from a 2 x 2 contingency table. The effect size estimate and standard
#' error output from this function can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions in
#' applications where compatible proportion differences from a combination of
#' 2-group and paired-samples studies are used in the meta-analysis.
#'
#'
#' @param f00 number of participants with y = 0 and x = 0
#' @param f01 number of participants with y = 0 and x = 1
#' @param f10 number of participants with y = 1 and x = 0
#' @param f11 number of participants with y = 1 and x = 1
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated proportion difference
#' * SE - standard error
#'
#'
#' @examples
#' se.prop.ps(16, 64, 5, 15)
#'
#' # Should return:
#' # Estimate SE
#' # Proportion difference: 0.5784314 0.05953213
#'
#'
#' @references
#' \insertRef{Bonett2012}{vcmeta}
#'
#'
#' @export
se.prop.ps <- function(f00, f01, f10, f11) {
n <- f00 + f01 + f10 + f11
p01 <- (f01 + 1)/(n + 2)
p10 <- (f10 + 1)/(n + 2)
est <- p01 - p10
se <- sqrt(((p01 + p10) - (p01 - p10)^2)/(n + 2))
out <- t(c(est, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Proportion difference: "
return(out)
}
# se.ave.mean2.dep ============================================================
#' Computes the standard error for the average of 2-group mean differences from
#' two parallel measurement response variables in the same sample
#'
#'
#' @description
#' In a study that reports a 2-group mean difference for two response
#' variables that satisfy the conditions of parallel measurments, this function
#' can be used to compute the standard error of the average of the two mean
#' differences using the two estimated means, estimated standard deviations,
#' estimated within-group correlation between the two response variables, and
#' the two sample sizes. The average mean difference and standard error output
#' from this function can then be used as input in the
#' \link[vcmeta]{meta.ave.gen}, \link[vcmeta]{meta.lc.gen}, and
#' \link[vcmeta]{meta.lm.gen} functions in a meta-analysis where some studies
#' have used one of the two parallel response variables and other studies have
#' used the other parallel response variable. Equality of variances is not
#' assumed.
#'
#'
#' @param m1A estimated mean for variable A in group 1
#' @param m2A estimated mean for variable A in group 2
#' @param sd1A estimated standard deviation for variable A in group 1
#' @param sd2A estimated standard deviation for variable A in group 2
#' @param m1B estimated mean for variable B in group 1
#' @param m2B estimated mean for variable B in group 2
#' @param sd1B estimated standard deviation for variable B in group 1
#' @param sd2B estimated standard deviation for variable B in group 2
#' @param rAB estimated within-group correlation between variables A and B
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated average mean difference
#' * SE - standard error
#' * VAR(A) - variance of mean difference for variable A
#' * VAR(B) - variance of mean difference for variable B
#' * COV(A,B) - covariance of mean differences for variables A and B
#'
#'
#' @examples
#' se.ave.mean2.dep(21.9, 16.1, 3.82, 3.21, 24.8, 17.1, 3.57, 3.64, .785, 40, 40)
#'
#' # Should return:
#' # Estimate SE VAR(A) VAR(B) COV(A,B)
#' # Average mean difference: 6.75 0.7526878 0.6224125 0.6498625 0.4969403
#'
#'
#' @export
se.ave.mean2.dep <- function(m1A, m2A, sd1A, sd2A, m1B, m2B, sd1B, sd2B, rAB, n1, n2) {
m1 <- (m1A + m1B)/2
m2 <- (m2A + m2B)/2
est <- m1 - m2
v1 <- sd1A^2/n1 + sd2A^2/n2
v2 <- sd1B^2/n1 + sd2B^2/n2
cov <- rAB*sd1A*sd1B/n1 + rAB*sd2A*sd2B/n2
se <- sqrt((v1 + v2 + 2*cov)/4)
out <- t(c(est, se, v1, v2, cov))
colnames(out) <- c("Estimate", "SE", "VAR(A)", "VAR(B)", "COV(A,B)")
rownames(out) <- "Average mean difference: "
return(out)
}
# se.ave.cor.over =============================================================
#' Computes the standard error for the average of two Pearson correlations with
#' one variable in common that have been estimated from the same sample
#'
#'
#' @description
#' In a study that reports the sample size and three correlations (cor12, cor13,
#' and cor23 where variable 1 is called the "overlapping" variable), and
#' variables 2 and 3 are different measurements of the same attribute, this
#' function can be used to compute the average of cor12 and cor13 and its
#' standard error. The average correlation and the standard error from this
#' function can be used as input in the \link[vcmeta]{meta.ave.cor.gen} function
#' in a meta-analysis where some studies have reported cor12 and other studies
#' have reported cor13.
#'
#'
#' @param cor12 estimated correlation between variables 1 and 2
#' @param cor13 estimated correlation between variables 1 and 3
#' @param cor23 estimated correlation between variables 2 and 3
#' @param n sample size
#'
#'
#' @return
#' Returns a two-row matrix. The first row gives results for the average
#' correlation and the second row gives the results with a Fisher
#' transformation. The columns are:
#' * Estimate - estimated average of cor12 and cor13
#' * SE - standard error
#' * VAR(cor12) - variance of cor12
#' * VAR(cor13) - variance of cor13
#' * COV(cor12,cor13) - covariance of cor12 and cor13
#'
#'
#' @examples
#' se.ave.cor.over(.462, .518, .755, 100)
#'
#' # Should return:
#' # Estimate SE VAR(cor12) VAR(cor13) COV(cor12,cor13)
#' # Correlation: 0.4900000 0.07087351 0.006378045 0.00551907 0.004097553
#' # Fisher: 0.5360603 0.09326690 0.010309278 0.01030928 0.007119936
#'
#'
#' @export
se.ave.cor.over <- function(cor12, cor13, cor23, n) {
est1 <- (cor12 + cor13)/2
cov1 <- ((cor23 - cor12*cor13/2)*(1 - cor12^2 - cor13^2 - cor23^2) + cor23^3)/(n - 3)
v1 <- (1 - cor12^2)^2/(n - 3)
v2 <- (1 - cor13^2)^2/(n - 3)
se1 <- sqrt((v1 + v2 + 2*cov1)/4)
est2 <- log((1 + est1)/(1 - est1))/2
se2 <- se1/(1 - est1^2)
cov2 <- cov1/((1 - cor12^2)*(1 - cor13^2))
v1.z <- 1/(n - 3)
v2.z <- 1/(n - 3)
out1 <- t(c(est1, se1, v1, v2, cov1))
out2 <- t(c(est2, se2, v1.z, v2.z, cov2))
out <- rbind(out1, out2)
colnames(out) <- c("Estimate", "SE", "VAR(cor12)", "VAR(cor13)", "COV(cor12,cor13)")
rownames(out) <- c("Correlation: ", "Fisher: ")
return(out)
}
# se.ave.cor.nonover ==========================================================
#' Computes the standard error for the average of two Pearson correlations with
#' no variables in common that have been estimated from the same sample
#'
#'
#' @description
#' In a study that reports the sample size and six correlations (cor12, cor34,
#' cor13, cor14, cor23, and cor24) where variables 1 and 3 are different
#' measurements of one attribute and variables 2 and 4 are different
#' measurements of a second attribute, this function can be used to compute the
#' average of cor12 and cor34 and its standard error. Note that cor12 and cor34
#' have no variable in common (i.e., no "overlapping" variable). The average
#' correlation and the standard error from this function can be used as
#' input in the \link[vcmeta]{meta.ave.cor.gen} function in a meta-analysis where
#' some studies have reported cor12 and other studies have reported cor34.
#'
#'
#' @param cor12 estimated correlation between variables 1 and 2
#' @param cor34 estimated correlation between variables 3 and 4
#' @param cor13 estimated correlation between variables 1 and 3
#' @param cor14 estimated correlation between variables 1 and 4
#' @param cor23 estimated correlation between variables 2 and 3
#' @param cor24 estimated correlation between variables 2 and 4
#' @param n sample size
#'
#'
#' @return
#' Returns a two-row matrix. The first row gives results for the average
#' correlation and the second row gives the results with a Fisher
#' transformation. The columns are:
#' * Estimate - estimated average of cor12 and cor34
#' * SE - standard error
#' * VAR(cor12) - variance of cor12
#' * VAR(cor34) - variance of cor34
#' * COV(cor12,cor34) - covariance of cor12 and cor34
#'
#'
#' @examples
#' se.ave.cor.nonover(.357, .398, .755, .331, .347, .821, 100)
#'
#' # Should return:
#' # Estimate SE VAR(cor12) VAR(cor34) COV(cor12,cor34)
#' # Correlation: 0.377500 0.07768887 0.00784892 0.007301895 0.004495714
#' # Fisher: 0.397141 0.09059993 0.01030928 0.010309278 0.006122153
#'
#'
#' @export
se.ave.cor.nonover <- function(cor12, cor34, cor13, cor14, cor23, cor24, n) {
est1 <- (cor12 + cor34)/2
c1 <- (cor12*cor34)*(cor13^2 + cor14^2 + cor23^2 + cor24^2)/2 + cor13*cor24 + cor14*cor23
c2 <- (cor12*cor13*cor14 + cor12*cor23*cor24 + cor13*cor23*cor34 + cor14*cor24*cor34)
cov1 <- (c1 - c2)/(n - 3)
v1 <- (1 - cor12^2)^2/(n - 3)
v2 <- (1 - cor34^2)^2/(n - 3)
se1 <- sqrt((v1 + v2 + 2*cov1)/4)
est2 <- log((1 + est1)/(1 - est1))/2
se2 <- se1/(1 - est1^2)
cov2 <- cov1/((1 - cor12^2)*(1 - cor34^2))
v1.z <- 1/(n - 3)
v2.z <- 1/(n - 3)
out1 <- t(c(est1, se1, v1, v2, cov1))
out2 <- t(c(est2, se2, v1.z, v2.z, cov2))
out <- rbind(out1, out2)
colnames(out) <- c("Estimate", "SE", "VAR(cor12)", "VAR(cor34)", "COV(cor12,cor34)")
rownames(out) <- c("Correlation: ", "Fisher: ")
return(out)
}
# se.tetra ==================================================================
#' Computes the standard error for a tetrachoric correlation approximation
#'
#'
#' @description
#' This function computes an estimate of a tetrachoric correlation
#' approximation and its standard error using the frequency counts
#' from a 2 x 2 contingency table for two artifically dichotomous variables.
#' A tetrachoric approximation could be compatible with a Pearson correlation
#' in a meta-analysis. The tetrachoric approximation and the standard error
#' from this function can be used as input in the \link[vcmeta]{meta.ave.cor.gen}
#' function in a meta-analysis where some studies have reported Pearson
#' correlations between quantitative variables x and y and other studies have
#' reported a 2 x 2 contingency table for dichotomous measurements of variables
#' x and y.
#'
#'
#' @param f00 number of participants with y = 0 and x = 0
#' @param f01 number of participants with y = 0 and x = 1
#' @param f10 number of participants with y = 1 and x = 0
#' @param f11 number of participants with y = 1 and x = 1
#'
#'
#' @references
#' \insertRef{Bonett2005}{vcmeta}
#'
#'
#' @return
#' Returns a 1-row matrix. The columns are:
#' * Estimate - estimated tetrachoric approximation
#' * SE - standard error
#'
#'
#' @examples
#' se.tetra(46, 15, 54, 85)
#'
#' # Should return:
#' # Estimate SE
#' # Tetrachoric: 0.5135167 0.09358336
#'
#'
#' @export
se.tetra <- function(f00, f01, f10, f11) {
n <- f00 + f01 + f10 + f11
or <- (f11 + .5)*(f00 + .5)/((f01 + .5)*(f10 + .5))
r1 <- (f00 + f01 + 1)/(n + 2)
r2 <- (f10 + f11 + 1)/(n + 2)
c1 <- (f00 + f10 + 1)/(n + 2)
c2 <- (f01 + f11 + 1)/(n + 2)
pmin <- min(c1, c2, r1, r2)
c <- (1 - abs(r1 - c1)/5 - (.5 - pmin)^2)/2
lor <- log(or)
se.lor <- sqrt(1/(f00 + .5) + 1/(f01 + .5) + 1/(f10 + .5) + 1/(f11 + .5))
tetra <- cos(3.14159/(1 + or^c))
k <- (3.14159*c*or^c)*sin(3.14159/(1 + or^c))/(1 + or^c)^2
se <- k*se.lor
out <- t(c(tetra, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Tetrachoric: "
return(out)
}
# se.biphi ==================================================================
#' Computes the standard error for a biserial-phi correlation
#'
#'
#' @description
#' This function computes an estimate of a biserial-phi
#' correlation and its standard error using the frequency counts from a 2 x 2
#' contingency table where one variable is naturally dichotomous and the other
#' variable is artifically dichotomous. A biserial-phi correlation could be
#' compatible with a point-biserial correlation in a meta-analysis. The
#' biserial-phi estimate and the standard error from this function can be used
#' as input in the \link[vcmeta]{meta.ave.cor.gen} function in a meta-analysis
#' where a point-biserial correlation has been obtained in some studies and
#' a biserial-phi correlation has been obtained in other studies.
#'
#'
#' @param f1 number of participants in group 1 who have the attribute
#' @param f2 number of participants in group 2 who have the attribute
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a 1-row matrix. The columns are:
#' * Estimate - estimated biserial-phi correlation
#' * SE - standard error
#'
#'
#' @examples
#' se.biphi(34, 22, 50, 50)
#'
#' # Should return:
#' # Estimate SE
#' # Biserial-phi: 0.27539 0.1074594
#'
#'
#' @export
se.biphi <- function(f1, f2, n1, n2) {
if (f1 > n1) {stop("f cannot be greater than n")}
if (f2 > n2) {stop("f cannot be greater than n")}
f00 <- f1
f10 <- n1 - f1
f01 <- f2
f11 <- n2 - f2
p1 <- n1/(n1 + n2)
p2 <- n2/(n1 + n2)
or <- (f11 + .5)*(f00 + .5)/((f01 + .5)*(f10 + .5))
lor <- log(or)
se.lor <- sqrt(1/(f00 + .5) + 1/(f01 + .5) + 1/(f10 + .5) + 1/(f11 + .5))
c <- 2.89/(p1*p2)
biphi <- lor/sqrt(lor^2 + c)
se.biphi <- sqrt(c^2/(lor^2 + c)^3)*se.lor
out <- t(c(biphi, se.biphi))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Biserial-phi: "
return(out)
}
# se.cohen ====================================================================
#' Computes the standard error for Cohen's d
#'
#'
#' @description
#' This function computes the standard error of Cohen's d using only the two
#' sample sizes and an estimate of Cohen's d. Cohen's d and its standard error
#' assume equal variances. The estimate of Cohen's d, with the standard error
#' output from this function, can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions in
#' applications where different types of compatible standardized mean
#' differences are used in the meta-analysis.
#'
#'
#' @param d estimated Cohen's d
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - Cohen's d (from input)
#' * SE - standard error
#'
#'
#' @examples
#' se.cohen(.78, 35, 50)
#'
#' # Should return:
#' # Estimate SE
#' # Cohen's d: 0.78 0.2288236
#'
#'
#' @seealso \link[vcmeta]{se.stdmean2}
#'
#'
#' @export
se.cohen <- function(d, n1, n2) {
df1 <- n1 - 1
df2 <- n2 - 1
se <- sqrt(d^2*(1/df1 + 1/df2)/8 + 1/n1 + 1/n2)
out <- t(c(d, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Cohen's d: "
return(out)
}
# se.bscor ===================================================================
#' Computes the standard error for a biserial correlation
#'
#'
#' @description
#' This function computes a biserial correlation and its standard error. A
#' biserial correlation can be used when one variable is quantitative and the
#' other variable has been artifically dichotmized. The biserial correlation
#' estimates the correlation between an observable quantitative variable and
#' an unobserved quantitative variable that is measured on a dichotomous
#' scale. This function requires the estimated mean, estimated standard
#' deviation, and samples size from each level of the dichotomized variable.
#' This function is useful in a meta-analysis of Pearson correlations where
#' some studies report a Pearson correlation and other studies report the
#' information needed to compute a biserial correlation. The biserial
#' correlation and standard error output from this function can be used as
#' input in the \link[vcmeta]{meta.ave.cor.gen} function.
#'
#'
#' @details
#' This function computes a point-biserial correlation and its standard error
#' as a function of a standardized mean difference with a weighted variance
#' standardizer. Then the point-biserial estimate is transformed into a
#' biserial correlation using the traditional adjustment. The adjustment is
#' also applied to the point-biserial standard error to obtain the standard
#' error for the biserial correlation.
#'
#' The biserial correlation assumes that the observed quantitative variable
#' and the unobserved quantitative variable have a bivariate normal
#' distribution. Bivariate normality is a crucial assumption underlying the
#' transformation of a point-biserial correlation to a biserial correlation.
#' Bivariate normality also implies equal variances of the observed
#' quantitative variable at each level of the dichotomized variable, and this
#' assumption is made in the computation of the standard error.
#'
#'
#' @param m1 estimated mean for level 1
#' @param m2 estimated mean for level 2
#' @param sd1 estimated standard deviation for level 1
#' @param sd2 estimated standard deviation for level 2
#' @param n1 sample size for level 1
#' @param n2 sample size for level 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated biserial correlation
#' * SE - standard error
#'
#'
#' @examples
#' se.bscor(21.9, 16.1, 3.82, 3.21, 40, 40)
#'
#' # Should return:
#' # Estimate SE
#' # Biserial correlation: 0.8018318 0.07451665
#'
#'
#' @references
#' \insertRef{Bonett2020b}{vcmeta}
#'
#'
#' @importFrom stats dnorm
#' @export
se.bscor <- function(m1, m2, sd1, sd2, n1, n2) {
df1 <- n1 - 1
df2 <- n2 - 1
u <- n1/(n1 + n2)
a <- sqrt(u*(1 - u))/dnorm(qnorm(u))
s <- sqrt((df1*sd1^2 + df2*sd2^2)/(df1 + df2))
d <- (m1 - m2)/s
c <- (df1 + df2)/((n1 + n2)*(u*(1 - u)))
pbcor <- d/sqrt(d^2 + c)
bscor <- pbcor*a
if (bscor > 1) {bscor = .99999}
if (bscor < -1) {bscor = -.99999}
se.d <- sqrt(d^2*(1/n1 + 1/n2)/8 + 1/n1 + 1/n2)
se.pbcor <- (c/(d^2 + c)^(3/2))*se.d
se.bscor <- se.pbcor*a
out <- t(c(bscor, se.bscor))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Biserial correlation: "
return(out)
}
dgbonett/vcmeta documentation built on July 12, 2024, 3:12 p.m.
R Package Documentation
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Defines functions se.bscor se.cohen se.biphi se.tetra se.ave.cor.nonover se.ave.cor.over se.ave.mean2.dep se.prop.ps se.prop2 se.slope se.meanratio.ps se.meanratio2 se.odds se.pbcor se.semipartial se.spear se.cor se.stdmean.ps se.stdmean2 se.mean.ps se.mean2
Documented in se.ave.cor.nonover se.ave.cor.over se.ave.mean2.dep se.biphi se.bscor se.cohen se.cor se.mean2 se.mean.ps se.meanratio2 se.meanratio.ps se.odds se.pbcor se.prop2 se.prop.ps se.semipartial se.slope se.spear se.stdmean2 se.stdmean.ps se.tetra
# se.mean2 =================================================================
#' Computes the standard error for a 2-group mean difference
#'
#'
#' @description
#' This function computes the standard error of a
#' 2-group mean difference using the estimated means, estimated
#' standard deviations, and sample sizes. The effect size estimate
#' and standard error output from this function can be used as input
#' in the \link[vcmeta]{meta.ave.gen}, \link[vcmeta]{meta.lc.gen},
#' and \link[vcmeta]{meta.lm.gen} functions in applications where
#' compatible mean differences from a combination of 2-group
#' and paired-samples experiments are used in the meta-analysis.
#' Equality of variances is not asumed.
#'
#'
#' @param m1 estimated mean for group 1
#' @param m2 estimated mean for group 2
#' @param sd1 estimated standard deviation for group 1
#' @param sd2 estimated standard deviation for group 2
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated mean difference
#' * SE - standard error
#'
#'
#' @examples
#' se.mean2(21.9, 16.1, 3.82, 3.21, 40, 40)
#'
# # Should return:
#' # Estimate SE
#' # Mean difference: 5.8 0.7889312
#'
#'
#' @references
#' \insertRef{Snedecor1980}{vcmeta}
#'
#'
#' @export
se.mean2 <- function(m1, m2, sd1, sd2, n1, n2) {
d <- m1 - m2
se <- sqrt(sd1^2/n1 + sd2^2/n2)
out <- t(c(d, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Mean difference: "
return(out)
}
# se.mean.ps =================================================================
#' Computes the standard error for a paired-samples mean difference
#'
#'
#' @description
#' This function computes the standard error of a
#' paired-samples mean difference using the estimated means,
#' estimated standard deviations, estimated Pearson correlation,
#' and sample size. The effect size estimate and standard error
#' output from this function can be used as input in the
#' \link[vcmeta]{meta.ave.gen}, \link[vcmeta]{meta.lc.gen},
#' and \link[vcmeta]{meta.lm.gen} functions in applications where
#' compatible mean differences from a combination of 2-group
#' and paired-samples experiments are used in the meta-analysis.
#' Equality of variances is not assumed.
#'
#'
#' @param m1 estimated mean for measurement 1
#' @param m2 estimated mean for measurement 2
#' @param sd1 estimated standard deviation for measurement 1
#' @param sd2 estimated standard deviation for measurement 2
#' @param cor estimated correlation for measurements 1 and 2
#' @param n sample size
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated mean difference
#' * SE - standard error
#'
#'
#' @examples
#' se.mean.ps(23.9, 25.1, 1.76, 2.01, .78, 25)
#'
#' # Should return:
#' # Estimate SE
#' # Mean difference: -1.2 0.2544833
#'
#' @references
#' \insertRef{Snedecor1980}{vcmeta}
#'
#'
#' @export
se.mean.ps <- function(m1, m2, sd1, sd2, cor, n) {
d <- m1 - m2
se <- sqrt((sd1^2 + sd2^2 - 2*cor*sd1*sd2)/n)
out <- t(c(d, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Mean difference: "
return(out)
}
# se.stdmean2 ================================================================
#' Computes the standard error for a 2-group standardized mean difference
#'
#'
#' @description
#' This function computes the standard error of a 2-group standardized
#' mean difference using the sample sizes and the estimated means
# and standard deviations. Use the square root average variance
#' standardizer (stdzr = 0) for 2-group experimental designs. Use the
#' square root weighted variance standardizer (stdzr = 3) for 2-group
#' nonexperimental designs with simple random sampling. The single-group
#' standardizers (stdzr = 1 and stdzr = 2) can be used with either
#' 2-group experimental or nonexperimental designs. The effect size
#' estimate and standard error output from this function can be used as
#' input in the \link[vcmeta]{meta.ave.gen}, \link[vcmeta]{meta.lc.gen},
#' and \link[vcmeta]{meta.lm.gen} functions in applications where compatible
#' standardized mean differences from a combination of 2-group and
#' paired-samples experiments are used in the meta-analysis. Equality
#' of variances is not assumed.
#'
#'
#' @param m1 estimated mean for group 1
#' @param m2 estimated mean for group 2
#' @param sd1 estimated standard deviation for group 1
#' @param sd2 estimated standard deviation for group 2
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#' @param stdzr
#' * set to 0 for square root average variance standardizer
#' * set to 1 for group 1 SD standardizer
#' * set to 2 for group 2 SD standardizer
#' * set to 3 for square root weighted variance standardizer
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated standardized mean difference
#' * SE - standard error
#'
#'
#' @examples
#' se.stdmean2(21.9, 16.1, 3.82, 3.21, 40, 40, 0)
#'
#' # Should return:
#' # Estimate SE
#' # Standardized mean difference: 1.643894 0.2629049
#'
#'
#' @references
#' \insertRef{Bonett2009a}{vcmeta}
#'
#'
#' @seealso \link[vcmeta]{se.cohen}
#'
#'
#' @export
se.stdmean2 <- function(m1, m2, sd1, sd2, n1, n2, stdzr) {
df1 <- n1 - 1
df2 <- n2 - 1
if (stdzr == 0) {
s <- sqrt((sd1^2 + sd2^2)/2)
d <- (m1 - m2)/s
se <- sqrt(d^2*(sd1^4/df1 + sd2^4/df2)/(8*s^4) + (sd1^2/df1 + sd2^2/df2)/s^2)
}
else if (stdzr == 1) {
s <- sd1
d <- (m1 - m2)/s
se <- sqrt(d^2/(2*df1) + 1/df1 + sd2^2/(df2*sd1^2))
}
else if (stdzr == 2) {
s <- sd2
d <- (m1 - m2)/s
se <- sqrt(d^2/(2*df2) + 1/df2 + sd1^2/(df1*sd2^2))
}
else {
s <- sqrt((df1*sd1^2 + df2*sd2^2)/(n1 + n2 - 2))
d <- (m1 - m2)/s
se <- sqrt(d^2*(1/df1 + 1/df2)/8 + (sd1^2/n1 + sd2^2/n2)/s^2)
}
out <- t(c(d, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Standardized mean difference: "
return(out)
}
# se.stdmean.ps ==============================================================
#' Computes the standard error for a paired-samples standardized mean
#' difference
#'
#'
#' @description
#' This function computes the standard error of a paired-samples standardized
#' mean difference using the sample size and estimated means, standard
#' deviations, and estimated correlation. The effect size estimate and standard error
#' output from this function can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions in
#' applications where compatible standardized mean differences from a combination
#' of 2-group and paired-samples experiments are used in the meta-analysis.
#' Equality of variances is not assumed.
#'
#'
#' @param m1 estimated mean for measurement 1
#' @param m2 estimated mean for measurement 2
#' @param sd1 estimated standard deviation for measurement 1
#' @param sd2 estimated standard deviation for measurement 2
#' @param cor estimated correlation for measurements 1 and 2
#' @param n sample size
#' @param stdzr
#' * set to 0 for square root average variance standardizer
#' * set to 1 for measurement 1 SD standardizer
#' * set to 2 for measurement 2 SD standardizer
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated standardized mean difference
#' * SE - standard error
#'
#'
#' @examples
#' se.stdmean.ps(23.9, 25.1, 1.76, 2.01, .78, 25, 0)
#'
#' # Should return:
#' # Estimate SE
#' # Standardizedd mean difference: -0.6352097 0.1602852
#'
#'
#' @references
#' \insertRef{Bonett2009a}{vcmeta}
#'
#'
#' @export
se.stdmean.ps <- function(m1, m2, sd1, sd2, cor, n, stdzr) {
df <- n - 1
v1 <- sd1^2
v2 <- sd2^2
vd <- v1 + v2 - 2*cor*sd1*sd2
if (stdzr == 0) {
s <- sqrt((sd1^2 + sd2^2)/2)
d <- (m1 - m2)/s
se <- sqrt(d^2*(v1^2 + v2^2 + 2*cor^2*v1*v2)/(8*df*s^4) + vd/(df*s^2))
}
else if (stdzr == 1) {
s <- sd1
d <- (m1 - m2)/s
se <- sqrt(d^2/(2*df) + vd/(df*v1))
}
else {
s <- sd2
d <- (m1 - m2)/s
se <- sqrt(d^2/(2*df) + vd/(df*v2))
}
out <- t(c(d, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Standardized mean difference: "
return(out)
}
# se.cor ==========================================================
#' Computes the standard error for a Pearson or partial correlation
#'
#'
#' @description
#' This function computes the standard error of a
#' Pearson or partial correlation using the estimated correlation,
#' sample size, and number of control variables. The correlation,
#' along with the standard error output from this function, can be used
#' as input in the \link[vcmeta]{meta.ave.cor.gen} function in applications
#' where a combination of different types of correlations are used in
#' the meta-analysis.
#'
#'
#' @param cor estimated Pearson or partial correlation
#' @param s number of control variables (set to 0 for Pearson)
#' @param n sample size
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - Pearson or partial correlation (from input)
#' * SE - standard error
#'
#'
#' @examples
#' se.cor(.40, 0, 55)
#'
#' # Should return:
#' # Estimate SE
#' # Correlation: 0.4 0.116487
#'
#'
#' @references
#' \insertRef{Bonett2008a}{vcmeta}
#'
#'
#' @export
se.cor <- function(cor, s, n) {
se.cor <- sqrt((1 - cor^2)^2/(n - 3 - s))
out <- t(c(cor, se.cor))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Correlation: "
return(out)
}
# se.spear ===================================================================
#' Computes the standard error for a Spearman correlation
#'
#'
#' @description
#' This function computes the Bonett-Wright standard
#' error of a Spearman correlation using the estimated correlation
#' and sample size. The standard error from this function can be used
#' as input in the \link[vcmeta]{meta.ave.cor.gen} function in applications
#' where a combination of different types of correlations are used in
#' the meta-analysis.
#'
#'
#' @param cor estimated Spearman correlation
#' @param n sample size
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - Spearman correlation (from input)
#' * SE - standard error
#'
#'
#' @examples
#' se.spear(.40, 55)
#'
#' # Should return:
#' # Estimate SE
#' # Spearman correlation: 0.4 0.1210569
#'
#'
#' @references
#' \insertRef{Bonett2000}{vcmeta}
#'
#'
#' @export
se.spear <- function(cor, n) {
se.cor <- sqrt((1 - cor^2)^2*(1 + cor^2/2)/(n - 3))
out <- t(c(cor, se.cor))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Spearman correlation: "
return(out)
}
# se.semipart ================================================================
#' Computes the standard error for a semipartial correlation
#'
#'
#' @description
#' This function computes the standard error of a
#' semipartial correlation using the estimated correlation, sample
#' size, and squared multiple correlation for the full model. The full
#' model includes the independent variable of interest and all control
#' variables. The effect size estimate and standard error output from this
#' function can be used as input in the \link[vcmeta]{meta.ave.cor.gen}
#' function in applications where a combination of different types
#' of correlations are used in the meta-analysis.
#'
#'
#' @param cor estimated semipartial correlation
#' @param r2 estimated squared multiple correlation for a model that
#' includes the IV and all control variables
#' @param n sample size
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - semipartial correlation (from input)
#' * SE - standard error
#'
#'
#' @examples
#' se.semipartial(.40, .25, 60)
#'
#' # Should return:
#' # Estimate SE
#' # Semipartial correlation: 0.4 0.1063262
#'
#'
#' @export
se.semipartial <- function(cor, r2, n) {
r0 <- r2 - cor^2
a <- r2^2 - 2*r2 + r0 - r0^2 + 1
se.cor <- sqrt(a/(n - 3))
out <- t(c(cor, se.cor))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Semipartial correlation: "
return(out)
}
# se.pbcor ==============================================================
#' Computes the standard error for a point-biserial correlation
#'
#'
#' @description
#' This function computes a point-biserial correlation and its standard
#' error for two types of point-biserial correlations in 2-group designs
#' using the estimated means, estimated standard deviations, and samples
#' sizes. Equality of variances is not assumed. One type of point-biserial
#' correlation uses an unweighted average of variances and is recommended
#' for 2-group experimental designs. The other type of point-biserial
#' correlation uses a weighted average of variances and is recommended for
#' 2-group nonexperimental designs with simple random sampling (but not
#' stratified random sampling). This function is useful in a meta-analysis
#' of compatible point-biserial correlations where some studies used a
#' 2-group experimental design and other studies used a 2-group
#' nonexperimental design. The effect size estimate and standard error
#' output from this function can be used as input in the
#' \link[vcmeta]{meta.ave.cor.gen} function.
#'
#'
#' @param m1 estimated mean for group 1
#' @param m2 estimated mean for group 2
#' @param sd1 estimated standard deviation for group 1
#' @param sd2 estimated standard deviation for group 2
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#' @param type
#' * set to 1 for weighted variance average
#' * set to 2 for unweighted variance average
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated point-biserial correlation
#' * SE - standard error
#'
#'
#' @examples
#' se.pbcor(21.9, 16.1, 3.82, 3.21, 40, 40, 1)
#'
#' # Should return:
#' # Estimate SE
#' # Point-biserial correlation: 0.6349786 0.05981325
#'
#'
#' @references
#' \insertRef{Bonett2020b}{vcmeta}
#'
#'
#' @export
se.pbcor <- function(m1, m2, sd1, sd2, n1, n2, type) {
df1 <- n1 - 1
df2 <- n2 - 1
if (type == 1) {
u <- n1/(n1 + n2)
s <- sqrt((df1*sd1^2 + df2*sd2^2)/(df1 + df2))
d <- (m1 - m2)/s
c <- 1/(u*(1 - u))
cor <- d/sqrt(d^2 + c)
se.d <- sqrt(d^2*(1/df1 + 1/df2)/8 + 1/n1 + 1/n2)
se.cor <- (c/(d^2 + c)^(3/2))*se.d
} else {
s <- sqrt((sd1^2 + sd2^2)/2)
d <- (m1 - m2)/s
cor <- d/sqrt(d^2 + 4)
se.d <- sqrt(d^2*(sd1^4/df1 + sd2^4/df2)/(8*s^4) + (sd1^2/df1 + sd2^2/df2)/s^2)
se.cor <- (4/(d^2 + 4)^(3/2))*se.d
}
out <- t(c(cor, se.cor))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Point-biserial correlation: "
return(out)
}
# se.odds ====================================================================
#' Computes the standard error for a log odds ratio
#'
#'
#' @description
#' This function computes a log odds ratio and its standard error using
#' the frequency counts and sample sizes in a 2-group design. These
#' frequency counts and sample sizes can be obtained from a 2x2
#' contingency table. This function is useful in a meta-analysis of
#' odds ratios where some studies report the sample odds ratio and its
#' standard error and other studies only report the frequency counts
#' or a 2x2 contingency table. The log odds ratio and standard error
#' output from this function can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions.
#'
#'
#' @param f1 number of participants who have the outcome in group 1
#' @param f2 number of participants who have the outcome in group 2
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated log odds ratio
#' * SE - standard error
#'
#'
#' @examples
#' se.odds(36, 50, 21, 50)
#'
#' # Should return:
#' # Estimate SE
#' # Log odds ratio: 1.239501 0.4204435
#'
#'
#' @references
#' \insertRef{Bonett2015}{vcmeta}
#'
#'
#' @export
se.odds <- function(f1, n1, f2, n2) {
log.OR <- log((f1 + .5)*(n2 - f2 + .5)/((f2 + .5)*(n1 - f1 + .5)))
se.log.OR <- sqrt(1/(f1 + .5) + 1/(f2 + .5) + 1/(n1 - f1 + .5) + 1/(n2 - f2 + .5))
out <- t(c(log.OR, se.log.OR))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Log odds ratio: "
return(out)
}
# se.meanratio2 =========================================================
#' Computes the standard error for a 2-group log mean ratio
#'
#'
#' @description
#' This function computes the standard error of a
#' 2-group log mean ratio using the estimated means, estimated standard
#' deviations, and sample sizes. The log mean estimate and standard
#' error output from this function can be used as input in the
#' \link[vcmeta]{meta.ave.gen}, \link[vcmeta]{meta.lc.gen}, and
#' \link[vcmeta]{meta.lm.gen} functions in application where compatible
#' mean ratios from a combination of 2-group and paired-samples experiments
#' are used in the meta-analysis. Equality of variances is not assumed.
#'
#'
#' @param m1 estimated mean for group 1
#' @param m2 estimated mean for group 2
#' @param sd1 estimated standard deviation for group 1
#' @param sd2 estimated standard deviation for group 2
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated log mean ratio
#' * SE - standard error
#'
#' @examples
#' se.meanratio2(21.9, 16.1, 3.82, 3.21, 40, 40)
#'
#' # Should return:
#' # Estimate SE
#' # Log mean ratio: 0.3076674 0.041886
#'
#'
#' @references
#' \insertRef{Bonett2020}{vcmeta}
#'
#'
#' @export
se.meanratio2 <- function(m1, m2, sd1, sd2, n1, n2) {
logratio <- log(m1/m2)
var1 <- sd1^2/(n1*m1^2)
var2 <- sd2^2/(n2*m2^2)
se <- sqrt(var1 + var2)
out <- t(c(logratio, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Log mean ratio: "
return(out)
}
# se.meanratio.ps =============================================================
#' Computes the standard error for a paired-samples log mean ratio
#'
#'
#' @description
#' This function computes the standard error of a
#' paired-samples log mean ratio using the estimated means, estimated
#' standard deviations, estimated Pearson correlation, and sample
#' size. The log-mean estimate and standard error output from
#' this function can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions in
#' applications where compatible mean ratios from a combination of 2-group
#' and paired-samples experiments are used in the meta-analysis.
#' Equality of variances is not assumed.
#'
#'
#' @param m1 estimated mean for measurement 1
#' @param m2 estimated mean for measurement 2
#' @param sd1 estimated standard deviation for measurement 1
#' @param sd2 estimated standard deviation for measurement 2
#' @param cor estimated correlation for measurements 1 and 2
#' @param n sample size
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated log mean ratio
#' * SE - standard error
#'
#' @examples
#' se.meanratio.ps(21.9, 16.1, 3.82, 3.21, .748, 40)
#'
#' # Should return:
#' # Estimate SE
#' # Log mean ratio: 0.3076674 0.02130161
#'
#'
#' @references
#' \insertRef{Bonett2020}{vcmeta}
#'
#'
#' @export
se.meanratio.ps <- function(m1, m2, sd1, sd2, cor, n) {
logratio <- log(m1/m2)
var1 <- sd1^2/(n*m1^2)
var2 <- sd2^2/(n*m2^2)
cov <- cor*sd1*sd2/(n*m1*m2)
se <- sqrt(var1 + var2 - 2*cov)
out <- t(c(logratio, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Log mean ratio: "
return(out)
}
# se.slope =================================================================
#' Computes a slope and standard error
#'
#'
#' @description
#' This function computes a slope and its standard error
#' for a simple linear regression model (random-x model) using the estimated
#' Pearson correlation and the estimated standard deviations of the response
#' variable and predictor variable. This function is useful in a meta-analysis
#' of slopes of a simple linear regression model where some studies report
#' the Pearson correlation but not the slope.
#'
#'
#' @param cor estimated Pearson correlation
#' @param sdy estimated standard deviation of the response variable
#' @param sdx estimated standard deviation of the predictor variable
#' @param n sample size
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated slope
#' * SE - standard error
#'
#'
#' @examples
#' se.slope(.392, 4.54, 2.89, 60)
#'
#' # Should return:
#' # Estimate SE
#' # Slope: 0.6158062 0.1897647
#'
#'
#' @references
#' \insertRef{Snedecor1980}{vcmeta}
#'
#'
#' @export
se.slope <- function(cor, sdy, sdx, n) {
slope <- cor*sdy/sdx
se.slope <- sqrt((sdy^2*(1 - cor^2)*(n - 1))/(sdx^2*(n - 1)*(n - 2)))
out <- t(c(slope, se.slope))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Slope: "
return(out)
}
# se.prop2 ===================================================================
#' Computes the estimate and standard error for a 2-group proportion
#' difference
#'
#'
#' @description
#' This function computes the Agresti-Caffo standard
#' error of a 2-group proportion difference using the frequency
#' counts and sample sizes. The effect size estimate and standard
#' error output from this function can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions in
#' applications where compatible proportion differences from a combination of
#' 2-group and paired-samples studies are used in the meta-analysis.
#'
#'
#' @param f1 number of participants in group 1 who have the outcome
#' @param f2 number of participants in group 2 who have the outcome
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated proportion difference
#' * SE - standard error
#'
#'
#' @examples
#' se.prop2(31, 16, 40, 40)
#'
#' # Should return:
#' # Estimate SE
#' # Proportion difference: 0.3571429 0.1002777
#'
#'
#' @references
#' \insertRef{Agresti2000}{vcmeta}
#'
#'
#' @export
se.prop2 <- function(f1, f2, n1, n2) {
p1 <- (f1 + 1)/(n1 + 2)
p2 <- (f2 + 1)/(n2 + 2)
est <- p1 - p2
se <- sqrt(p1*(1 - p1)/(n1 + 2) + p2*(1 - p2)/(n2 + 2))
out <- t(c(est, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Proportion difference: "
return(out)
}
# se.prop.ps ==============================================================
#' Computes the estimate and standard error for a paired-samples
#' proportion difference
#'
#'
#' @description
#' This function computes the Bonett-Price standard error
#' of a paired-samples proportion difference using the frequency counts
#' from a 2 x 2 contingency table. The effect size estimate and standard
#' error output from this function can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions in
#' applications where compatible proportion differences from a combination of
#' 2-group and paired-samples studies are used in the meta-analysis.
#'
#'
#' @param f00 number of participants with y = 0 and x = 0
#' @param f01 number of participants with y = 0 and x = 1
#' @param f10 number of participants with y = 1 and x = 0
#' @param f11 number of participants with y = 1 and x = 1
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated proportion difference
#' * SE - standard error
#'
#'
#' @examples
#' se.prop.ps(16, 64, 5, 15)
#'
#' # Should return:
#' # Estimate SE
#' # Proportion difference: 0.5784314 0.05953213
#'
#'
#' @references
#' \insertRef{Bonett2012}{vcmeta}
#'
#'
#' @export
se.prop.ps <- function(f00, f01, f10, f11) {
n <- f00 + f01 + f10 + f11
p01 <- (f01 + 1)/(n + 2)
p10 <- (f10 + 1)/(n + 2)
est <- p01 - p10
se <- sqrt(((p01 + p10) - (p01 - p10)^2)/(n + 2))
out <- t(c(est, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Proportion difference: "
return(out)
}
# se.ave.mean2.dep ============================================================
#' Computes the standard error for the average of 2-group mean differences from
#' two parallel measurement response variables in the same sample
#'
#'
#' @description
#' In a study that reports a 2-group mean difference for two response
#' variables that satisfy the conditions of parallel measurments, this function
#' can be used to compute the standard error of the average of the two mean
#' differences using the two estimated means, estimated standard deviations,
#' estimated within-group correlation between the two response variables, and
#' the two sample sizes. The average mean difference and standard error output
#' from this function can then be used as input in the
#' \link[vcmeta]{meta.ave.gen}, \link[vcmeta]{meta.lc.gen}, and
#' \link[vcmeta]{meta.lm.gen} functions in a meta-analysis where some studies
#' have used one of the two parallel response variables and other studies have
#' used the other parallel response variable. Equality of variances is not
#' assumed.
#'
#'
#' @param m1A estimated mean for variable A in group 1
#' @param m2A estimated mean for variable A in group 2
#' @param sd1A estimated standard deviation for variable A in group 1
#' @param sd2A estimated standard deviation for variable A in group 2
#' @param m1B estimated mean for variable B in group 1
#' @param m2B estimated mean for variable B in group 2
#' @param sd1B estimated standard deviation for variable B in group 1
#' @param sd2B estimated standard deviation for variable B in group 2
#' @param rAB estimated within-group correlation between variables A and B
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated average mean difference
#' * SE - standard error
#' * VAR(A) - variance of mean difference for variable A
#' * VAR(B) - variance of mean difference for variable B
#' * COV(A,B) - covariance of mean differences for variables A and B
#'
#'
#' @examples
#' se.ave.mean2.dep(21.9, 16.1, 3.82, 3.21, 24.8, 17.1, 3.57, 3.64, .785, 40, 40)
#'
#' # Should return:
#' # Estimate SE VAR(A) VAR(B) COV(A,B)
#' # Average mean difference: 6.75 0.7526878 0.6224125 0.6498625 0.4969403
#'
#'
#' @export
se.ave.mean2.dep <- function(m1A, m2A, sd1A, sd2A, m1B, m2B, sd1B, sd2B, rAB, n1, n2) {
m1 <- (m1A + m1B)/2
m2 <- (m2A + m2B)/2
est <- m1 - m2
v1 <- sd1A^2/n1 + sd2A^2/n2
v2 <- sd1B^2/n1 + sd2B^2/n2
cov <- rAB*sd1A*sd1B/n1 + rAB*sd2A*sd2B/n2
se <- sqrt((v1 + v2 + 2*cov)/4)
out <- t(c(est, se, v1, v2, cov))
colnames(out) <- c("Estimate", "SE", "VAR(A)", "VAR(B)", "COV(A,B)")
rownames(out) <- "Average mean difference: "
return(out)
}
# se.ave.cor.over =============================================================
#' Computes the standard error for the average of two Pearson correlations with
#' one variable in common that have been estimated from the same sample
#'
#'
#' @description
#' In a study that reports the sample size and three correlations (cor12, cor13,
#' and cor23 where variable 1 is called the "overlapping" variable), and
#' variables 2 and 3 are different measurements of the same attribute, this
#' function can be used to compute the average of cor12 and cor13 and its
#' standard error. The average correlation and the standard error from this
#' function can be used as input in the \link[vcmeta]{meta.ave.cor.gen} function
#' in a meta-analysis where some studies have reported cor12 and other studies
#' have reported cor13.
#'
#'
#' @param cor12 estimated correlation between variables 1 and 2
#' @param cor13 estimated correlation between variables 1 and 3
#' @param cor23 estimated correlation between variables 2 and 3
#' @param n sample size
#'
#'
#' @return
#' Returns a two-row matrix. The first row gives results for the average
#' correlation and the second row gives the results with a Fisher
#' transformation. The columns are:
#' * Estimate - estimated average of cor12 and cor13
#' * SE - standard error
#' * VAR(cor12) - variance of cor12
#' * VAR(cor13) - variance of cor13
#' * COV(cor12,cor13) - covariance of cor12 and cor13
#'
#'
#' @examples
#' se.ave.cor.over(.462, .518, .755, 100)
#'
#' # Should return:
#' # Estimate SE VAR(cor12) VAR(cor13) COV(cor12,cor13)
#' # Correlation: 0.4900000 0.07087351 0.006378045 0.00551907 0.004097553
#' # Fisher: 0.5360603 0.09326690 0.010309278 0.01030928 0.007119936
#'
#'
#' @export
se.ave.cor.over <- function(cor12, cor13, cor23, n) {
est1 <- (cor12 + cor13)/2
cov1 <- ((cor23 - cor12*cor13/2)*(1 - cor12^2 - cor13^2 - cor23^2) + cor23^3)/(n - 3)
v1 <- (1 - cor12^2)^2/(n - 3)
v2 <- (1 - cor13^2)^2/(n - 3)
se1 <- sqrt((v1 + v2 + 2*cov1)/4)
est2 <- log((1 + est1)/(1 - est1))/2
se2 <- se1/(1 - est1^2)
cov2 <- cov1/((1 - cor12^2)*(1 - cor13^2))
v1.z <- 1/(n - 3)
v2.z <- 1/(n - 3)
out1 <- t(c(est1, se1, v1, v2, cov1))
out2 <- t(c(est2, se2, v1.z, v2.z, cov2))
out <- rbind(out1, out2)
colnames(out) <- c("Estimate", "SE", "VAR(cor12)", "VAR(cor13)", "COV(cor12,cor13)")
rownames(out) <- c("Correlation: ", "Fisher: ")
return(out)
}
# se.ave.cor.nonover ==========================================================
#' Computes the standard error for the average of two Pearson correlations with
#' no variables in common that have been estimated from the same sample
#'
#'
#' @description
#' In a study that reports the sample size and six correlations (cor12, cor34,
#' cor13, cor14, cor23, and cor24) where variables 1 and 3 are different
#' measurements of one attribute and variables 2 and 4 are different
#' measurements of a second attribute, this function can be used to compute the
#' average of cor12 and cor34 and its standard error. Note that cor12 and cor34
#' have no variable in common (i.e., no "overlapping" variable). The average
#' correlation and the standard error from this function can be used as
#' input in the \link[vcmeta]{meta.ave.cor.gen} function in a meta-analysis where
#' some studies have reported cor12 and other studies have reported cor34.
#'
#'
#' @param cor12 estimated correlation between variables 1 and 2
#' @param cor34 estimated correlation between variables 3 and 4
#' @param cor13 estimated correlation between variables 1 and 3
#' @param cor14 estimated correlation between variables 1 and 4
#' @param cor23 estimated correlation between variables 2 and 3
#' @param cor24 estimated correlation between variables 2 and 4
#' @param n sample size
#'
#'
#' @return
#' Returns a two-row matrix. The first row gives results for the average
#' correlation and the second row gives the results with a Fisher
#' transformation. The columns are:
#' * Estimate - estimated average of cor12 and cor34
#' * SE - standard error
#' * VAR(cor12) - variance of cor12
#' * VAR(cor34) - variance of cor34
#' * COV(cor12,cor34) - covariance of cor12 and cor34
#'
#'
#' @examples
#' se.ave.cor.nonover(.357, .398, .755, .331, .347, .821, 100)
#'
#' # Should return:
#' # Estimate SE VAR(cor12) VAR(cor34) COV(cor12,cor34)
#' # Correlation: 0.377500 0.07768887 0.00784892 0.007301895 0.004495714
#' # Fisher: 0.397141 0.09059993 0.01030928 0.010309278 0.006122153
#'
#'
#' @export
se.ave.cor.nonover <- function(cor12, cor34, cor13, cor14, cor23, cor24, n) {
est1 <- (cor12 + cor34)/2
c1 <- (cor12*cor34)*(cor13^2 + cor14^2 + cor23^2 + cor24^2)/2 + cor13*cor24 + cor14*cor23
c2 <- (cor12*cor13*cor14 + cor12*cor23*cor24 + cor13*cor23*cor34 + cor14*cor24*cor34)
cov1 <- (c1 - c2)/(n - 3)
v1 <- (1 - cor12^2)^2/(n - 3)
v2 <- (1 - cor34^2)^2/(n - 3)
se1 <- sqrt((v1 + v2 + 2*cov1)/4)
est2 <- log((1 + est1)/(1 - est1))/2
se2 <- se1/(1 - est1^2)
cov2 <- cov1/((1 - cor12^2)*(1 - cor34^2))
v1.z <- 1/(n - 3)
v2.z <- 1/(n - 3)
out1 <- t(c(est1, se1, v1, v2, cov1))
out2 <- t(c(est2, se2, v1.z, v2.z, cov2))
out <- rbind(out1, out2)
colnames(out) <- c("Estimate", "SE", "VAR(cor12)", "VAR(cor34)", "COV(cor12,cor34)")
rownames(out) <- c("Correlation: ", "Fisher: ")
return(out)
}
# se.tetra ==================================================================
#' Computes the standard error for a tetrachoric correlation approximation
#'
#'
#' @description
#' This function computes an estimate of a tetrachoric correlation
#' approximation and its standard error using the frequency counts
#' from a 2 x 2 contingency table for two artifically dichotomous variables.
#' A tetrachoric approximation could be compatible with a Pearson correlation
#' in a meta-analysis. The tetrachoric approximation and the standard error
#' from this function can be used as input in the \link[vcmeta]{meta.ave.cor.gen}
#' function in a meta-analysis where some studies have reported Pearson
#' correlations between quantitative variables x and y and other studies have
#' reported a 2 x 2 contingency table for dichotomous measurements of variables
#' x and y.
#'
#'
#' @param f00 number of participants with y = 0 and x = 0
#' @param f01 number of participants with y = 0 and x = 1
#' @param f10 number of participants with y = 1 and x = 0
#' @param f11 number of participants with y = 1 and x = 1
#'
#'
#' @references
#' \insertRef{Bonett2005}{vcmeta}
#'
#'
#' @return
#' Returns a 1-row matrix. The columns are:
#' * Estimate - estimated tetrachoric approximation
#' * SE - standard error
#'
#'
#' @examples
#' se.tetra(46, 15, 54, 85)
#'
#' # Should return:
#' # Estimate SE
#' # Tetrachoric: 0.5135167 0.09358336
#'
#'
#' @export
se.tetra <- function(f00, f01, f10, f11) {
n <- f00 + f01 + f10 + f11
or <- (f11 + .5)*(f00 + .5)/((f01 + .5)*(f10 + .5))
r1 <- (f00 + f01 + 1)/(n + 2)
r2 <- (f10 + f11 + 1)/(n + 2)
c1 <- (f00 + f10 + 1)/(n + 2)
c2 <- (f01 + f11 + 1)/(n + 2)
pmin <- min(c1, c2, r1, r2)
c <- (1 - abs(r1 - c1)/5 - (.5 - pmin)^2)/2
lor <- log(or)
se.lor <- sqrt(1/(f00 + .5) + 1/(f01 + .5) + 1/(f10 + .5) + 1/(f11 + .5))
tetra <- cos(3.14159/(1 + or^c))
k <- (3.14159*c*or^c)*sin(3.14159/(1 + or^c))/(1 + or^c)^2
se <- k*se.lor
out <- t(c(tetra, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Tetrachoric: "
return(out)
}
# se.biphi ==================================================================
#' Computes the standard error for a biserial-phi correlation
#'
#'
#' @description
#' This function computes an estimate of a biserial-phi
#' correlation and its standard error using the frequency counts from a 2 x 2
#' contingency table where one variable is naturally dichotomous and the other
#' variable is artifically dichotomous. A biserial-phi correlation could be
#' compatible with a point-biserial correlation in a meta-analysis. The
#' biserial-phi estimate and the standard error from this function can be used
#' as input in the \link[vcmeta]{meta.ave.cor.gen} function in a meta-analysis
#' where a point-biserial correlation has been obtained in some studies and
#' a biserial-phi correlation has been obtained in other studies.
#'
#'
#' @param f1 number of participants in group 1 who have the attribute
#' @param f2 number of participants in group 2 who have the attribute
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a 1-row matrix. The columns are:
#' * Estimate - estimated biserial-phi correlation
#' * SE - standard error
#'
#'
#' @examples
#' se.biphi(34, 22, 50, 50)
#'
#' # Should return:
#' # Estimate SE
#' # Biserial-phi: 0.27539 0.1074594
#'
#'
#' @export
se.biphi <- function(f1, f2, n1, n2) {
if (f1 > n1) {stop("f cannot be greater than n")}
if (f2 > n2) {stop("f cannot be greater than n")}
f00 <- f1
f10 <- n1 - f1
f01 <- f2
f11 <- n2 - f2
p1 <- n1/(n1 + n2)
p2 <- n2/(n1 + n2)
or <- (f11 + .5)*(f00 + .5)/((f01 + .5)*(f10 + .5))
lor <- log(or)
se.lor <- sqrt(1/(f00 + .5) + 1/(f01 + .5) + 1/(f10 + .5) + 1/(f11 + .5))
c <- 2.89/(p1*p2)
biphi <- lor/sqrt(lor^2 + c)
se.biphi <- sqrt(c^2/(lor^2 + c)^3)*se.lor
out <- t(c(biphi, se.biphi))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Biserial-phi: "
return(out)
}
# se.cohen ====================================================================
#' Computes the standard error for Cohen's d
#'
#'
#' @description
#' This function computes the standard error of Cohen's d using only the two
#' sample sizes and an estimate of Cohen's d. Cohen's d and its standard error
#' assume equal variances. The estimate of Cohen's d, with the standard error
#' output from this function, can be used as input in the \link[vcmeta]{meta.ave.gen},
#' \link[vcmeta]{meta.lc.gen}, and \link[vcmeta]{meta.lm.gen} functions in
#' applications where different types of compatible standardized mean
#' differences are used in the meta-analysis.
#'
#'
#' @param d estimated Cohen's d
#' @param n1 sample size for group 1
#' @param n2 sample size for group 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - Cohen's d (from input)
#' * SE - standard error
#'
#'
#' @examples
#' se.cohen(.78, 35, 50)
#'
#' # Should return:
#' # Estimate SE
#' # Cohen's d: 0.78 0.2288236
#'
#'
#' @seealso \link[vcmeta]{se.stdmean2}
#'
#'
#' @export
se.cohen <- function(d, n1, n2) {
df1 <- n1 - 1
df2 <- n2 - 1
se <- sqrt(d^2*(1/df1 + 1/df2)/8 + 1/n1 + 1/n2)
out <- t(c(d, se))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Cohen's d: "
return(out)
}
# se.bscor ===================================================================
#' Computes the standard error for a biserial correlation
#'
#'
#' @description
#' This function computes a biserial correlation and its standard error. A
#' biserial correlation can be used when one variable is quantitative and the
#' other variable has been artifically dichotmized. The biserial correlation
#' estimates the correlation between an observable quantitative variable and
#' an unobserved quantitative variable that is measured on a dichotomous
#' scale. This function requires the estimated mean, estimated standard
#' deviation, and samples size from each level of the dichotomized variable.
#' This function is useful in a meta-analysis of Pearson correlations where
#' some studies report a Pearson correlation and other studies report the
#' information needed to compute a biserial correlation. The biserial
#' correlation and standard error output from this function can be used as
#' input in the \link[vcmeta]{meta.ave.cor.gen} function.
#'
#'
#' @details
#' This function computes a point-biserial correlation and its standard error
#' as a function of a standardized mean difference with a weighted variance
#' standardizer. Then the point-biserial estimate is transformed into a
#' biserial correlation using the traditional adjustment. The adjustment is
#' also applied to the point-biserial standard error to obtain the standard
#' error for the biserial correlation.
#'
#' The biserial correlation assumes that the observed quantitative variable
#' and the unobserved quantitative variable have a bivariate normal
#' distribution. Bivariate normality is a crucial assumption underlying the
#' transformation of a point-biserial correlation to a biserial correlation.
#' Bivariate normality also implies equal variances of the observed
#' quantitative variable at each level of the dichotomized variable, and this
#' assumption is made in the computation of the standard error.
#'
#'
#' @param m1 estimated mean for level 1
#' @param m2 estimated mean for level 2
#' @param sd1 estimated standard deviation for level 1
#' @param sd2 estimated standard deviation for level 2
#' @param n1 sample size for level 1
#' @param n2 sample size for level 2
#'
#'
#' @return
#' Returns a one-row matrix:
#' * Estimate - estimated biserial correlation
#' * SE - standard error
#'
#'
#' @examples
#' se.bscor(21.9, 16.1, 3.82, 3.21, 40, 40)
#'
#' # Should return:
#' # Estimate SE
#' # Biserial correlation: 0.8018318 0.07451665
#'
#'
#' @references
#' \insertRef{Bonett2020b}{vcmeta}
#'
#'
#' @importFrom stats dnorm
#' @export
se.bscor <- function(m1, m2, sd1, sd2, n1, n2) {
df1 <- n1 - 1
df2 <- n2 - 1
u <- n1/(n1 + n2)
a <- sqrt(u*(1 - u))/dnorm(qnorm(u))
s <- sqrt((df1*sd1^2 + df2*sd2^2)/(df1 + df2))
d <- (m1 - m2)/s
c <- (df1 + df2)/((n1 + n2)*(u*(1 - u)))
pbcor <- d/sqrt(d^2 + c)
bscor <- pbcor*a
if (bscor > 1) {bscor = .99999}
if (bscor < -1) {bscor = -.99999}
se.d <- sqrt(d^2*(1/n1 + 1/n2)/8 + 1/n1 + 1/n2)
se.pbcor <- (c/(d^2 + c)^(3/2))*se.d
se.bscor <- se.pbcor*a
out <- t(c(bscor, se.bscor))
colnames(out) <- c("Estimate", "SE")
rownames(out) <- "Biserial correlation: "
return(out)
}
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