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p-curve.R
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# ---------------------------------------------------------------------
# These p-curve functions are partially copied, partially adapted from Uri Simonsohn's ([email protected]) original p-curve functions
# http://p-curve.com/Supplement/Rcode_other/R%20Code%20behind%20p-curve%20app%203.0%20-%20distributable.R
# ---------------------------------------------------------------------
# p-curve-app 3.0 functions
# functions that find noncentrality parameter for t,f,chi distributions that gives 33% power for those d.f.
#t-test
ncp33t <- function(df, power=1/3, p.crit=.05) {
xc = qt(p=1-p.crit/2, df=df)
#Find noncentrality parameter (ncp) that leads 33% power to obtain xc
f = function(delta, pr, x, df) pt(x, df = df, ncp = delta) - (1-power)
out = uniroot(f, c(0, 37.62), x = xc, df = df)
return(out$root)
}
ncp33z <- function(power=1/3, p.crit=.05) {
xc = qnorm(p=1-p.crit/2)
#Find noncentrality parameter (ncp) that leads 33% power to obtain xc
f = function(delta, pr, x) pnorm(x, mean = delta) - (1-power)
out = uniroot(f, c(0, 37.62), x = xc)
return(out$root)
}
#F-test
ncp33f <- function(df1, df2, power=1/3, p.crit=.05) {
xc=qf(p=1-p.crit,df1=df1,df2=df2)
f = function(delta, pr, x, df1,df2) pf(x, df1 = df1, df2=df2, ncp = delta) - (1-power)
out = uniroot(f, c(0, 37.62), x = xc, df1=df1, df2=df2)
return(out$root)
}
#chi-square
ncp33chi <- function(df, power=1/3, p.crit=.05) {
xc=qchisq(p=1-p.crit, df=df)
#Find noncentrality parameter (ncp) that leads 33% power to obtain xc
f = function(delta, pr, x, df) pchisq(x, df = df, ncp = delta) - (1-power)
out = uniroot(f, c(0, 37.62), x = xc, df = df)
return(out$root)
}
type=c("t", "p")
statistic=c(2.5, 0.01588969)
df=c(48, NA)
df2=c(NA, NA)
get_pp_values <- function(type, statistic, df, df2, p.crit=.05, power=1/3) {
# convert r to t values
type <- as.character(type)
statistic[tolower(type)=="r"] <- statistic[tolower(type)=="r"] / sqrt( (1 - statistic[tolower(type)=="r"]^2) / df[tolower(type)=="r"])
type[tolower(type)=="r"] <- "t"
statistic <- abs(statistic)
res <- data.frame()
ncp <- data.frame()
for (i in 1:length(type)) {
switch(tolower(type[i]),
"t" = {
p <- 2*(1-pt(abs(statistic[i]),df=df[i]))
ppr <- p*(1/p.crit) # pp-value for right-skew
ppl <- 1-ppr # pp-value for left-skew
ncp33 <- ncp33t(df[i], power=power, p.crit=p.crit)
pp33 <- (pt(statistic[i], df=df[i], ncp=ncp33)-(1-power))*(1/power)
},
"f" = {
p <- 1-pf(abs(statistic[i]), df1=df[i], df2=df2[i])
ppr <- p*(1/p.crit) # pp-value for right-skew
ppl <- 1-ppr # pp-value for left-skew
ncp33 <- ncp33f(df1=df[i], df2=df2[i], power=power, p.crit=p.crit)
pp33 <- (pf(statistic[i], df1=df[i], df2=df2[i], ncp=ncp33)-(1-power))*(1/power)
},
"z" = {
p <- 2*(1-pnorm(abs(statistic[i])))
ppr <- p*(1/p.crit) # pp-value for right-skew
ppl <- 1-ppr # pp-value for left-skew
ncp33 <- ncp33z(power=power, p.crit=p.crit)
pp33 <- (pnorm(statistic[i], mean=ncp33, sd=1)-(1-power))*(1/power)
},
"p" = {
p <- statistic[i]
z <- qnorm(p/2, lower.tail=FALSE)
ppr <- p*(1/p.crit) # pp-value for right-skew
ppl <- 1-ppr # pp-value for left-skew
ncp33 <- ncp33z(power=power, p.crit=p.crit)
pp33 <- (pnorm(z, mean=ncp33, sd=1)-(1-power))*(1/power)
},
"chi2" = {
p <- 1-pchisq(abs(statistic[i]), df=df[i])
ppr <- p*(1/p.crit) # pp-value for right-skew
ppl <- 1-ppr # pp-value for left-skew
ncp33 <- ncp33chi(df[i], power=power, p.crit=p.crit)
pp33 <- (pchisq(statistic[i], df=df[i], ncp=ncp33)-(1-power))*(1/power)
},
{
# default
warning(paste0("Test statistic ", type[i], " not suported by p-curve."))
}
)
res <- rbind(res, data.frame(p=p, ppr=ppr, ppl=ppl, pp33=pp33))
ncp <- rbind(ncp, data.frame(type=type[i], df=df[i], df2=df2[i], ncp=ncp33))
}
if (nrow(res) > 0) {
# clamp to extreme values
res$ppr <- clamp(res$ppr, MIN=.00001, MAX=.99999)
res$ppl <- clamp(res$ppl, MIN=.00001, MAX=.99999)
res$pp33 <- clamp(res$pp33, MIN=.00001, MAX=.99999)
# remove non-significant values
res[res$p > p.crit, ] <- NA
return(list(res=res, ncp=ncp))
} else {
return(NULL)
}
}
# ---------------------------------------------------------------------
# New p-curve computation (p-curve app 3.0, http://www.p-curve.com/app3/)
p_curve_3 <- function(pps) {
pps <- na.omit(pps)
# STOUFFER: Overall tests aggregating pp-values
ktot <- sum(!is.na(pps$ppr))
Z_ppr <- sum(qnorm(pps$ppr))/sqrt(ktot) # right skew
Z_ppl <- sum(qnorm(pps$ppl))/sqrt(ktot) # left skew
Z_pp33<- sum(qnorm(pps$pp33))/sqrt(ktot) # 33%
p_ppr <- pnorm(Z_ppr)
p_ppl <- pnorm(Z_ppl)
p_pp33<- pnorm(Z_pp33)
return(list(
Z_evidence = Z_ppr,
p_evidence = p_ppr,
Z_hack = Z_ppl,
p_hack = p_ppl,
Z_lack = Z_pp33,
p_lack = p_pp33,
inconclusive = ifelse(p_ppr>.05 & p_ppl>.05 & p_pp33>.05, TRUE, FALSE)))
}
# ---------------------------------------------------------------------
# Old p-curve computation (p-curve app 2.0, http://www.p-curve.com/app2/)
p_curve_2 <- function(pps) {
pps <- na.omit(pps)
df <- 2*sum(nrow(pps))
chi2_evidence <- -2*sum(log(pps$ppr), na.rm=TRUE)
p_evidence <- pchisq(chi2_evidence, df=df, lower.tail=FALSE)
chi2_hack <- -2*sum(log(pps$ppl), na.rm=TRUE)
p_hack <- pchisq(chi2_hack, df=df, lower.tail=FALSE)
chi2_lack <- -2*sum(log(pps$pp33), na.rm=TRUE)
p_lack <- pchisq(chi2_lack, df=df, lower.tail=FALSE)
return(list(
chi2_evidence = chi2_evidence,
p_evidence = p_evidence,
chi2_hack = chi2_hack,
p_hack = p_hack,
chi2_lack = chi2_lack,
p_lack = p_lack,
df = df,
inconclusive = ifelse(p_evidence>.05 & p_hack>.05 & p_lack>.05, TRUE, FALSE)))
}
theoretical_power_curve <- function(power=1/3, p.max=.05, normalize=TRUE) {
# compute arbitrary test statistics for requested power
library(pwr)
d <- 0.2
n <- pwr.t.test(d=0.2, power=power)$n*2
crit <- seq(0.01, p.max, by=.01)
pdens <- c()
for (cr in crit) {
pdens <- c(pdens, pwr.t.test(d=0.2, power=NULL, n=n/2, sig.level=cr)$power)
}
p.dens <- diff(c(0, pdens))
if (normalize == TRUE) p.dens <- p.dens/sum(p.dens)
names(p.dens) <- as.character(crit)
return(p.dens)
}