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R/tt.2group.R
In lessR: Less Code, More Results
Defines functions
.TwoGroup
.TwoGroup <-
function(YA, YB, n1, n2, m1, m2, s1, s2, from.data,
Ynm, Xnm, X1nm, X2nm, brief, digits_d,
conf_level, alternative, mmd, msmd, Edesired, bw1, bw2,
graph, xlab, line_chart, show_title,
quiet, pdf_file, width, height, ...) {
if ( brief && !quiet && (!is.null(mmd) || !is.null(msmd)) ) {
cat("\n"); stop(call.=FALSE, "\n","------\n",
"mmd and msmd do not work with the brief version.\n\n")
}
# get lab_x_cex lab_y_cex
lab_cex <- getOption("lab_cex")
lab_x_cex <- getOption("lab_x_cex")
lab_x_cex <- ifelse(is.null(lab_x_cex), lab_cex, lab_x_cex)
adj <- .RSadj(lab_cex=lab_x_cex); lab_x_cex <- adj$lab_cex
# get variable labels if exist plus axes labels
gl <- .getlabels(xlab=NULL, ylab=xlab, main=NULL, lab_x_cex=lab_x_cex,
graph.win=FALSE) # # graphics window not yet set-up
x.name <- gl$yn; x.lbl <- gl$yl; x.lab <- gl$yb
# get variable labels if exist
options(xname = Xnm)
options(yname = Ynm)
gl <- .getlabels(graph.win=FALSE) # graphics window not yet set-up
x.lbl <- gl$xl
y.lbl <- gl$yl
if (is.null(y.lbl)) y.lbl <- Ynm
if (!quiet) {
cat("Compare", Ynm, "across", Xnm, "with levels", X1nm, "and", X2nm, "\n")
# cat("--------------------------------------------------------------\n\n")
if (!is.null(x.lbl))
cat("Grouping Variable: ", Xnm, ", ", as.character(x.lbl), sep="", "\n")
else
cat("Grouping Variable: ", Xnm, sep="", "\n")
if (Ynm != as.character(y.lbl))
cat("Response Variable: ", Ynm, ", ", as.character(y.lbl), sep="", "\n")
else
cat("Response Variable: ", Ynm, sep="", "\n")
cat("\n")
if (!brief)
cat("\n------ Describe ------\n\n")
else
cat("\n --- Describe ---\n\n")
} # end !quiet
if (from.data) {
n1 <- sum(!is.na(YA))
n2 <- sum(!is.na(YB))
n1.miss <- sum(is.na(YA))
n2.miss <- sum(is.na(YB))
YA <- na.omit(YA)
YB <- na.omit(YB)
m1 <- mean(YA)
m2 <- mean(YB)
s1 <- sd(YA)
s2 <- sd(YB)
v1 <- var(YA)
v2 <- var(YB)
}
else {
v1 <- s1^2
v2 <- s2^2
}
if (from.data) dig.smr.d <- digits_d else dig.smr.d <- digits_d - 1
clpct <- paste(toString(round((conf_level)*100, 2)), "%", sep="")
Xnmval <- paste(Xnm, X1nm)
if (!quiet) {
cat(Ynm, " for ", Xnmval, ": ", sep="")
if (from.data) cat("n.miss = ", n1.miss, ", ", sep="")
cat("n = ", n1, sep="")
cat(", mean = ", .fmt(m1,dig.smr.d), ", sd = ", .fmt(s1,dig.smr.d),
sep="", "\n")
} # end !quiet
Xnmval <- paste(Xnm, X2nm)
if (!quiet) {
cat(Ynm, " for ", Xnmval, ": ", sep="")
if (from.data) cat("n.miss = ", n2.miss, ", ", sep="")
cat("n = ", n2, sep="")
cat(", mean = ", .fmt(m2,dig.smr.d), ", sd = ", .fmt(s2,dig.smr.d),
sep="", "\n")
cat("\n")
} # end !quiet
# sample mean difference
mdiff <- m1 - m2
if (!quiet)
cat("Mean Difference of ", Ynm, ": " , .fmt(mdiff), sep="", "\n")
if (!brief) cat("\n")
# sw
df1 <- n1 - 1
df2 <- n2 - 1
swsq <- (df1*v1 + df2*v2) / (df1 + df2)
sw <- sqrt(swsq)
if (!quiet)
cat("Weighted Average Standard Deviation: ", .fmt(sw), "\n")
smd <- mdiff/sw
if (brief && !quiet)
cat("Standardized Mean Difference of ", Ynm, ": ",
.fmt(smd), sep="", "\n")
if (!brief) {
if (!quiet) {
cat("\n\n------ Assumptions ------\n\n")
cat("Note: These hypothesis tests can perform poorly, and the", "\n")
cat(" t-test is typically robust to violations of assumptions.",
"\n")
cat(" Use as heuristic guides instead of interpreting literally.",
"\n\n")
} # end !quiet
if (from.data) {
if (!quiet) {
# Normality
cat("Null hypothesis, for each group, is a normal distribution of ",
sep="")
cat(Ynm, ".", sep="", "\n")
if (n1 > 30) {
cat("Group " , X1nm, ": ", sep="")
cat("Sample mean assumed normal because n > 30, so no test needed.",
sep="", "\n")
}
else {
cat("Group", X1nm, " ")
if (n1 > 2 && n1 < 5000) {
nrm1 <- shapiro.test(YA)
W.1 <- nrm1$statistic
p.val1 <- nrm1$p.value
cat(nrm1$method, ": W = ", .fmt(W.1,3), ", p-value = ",
.fmt(p.val1,3), sep="", "\n")
}
else
cat("Sample size out of range for Shapiro-Wilk normality test.", "\n")
}
if (n2 > 30) {
cat("Group " , X2nm, ": ", sep="")
cat("Sample mean assumed normal because n > 30, so no test needed.",
sep="", "\n")
}
else {
cat("Group", X2nm, " ")
if (n2 > 2 && n2 < 5000) {
nrm2 <- shapiro.test(YB)
W.2 <- nrm2$statistic
p.val2 <- nrm2$p.value
cat(nrm2$method, ": W = ", .fmt(W.2,3), ", p-value = ",
.fmt(p.val2,3), sep="", "\n")
}
else
cat("Sample size out of range for Shapiro-Wilk normality test.", "\n")
}
cat("\n")
} # end !quiet
}
# Homogeneity of Variance
# Var Ratio
if (v1 >= v2) {
vratio <- v1/v2
vr <- paste(.fmt(v1), "/", .fmt(v2), sep="")
df.num <- df1
df.den <- df2
}
else {
vratio <- v2/v1
vr <- paste(.fmt(v2), "/", .fmt(v1), sep="")
df.num <- df2
df.den <- df1
}
p.var <- pf(vratio, df1=df.num, df2=df.den)
# adjust for two-sided test, results same as var.test{stats}
p.var <- 2 * min(p.var, 1-p.var)
if (!quiet) {
cat("Null hypothesis is equal variances of ")
cat(Ynm, ", homogeneous.", sep="", "\n")
cat("Variance Ratio test: F = ", vr, " = ", .fmt(vratio),
", df = ", df.num, ";",
df.den, ", p-value = ", .fmt(p.var,3), sep="", "\n")
} # end !quiet
if (from.data) { # Levene
YAm <- abs(YA - median(YA))
YBm <- abs(YB - median(YB))
t.bf <- t.test(YAm, YBm, var.equal=TRUE)
tvalue.bf <- t.bf$statistic
df.bf <- t.bf$parameter
pvalue.bf <- t.bf$p.value
if (!quiet) {
cat("Levene's test, Brown-Forsythe: t = ", .fmt(tvalue.bf,3),
", df = ", df.bf, sep="")
cat(", p-value = ", .fmt(pvalue.bf,3), sep="", "\n")
} # end !quiet
}
}
if (!quiet) {
if (!brief)
cat("\n\n------ Infer ------\n\n")
else
cat("\n --- Infer ---\n\n")
} # end !quiet
# t-test
if (alternative == "two_sided")
alt <- "two.sided"
else
alt <- alternative
sterr <- sw * sqrt(1/n1 + 1/n2)
df <- df1 + df2
if (alternative == "two_sided")
tcut <- qt((1-conf_level)/2, df=df, lower.tail=FALSE)
else if (alternative == "less")
tcut <- qt(1-conf_level, df=df, lower.tail=FALSE)
else if (alternative == "greater")
tcut <- qt(1-conf_level, df=df, lower.tail=TRUE)
if (from.data) {
ttest <- t.test(YA, YB, var.equal=TRUE, conf_level=conf_level,
alternative=alt)
lb <- ttest$conf[1]
ub <- ttest$conf[2]
E <- (ub-lb) / 2
tvalue <- ttest$statistic
pvalue <- ttest$p.value
}
else {
sterr <- sw * sqrt(1/n1 + 1/n2)
E <- tcut*sterr
lb <- mdiff-E
ub <- mdiff+E
tvalue <- mdiff/sterr
if (alternative == "two_sided")
pvalue <- 2 * pt(abs(tvalue), df=df, lower.tail=FALSE)
else if (alternative == "less")
pvalue <- pt(abs(tvalue), df=df, lower.tail=FALSE)
else if (alternative == "greater")
pvalue <- pt(abs(tvalue), df=df, lower.tail=TRUE)
}
if (!quiet) {
if (!brief)
cat("--- Assume equal population variances of", Ynm, "for each", Xnm,
"\n\n")
cat("t-cutoff for 95% range of variation: tcut = ", .fmt(tcut,3), "\n")
cat("Standard Error of Mean Difference: SE = ", .fmt(sterr), "\n")
mytitle <- "\nHypothesis Test of 0 Mean Diff: t-value = "
if (alt != "two.sided")
cat("\nAlternative hypothesis: Population mean difference is", alt,
"than 0")
cat(mytitle, .fmt(tvalue,3), ", df = ", df, ", p-value = ", .fmt(pvalue,3),
sep="", "\n\n")
cat("Margin of Error for ", clpct, " Confidence Level: ", .fmt(E), sep="",
"\n")
cat(clpct," Confidence Interval for Mean Difference: ", .fmt(lb), " to ",
.fmt(ub), sep="", "\n\n")
} # end !quiet
if (!brief) {
k1 <- v1/n1
k2 <- v2/n2
df.ne <- ((k1 + k2)^2) / ((k1^2)/(n1-1) + (k2^2)/(n2-1))
sterr.ne <- sqrt(k1 + k2)
if (alternative == "two_sided")
tcut.ne <- qt((1-conf_level)/2, df=df.ne, lower.tail=FALSE)
else if (alternative == "less")
tcut.ne <- qt(1-conf_level, df=df.ne, lower.tail=FALSE)
else if (alternative == "greater")
tcut.ne <- qt(1-conf_level, df=df.ne, lower.tail=TRUE)
if (from.data) {
ttne <- t.test(YA, YB, var.equal=FALSE, conf_level=conf_level,
alternative=alt)
df.ne <- ttne$parameter
lb.ne <- ttne$conf[1]
ub.ne <- ttne$conf[2]
E.ne <- (ub.ne-lb.ne)/2
tvalue.ne <- ttne$statistic
pvalue.ne <- ttne$p.value
}
else {
E.ne <- tcut.ne*sterr.ne
lb.ne <- mdiff-E.ne
ub.ne <- mdiff+E.ne
tvalue.ne <- mdiff / sterr.ne
if (alternative == "two_sided")
pvalue.ne <- 2 * pt(abs(tvalue.ne), df=df.ne, lower.tail=FALSE)
else if (alternative == "less")
pvalue.ne <- pt(abs(tvalue.ne), df=df.ne, lower.tail=FALSE)
else if (alternative == "greater")
pvalue.ne <- pt(abs(tvalue.ne), df=df.ne, lower.tail=TRUE)
}
if (!quiet) {
cat("\n--- Do not assume equal population variances of", Ynm, "for each",
Xnm, "\n\n")
cat("t-cutoff: tcut = ", .fmt(tcut.ne,3), "\n")
cat("Standard Error of Mean Difference: SE = ", .fmt(sterr.ne), "\n")
mytitle <- "\nHypothesis Test of 0 Mean Diff: t = "
cat(mytitle, .fmt(tvalue.ne,3), ", df = ", .fmt(df.ne,3),
", p-value = ", .fmt(pvalue.ne,3), sep="", "\n\n")
cat("Margin of Error for ", clpct, " Confidence Level: ", .fmt(E.ne),
sep="", "\n")
cat(clpct," Confidence Interval for Mean Difference: ", .fmt(lb.ne),
" to ", .fmt(ub.ne), sep="", "\n")
} # end !quiet
}
# mean difference and standardized mean difference
if (!brief && !quiet) {
cat("\n\n------ Effect Size ------\n\n")
cat("--- Assume equal population variances of", Ynm, "for each", Xnm,
"\n\n")
cat("Standardized Mean Difference of ", Ynm, ", ",
"Cohen's d: ", .fmt(smd), sep="", "\n")
} # end !quiet
# MBESS function
#cid <- ci.smd(smd=smd, n.1=n1, n.2=n2, conf_level=conf_level)
#deltaL <-cid$Lower.Conf.Limit.smd
#deltaU <- cid$Upper.Conf.Limit.smd
#if (!brief) cat("\n")
#cat(clpct," Confidence Interval for smd: ",
#.fmt(deltaL), " to ", .fmt(deltaU), sep="", "\n")
if (!brief) {
if ( !is.null(mmd) | !is.null(msmd) ) {
if (!is.null(mmd)) msmd <- mmd / sw
if (!is.null(msmd)) mmd <- msmd * sw
}
}
if (!brief && !quiet) {
cat("\n\n------ Practical Importance ------\n\n")
cat("Minimum Mean Difference of practical importance: mmd\n")
if ( !is.null(mmd) | !is.null(msmd) ) {
cat("Compare mmd =", .fmt(mmd,digits_d),
" to the obtained value of md = ", .fmt(mdiff), "\n")
cat("Compare mmd to the confidence interval for md: ", .fmt(lb), " to ",
.fmt(ub), "\n\n")
cat("Minimum Standardized Mean Difference of practical importance: msmd\n")
cat("Compare msmd = ", .fmt(msmd,digits_d),
" to the obtained value of smd = ", .fmt(smd),"\n")
}
else {
cat("Minimum Standardized Mean Difference of practical importance: msmd\n")
cat("Neither value specified, so no analysis\n")
}
}
# needed sample size from Edesired
if (!is.null(Edesired)) {
zcut <- qnorm((1-conf_level)/2)
ns <- 2*((zcut*sw)/Edesired)^2
n.needed <- ceiling(1.099*ns + 4.863)
if (!quiet) {
cat("\n\n------ Needed Sample Size ------\n\n")
if (Edesired > E) {
cat("Note: Desired margin of error,", .fmt(Edesired),
"is worse than what was obtained,", .fmt(E), "\n\n")
}
cat("Desired Margin of Error: ", .fmt(Edesired), "\n")
cat("\n")
cat("For the following sample size there is a 0.9 probability of obtaining\n")
cat("the desired margin of error for the resulting 95% confidence interval.\n")
cat("-------\n")
cat("Needed sample size per group: ", n.needed, "\n")
cat("\n")
cat("Additional data values needed Group 1: ", n.needed-n1, "\n")
cat("Additional data values needed Group 2: ", n.needed-n2, "\n")
} # end !quiet
}
# graphs
if (from.data && graph) {
# keep track of the number of plots in this routine, see if manage graphics
plt.i <- 0
plt.title <- character(length=0)
manage.gr <- .graphman()
if (is.null(pdf_file)) {
if (manage.gr) {
n.win <- ifelse (!line_chart, 1, 3)
.graphwin(n.win, width, height)
i.win <- 2 # start first graphics window on 3
orig.params <- par(no.readonly=TRUE)
on.exit(par(orig.params))
}
}
if (line_chart) {
if (!is.null(pdf_file))
pdf(file=paste("LineChart_",X1nm,".pdf",sep=""),
width=width, height=height)
if (manage.gr) {
i.win <- i.win + 1
dev.set(which=i.win)
}
plt.i <- plt.i + 1
plt.title[plt.i] <- paste("Sequentially Ordered Data:", paste(Xnm, X1nm))
YA.df <- data.frame(YA)
x.df <- data.frame(1:nrow(YA.df))
.plt.main(x.df, YA.df, segments=TRUE, size=.85,
center_line="median", fill=getOption("pt_fill"),
xlab="Index", ylab=paste(Ynm,": ",X1nm, sep=""),
main=plt.title[plt.i])
if (!is.null(pdf_file)) {
dev.off()
.showfile(paste("LineChart_", X1nm, ".pdf", sep=""),
paste("line chart of", X1nm))
}
if (manage.gr) {
i.win <- i.win + 1
dev.set(which=i.win)
}
plt.i <- plt.i + 1
plt.title[plt.i] <- paste("Sequentially Ordered Data:", paste(Xnm, X2nm))
YB.df <- data.frame(YB)
x.df <- data.frame(1:nrow(YB.df))
.plt.main(x.df, YB.df, segments=TRUE, size=.85,
center_line="median", fill=getOption("pt_fill"),
xlab="Index", ylab=paste(Ynm,": ",X2nm, sep=""),
main=plt.title[plt.i])
if (!is.null(pdf_file)) {
dev.off()
.showfile(paste("LineChart_", X2nm, ".pdf", sep=""),
paste("line chart of", X2nm))
}
}
# two density graphs
# prepare graphics window, dev or pdf
if (!is.null(pdf_file))
.opendev(pdf_file, width, height)
else {
if (manage.gr) {
i.win <- i.win + 1
dev.set(which=i.win)
}
}
plt.i <- plt.i + 1
plt.title[plt.i] <- "Two-Group Plot"
.TwoGraph(YA, YB, bw1, bw2, Ynm, Xnm, X1nm, X2nm, y.lbl, digits_d, brief,
n1, m1, s1, n2, m2, s2, df, mdiff, sw, smd, mmd, msmd,
clpct, tvalue, pvalue, ub, lb, x.lab, alt, show_title, quiet)
if (!quiet) cat("\n")
if (!is.null(pdf_file)) {
dev.off()
.showfile(pdf_file, paste("density plots of", Ynm, "for both groups"))
}
return(list(i=plt.i, ttl=plt.title))
}
} # End Two Group
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Defines functions .TwoGroup
.TwoGroup <-
function(YA, YB, n1, n2, m1, m2, s1, s2, from.data,
Ynm, Xnm, X1nm, X2nm, brief, digits_d,
conf_level, alternative, mmd, msmd, Edesired, bw1, bw2,
graph, xlab, line_chart, show_title,
quiet, pdf_file, width, height, ...) {
if ( brief && !quiet && (!is.null(mmd) || !is.null(msmd)) ) {
cat("\n"); stop(call.=FALSE, "\n","------\n",
"mmd and msmd do not work with the brief version.\n\n")
}
# get lab_x_cex lab_y_cex
lab_cex <- getOption("lab_cex")
lab_x_cex <- getOption("lab_x_cex")
lab_x_cex <- ifelse(is.null(lab_x_cex), lab_cex, lab_x_cex)
adj <- .RSadj(lab_cex=lab_x_cex); lab_x_cex <- adj$lab_cex
# get variable labels if exist plus axes labels
gl <- .getlabels(xlab=NULL, ylab=xlab, main=NULL, lab_x_cex=lab_x_cex,
graph.win=FALSE) # # graphics window not yet set-up
x.name <- gl$yn; x.lbl <- gl$yl; x.lab <- gl$yb
# get variable labels if exist
options(xname = Xnm)
options(yname = Ynm)
gl <- .getlabels(graph.win=FALSE) # graphics window not yet set-up
x.lbl <- gl$xl
y.lbl <- gl$yl
if (is.null(y.lbl)) y.lbl <- Ynm
if (!quiet) {
cat("Compare", Ynm, "across", Xnm, "with levels", X1nm, "and", X2nm, "\n")
# cat("--------------------------------------------------------------\n\n")
if (!is.null(x.lbl))
cat("Grouping Variable: ", Xnm, ", ", as.character(x.lbl), sep="", "\n")
else
cat("Grouping Variable: ", Xnm, sep="", "\n")
if (Ynm != as.character(y.lbl))
cat("Response Variable: ", Ynm, ", ", as.character(y.lbl), sep="", "\n")
else
cat("Response Variable: ", Ynm, sep="", "\n")
cat("\n")
if (!brief)
cat("\n------ Describe ------\n\n")
else
cat("\n --- Describe ---\n\n")
} # end !quiet
if (from.data) {
n1 <- sum(!is.na(YA))
n2 <- sum(!is.na(YB))
n1.miss <- sum(is.na(YA))
n2.miss <- sum(is.na(YB))
YA <- na.omit(YA)
YB <- na.omit(YB)
m1 <- mean(YA)
m2 <- mean(YB)
s1 <- sd(YA)
s2 <- sd(YB)
v1 <- var(YA)
v2 <- var(YB)
}
else {
v1 <- s1^2
v2 <- s2^2
}
if (from.data) dig.smr.d <- digits_d else dig.smr.d <- digits_d - 1
clpct <- paste(toString(round((conf_level)*100, 2)), "%", sep="")
Xnmval <- paste(Xnm, X1nm)
if (!quiet) {
cat(Ynm, " for ", Xnmval, ": ", sep="")
if (from.data) cat("n.miss = ", n1.miss, ", ", sep="")
cat("n = ", n1, sep="")
cat(", mean = ", .fmt(m1,dig.smr.d), ", sd = ", .fmt(s1,dig.smr.d),
sep="", "\n")
} # end !quiet
Xnmval <- paste(Xnm, X2nm)
if (!quiet) {
cat(Ynm, " for ", Xnmval, ": ", sep="")
if (from.data) cat("n.miss = ", n2.miss, ", ", sep="")
cat("n = ", n2, sep="")
cat(", mean = ", .fmt(m2,dig.smr.d), ", sd = ", .fmt(s2,dig.smr.d),
sep="", "\n")
cat("\n")
} # end !quiet
# sample mean difference
mdiff <- m1 - m2
if (!quiet)
cat("Mean Difference of ", Ynm, ": " , .fmt(mdiff), sep="", "\n")
if (!brief) cat("\n")
# sw
df1 <- n1 - 1
df2 <- n2 - 1
swsq <- (df1*v1 + df2*v2) / (df1 + df2)
sw <- sqrt(swsq)
if (!quiet)
cat("Weighted Average Standard Deviation: ", .fmt(sw), "\n")
smd <- mdiff/sw
if (brief && !quiet)
cat("Standardized Mean Difference of ", Ynm, ": ",
.fmt(smd), sep="", "\n")
if (!brief) {
if (!quiet) {
cat("\n\n------ Assumptions ------\n\n")
cat("Note: These hypothesis tests can perform poorly, and the", "\n")
cat(" t-test is typically robust to violations of assumptions.",
"\n")
cat(" Use as heuristic guides instead of interpreting literally.",
"\n\n")
} # end !quiet
if (from.data) {
if (!quiet) {
# Normality
cat("Null hypothesis, for each group, is a normal distribution of ",
sep="")
cat(Ynm, ".", sep="", "\n")
if (n1 > 30) {
cat("Group " , X1nm, ": ", sep="")
cat("Sample mean assumed normal because n > 30, so no test needed.",
sep="", "\n")
}
else {
cat("Group", X1nm, " ")
if (n1 > 2 && n1 < 5000) {
nrm1 <- shapiro.test(YA)
W.1 <- nrm1$statistic
p.val1 <- nrm1$p.value
cat(nrm1$method, ": W = ", .fmt(W.1,3), ", p-value = ",
.fmt(p.val1,3), sep="", "\n")
}
else
cat("Sample size out of range for Shapiro-Wilk normality test.", "\n")
}
if (n2 > 30) {
cat("Group " , X2nm, ": ", sep="")
cat("Sample mean assumed normal because n > 30, so no test needed.",
sep="", "\n")
}
else {
cat("Group", X2nm, " ")
if (n2 > 2 && n2 < 5000) {
nrm2 <- shapiro.test(YB)
W.2 <- nrm2$statistic
p.val2 <- nrm2$p.value
cat(nrm2$method, ": W = ", .fmt(W.2,3), ", p-value = ",
.fmt(p.val2,3), sep="", "\n")
}
else
cat("Sample size out of range for Shapiro-Wilk normality test.", "\n")
}
cat("\n")
} # end !quiet
}
# Homogeneity of Variance
# Var Ratio
if (v1 >= v2) {
vratio <- v1/v2
vr <- paste(.fmt(v1), "/", .fmt(v2), sep="")
df.num <- df1
df.den <- df2
}
else {
vratio <- v2/v1
vr <- paste(.fmt(v2), "/", .fmt(v1), sep="")
df.num <- df2
df.den <- df1
}
p.var <- pf(vratio, df1=df.num, df2=df.den)
# adjust for two-sided test, results same as var.test{stats}
p.var <- 2 * min(p.var, 1-p.var)
if (!quiet) {
cat("Null hypothesis is equal variances of ")
cat(Ynm, ", homogeneous.", sep="", "\n")
cat("Variance Ratio test: F = ", vr, " = ", .fmt(vratio),
", df = ", df.num, ";",
df.den, ", p-value = ", .fmt(p.var,3), sep="", "\n")
} # end !quiet
if (from.data) { # Levene
YAm <- abs(YA - median(YA))
YBm <- abs(YB - median(YB))
t.bf <- t.test(YAm, YBm, var.equal=TRUE)
tvalue.bf <- t.bf$statistic
df.bf <- t.bf$parameter
pvalue.bf <- t.bf$p.value
if (!quiet) {
cat("Levene's test, Brown-Forsythe: t = ", .fmt(tvalue.bf,3),
", df = ", df.bf, sep="")
cat(", p-value = ", .fmt(pvalue.bf,3), sep="", "\n")
} # end !quiet
}
}
if (!quiet) {
if (!brief)
cat("\n\n------ Infer ------\n\n")
else
cat("\n --- Infer ---\n\n")
} # end !quiet
# t-test
if (alternative == "two_sided")
alt <- "two.sided"
else
alt <- alternative
sterr <- sw * sqrt(1/n1 + 1/n2)
df <- df1 + df2
if (alternative == "two_sided")
tcut <- qt((1-conf_level)/2, df=df, lower.tail=FALSE)
else if (alternative == "less")
tcut <- qt(1-conf_level, df=df, lower.tail=FALSE)
else if (alternative == "greater")
tcut <- qt(1-conf_level, df=df, lower.tail=TRUE)
if (from.data) {
ttest <- t.test(YA, YB, var.equal=TRUE, conf_level=conf_level,
alternative=alt)
lb <- ttest$conf[1]
ub <- ttest$conf[2]
E <- (ub-lb) / 2
tvalue <- ttest$statistic
pvalue <- ttest$p.value
}
else {
sterr <- sw * sqrt(1/n1 + 1/n2)
E <- tcut*sterr
lb <- mdiff-E
ub <- mdiff+E
tvalue <- mdiff/sterr
if (alternative == "two_sided")
pvalue <- 2 * pt(abs(tvalue), df=df, lower.tail=FALSE)
else if (alternative == "less")
pvalue <- pt(abs(tvalue), df=df, lower.tail=FALSE)
else if (alternative == "greater")
pvalue <- pt(abs(tvalue), df=df, lower.tail=TRUE)
}
if (!quiet) {
if (!brief)
cat("--- Assume equal population variances of", Ynm, "for each", Xnm,
"\n\n")
cat("t-cutoff for 95% range of variation: tcut = ", .fmt(tcut,3), "\n")
cat("Standard Error of Mean Difference: SE = ", .fmt(sterr), "\n")
mytitle <- "\nHypothesis Test of 0 Mean Diff: t-value = "
if (alt != "two.sided")
cat("\nAlternative hypothesis: Population mean difference is", alt,
"than 0")
cat(mytitle, .fmt(tvalue,3), ", df = ", df, ", p-value = ", .fmt(pvalue,3),
sep="", "\n\n")
cat("Margin of Error for ", clpct, " Confidence Level: ", .fmt(E), sep="",
"\n")
cat(clpct," Confidence Interval for Mean Difference: ", .fmt(lb), " to ",
.fmt(ub), sep="", "\n\n")
} # end !quiet
if (!brief) {
k1 <- v1/n1
k2 <- v2/n2
df.ne <- ((k1 + k2)^2) / ((k1^2)/(n1-1) + (k2^2)/(n2-1))
sterr.ne <- sqrt(k1 + k2)
if (alternative == "two_sided")
tcut.ne <- qt((1-conf_level)/2, df=df.ne, lower.tail=FALSE)
else if (alternative == "less")
tcut.ne <- qt(1-conf_level, df=df.ne, lower.tail=FALSE)
else if (alternative == "greater")
tcut.ne <- qt(1-conf_level, df=df.ne, lower.tail=TRUE)
if (from.data) {
ttne <- t.test(YA, YB, var.equal=FALSE, conf_level=conf_level,
alternative=alt)
df.ne <- ttne$parameter
lb.ne <- ttne$conf[1]
ub.ne <- ttne$conf[2]
E.ne <- (ub.ne-lb.ne)/2
tvalue.ne <- ttne$statistic
pvalue.ne <- ttne$p.value
}
else {
E.ne <- tcut.ne*sterr.ne
lb.ne <- mdiff-E.ne
ub.ne <- mdiff+E.ne
tvalue.ne <- mdiff / sterr.ne
if (alternative == "two_sided")
pvalue.ne <- 2 * pt(abs(tvalue.ne), df=df.ne, lower.tail=FALSE)
else if (alternative == "less")
pvalue.ne <- pt(abs(tvalue.ne), df=df.ne, lower.tail=FALSE)
else if (alternative == "greater")
pvalue.ne <- pt(abs(tvalue.ne), df=df.ne, lower.tail=TRUE)
}
if (!quiet) {
cat("\n--- Do not assume equal population variances of", Ynm, "for each",
Xnm, "\n\n")
cat("t-cutoff: tcut = ", .fmt(tcut.ne,3), "\n")
cat("Standard Error of Mean Difference: SE = ", .fmt(sterr.ne), "\n")
mytitle <- "\nHypothesis Test of 0 Mean Diff: t = "
cat(mytitle, .fmt(tvalue.ne,3), ", df = ", .fmt(df.ne,3),
", p-value = ", .fmt(pvalue.ne,3), sep="", "\n\n")
cat("Margin of Error for ", clpct, " Confidence Level: ", .fmt(E.ne),
sep="", "\n")
cat(clpct," Confidence Interval for Mean Difference: ", .fmt(lb.ne),
" to ", .fmt(ub.ne), sep="", "\n")
} # end !quiet
}
# mean difference and standardized mean difference
if (!brief && !quiet) {
cat("\n\n------ Effect Size ------\n\n")
cat("--- Assume equal population variances of", Ynm, "for each", Xnm,
"\n\n")
cat("Standardized Mean Difference of ", Ynm, ", ",
"Cohen's d: ", .fmt(smd), sep="", "\n")
} # end !quiet
# MBESS function
#cid <- ci.smd(smd=smd, n.1=n1, n.2=n2, conf_level=conf_level)
#deltaL <-cid$Lower.Conf.Limit.smd
#deltaU <- cid$Upper.Conf.Limit.smd
#if (!brief) cat("\n")
#cat(clpct," Confidence Interval for smd: ",
#.fmt(deltaL), " to ", .fmt(deltaU), sep="", "\n")
if (!brief) {
if ( !is.null(mmd) | !is.null(msmd) ) {
if (!is.null(mmd)) msmd <- mmd / sw
if (!is.null(msmd)) mmd <- msmd * sw
}
}
if (!brief && !quiet) {
cat("\n\n------ Practical Importance ------\n\n")
cat("Minimum Mean Difference of practical importance: mmd\n")
if ( !is.null(mmd) | !is.null(msmd) ) {
cat("Compare mmd =", .fmt(mmd,digits_d),
" to the obtained value of md = ", .fmt(mdiff), "\n")
cat("Compare mmd to the confidence interval for md: ", .fmt(lb), " to ",
.fmt(ub), "\n\n")
cat("Minimum Standardized Mean Difference of practical importance: msmd\n")
cat("Compare msmd = ", .fmt(msmd,digits_d),
" to the obtained value of smd = ", .fmt(smd),"\n")
}
else {
cat("Minimum Standardized Mean Difference of practical importance: msmd\n")
cat("Neither value specified, so no analysis\n")
}
}
# needed sample size from Edesired
if (!is.null(Edesired)) {
zcut <- qnorm((1-conf_level)/2)
ns <- 2*((zcut*sw)/Edesired)^2
n.needed <- ceiling(1.099*ns + 4.863)
if (!quiet) {
cat("\n\n------ Needed Sample Size ------\n\n")
if (Edesired > E) {
cat("Note: Desired margin of error,", .fmt(Edesired),
"is worse than what was obtained,", .fmt(E), "\n\n")
}
cat("Desired Margin of Error: ", .fmt(Edesired), "\n")
cat("\n")
cat("For the following sample size there is a 0.9 probability of obtaining\n")
cat("the desired margin of error for the resulting 95% confidence interval.\n")
cat("-------\n")
cat("Needed sample size per group: ", n.needed, "\n")
cat("\n")
cat("Additional data values needed Group 1: ", n.needed-n1, "\n")
cat("Additional data values needed Group 2: ", n.needed-n2, "\n")
} # end !quiet
}
# graphs
if (from.data && graph) {
# keep track of the number of plots in this routine, see if manage graphics
plt.i <- 0
plt.title <- character(length=0)
manage.gr <- .graphman()
if (is.null(pdf_file)) {
if (manage.gr) {
n.win <- ifelse (!line_chart, 1, 3)
.graphwin(n.win, width, height)
i.win <- 2 # start first graphics window on 3
orig.params <- par(no.readonly=TRUE)
on.exit(par(orig.params))
}
}
if (line_chart) {
if (!is.null(pdf_file))
pdf(file=paste("LineChart_",X1nm,".pdf",sep=""),
width=width, height=height)
if (manage.gr) {
i.win <- i.win + 1
dev.set(which=i.win)
}
plt.i <- plt.i + 1
plt.title[plt.i] <- paste("Sequentially Ordered Data:", paste(Xnm, X1nm))
YA.df <- data.frame(YA)
x.df <- data.frame(1:nrow(YA.df))
.plt.main(x.df, YA.df, segments=TRUE, size=.85,
center_line="median", fill=getOption("pt_fill"),
xlab="Index", ylab=paste(Ynm,": ",X1nm, sep=""),
main=plt.title[plt.i])
if (!is.null(pdf_file)) {
dev.off()
.showfile(paste("LineChart_", X1nm, ".pdf", sep=""),
paste("line chart of", X1nm))
}
if (manage.gr) {
i.win <- i.win + 1
dev.set(which=i.win)
}
plt.i <- plt.i + 1
plt.title[plt.i] <- paste("Sequentially Ordered Data:", paste(Xnm, X2nm))
YB.df <- data.frame(YB)
x.df <- data.frame(1:nrow(YB.df))
.plt.main(x.df, YB.df, segments=TRUE, size=.85,
center_line="median", fill=getOption("pt_fill"),
xlab="Index", ylab=paste(Ynm,": ",X2nm, sep=""),
main=plt.title[plt.i])
if (!is.null(pdf_file)) {
dev.off()
.showfile(paste("LineChart_", X2nm, ".pdf", sep=""),
paste("line chart of", X2nm))
}
}
# two density graphs
# prepare graphics window, dev or pdf
if (!is.null(pdf_file))
.opendev(pdf_file, width, height)
else {
if (manage.gr) {
i.win <- i.win + 1
dev.set(which=i.win)
}
}
plt.i <- plt.i + 1
plt.title[plt.i] <- "Two-Group Plot"
.TwoGraph(YA, YB, bw1, bw2, Ynm, Xnm, X1nm, X2nm, y.lbl, digits_d, brief,
n1, m1, s1, n2, m2, s2, df, mdiff, sw, smd, mmd, msmd,
clpct, tvalue, pvalue, ub, lb, x.lab, alt, show_title, quiet)
if (!quiet) cat("\n")
if (!is.null(pdf_file)) {
dev.off()
.showfile(pdf_file, paste("density plots of", Ynm, "for both groups"))
}
return(list(i=plt.i, ttl=plt.title))
}
} # End Two Group
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