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#' @title Plot normal distributions
#' @name dist_norm
#'
#' @description This function plots a simple normal distribution or a normal distribution
#' with shaded areas that indicate at which value a significant p-level
#' is reached.
#'
#' @param norm Numeric, optional. If specified, a normal distribution with \code{mean} and \code{sd}
#' is plotted and a shaded area at \code{norm} value position is plotted that
#' indicates whether or not the specified value is significant or not.
#' If both \code{norm} and \code{p} are not specified, a distribution without shaded
#' area is plotted.
#' @param mean Numeric. Mean value for normal distribution. By default 0.
#' @param sd Numeric. Standard deviation for normal distribution. By default 1.
#' @param p Numeric, optional. If specified, a normal distribution with \code{mean} and \code{sd}
#' is plotted and a shaded area at the position where the specified p-level
#' starts is plotted. If both \code{norm} and \code{p} are not specified, a distribution
#' without shaded area is plotted.
#' @param xmax Numeric, optional. Specifies the maximum x-axis-value. If not specified, the x-axis
#' ranges to a value where a p-level of 0.00001 is reached.
#' @param geom.alpha Specifies the alpha-level of the shaded area. Default is 0.7, range between 0 to 1.
#'
#' @inheritParams plot_grpfrq
#'
#' @examples
#' # a simple normal distribution
#' dist_norm()
#'
#' # a simple normal distribution with different mean and sd.
#' # note that curve looks similar to above plot, but axis range
#' # has changed.
#' dist_norm(mean = 2, sd = 4)
#'
#' # a simple normal distribution
#' dist_norm(norm = 1)
#'
#' # a simple normal distribution
#' dist_norm(p = 0.2)
#'
#' @import ggplot2
#' @importFrom stats qchisq pchisq dchisq qf pf df qnorm pnorm dnorm qt pt dt
#' @export
dist_norm <- function(norm = NULL,
mean = 0,
sd = 1,
p = NULL,
xmax = NULL,
geom.colors = NULL,
geom.alpha = 0.7) {
# --------------------------------------
# determine maximum range of x-axis.
# --------------------------------------
if (is.null(xmax)) {
if (is.null(norm)) {
n.max <- stats::qnorm(0.00001, mean, sd, lower.tail = F)
}
# --------------------------------------
# else, if we have a x-value, take into
# account all possible x-valuess that would lead
# to a theoretical p-value of 0.00001.
# --------------------------------------
else {
n.max <- norm
while (stats::pnorm(n.max, mean, sd, lower.tail = F) > 0.00001) {
n.max <- n.max + 1
}
}
}
else {
n.max <- xmax
}
# --------------------------------------
# create data frame
# --------------------------------------
mydat <- data.frame(x = seq(-n.max, n.max, length.out = 20 * n.max))
# density normal distribution
mydat$y <- stats::dnorm(mydat$x, mean, sd)
# base plot with normal-distribution
gp <- ggplot(mydat, aes_string(x = "x", y = "y")) + geom_line()
sub.df <- NULL
if (!is.null(p)) {
# plot area for indicated x-value...
sub.df <- mydat[mydat$x > stats::qnorm(p, mean, sd, lower.tail = F), ]
}
else if (!is.null(norm)) {
# resp. for p-value...
sub.df <- mydat[mydat$x > norm, ]
}
if (!is.null(sub.df)) {
sub.df$p.level <- ifelse(sub.df$x > stats::qnorm(0.05, mean, sd, lower.tail = F), "sig", "non-sig")
cs <- stats::qnorm(0.05, mean, sd, lower.tail = F)
gp <- gp +
geom_ribbon(data = sub.df,
aes_string(ymax = "y", fill = "p.level"),
ymin = 0,
alpha = geom.alpha) +
annotate("text",
label = sprintf("x = %.2f", cs),
x = cs,
y = 0,
vjust = 1.3)
# add limit of p-value
if (!is.null(norm)) {
pv <- stats::pnorm(norm, mean, sd, lower.tail = F)
if (pv >= 0.05) {
gp <- gp +
annotate("text",
label = sprintf("p = %.2f", pv),
x = norm,
y = 0,
hjust = -0.1,
vjust = -0.5,
angle = 90)
}
}
}
gp <- sj.setGeomColors(gp, geom.colors, pal.len = 2, labels = c("p > 5%", "p < 0.05"))
gp <- gp + ylab(NULL) + xlab(NULL)
print(gp)
}
#' @title Plot chi-squared distributions
#' @name dist_chisq
#'
#' @description This function plots a simple chi-squared distribution or a chi-squared distribution
#' with shaded areas that indicate at which chi-squared value a significant p-level
#' is reached.
#'
#' @param chi2 Numeric, optional. If specified, a chi-squared distribution with \code{deg.f} degrees
#' of freedom is plotted and a shaded area at \code{chi2} value position is plotted that
#' indicates whether or not the specified value is significant or not.
#' If both \code{chi2} and \code{p} are not specified, a distribution without shaded
#' area is plotted.
#' @param deg.f Numeric. The degrees of freedom for the chi-squared distribution. Needs to
#' be specified.
#' @param p Numeric, optional. If specified, a chi-squared distribution with \code{deg.f} degrees
#' of freedom is plotted and a shaded area at the position where the specified p-level
#' starts is plotted. If both \code{chi2} and \code{p} are not specified, a distribution
#' without shaded area is plotted.
#' @param xmax Numeric, optional. Specifies the maximum x-axis-value. If not specified, the x-axis
#' ranges to a value where a p-level of 0.00001 is reached.
#'
#' @inheritParams dist_norm
#' @inheritParams plot_grpfrq
#'
#' @examples
#' # a simple chi-squared distribution
#' # for 6 degrees of freedom
#' dist_chisq(deg.f = 6)
#'
#' # a chi-squared distribution for 6 degrees of freedom,
#' # and a shaded area starting at chi-squared value of ten.
#' # With a df of 6, a chi-squared value of 12.59 would be "significant",
#' # thus the shaded area from 10 to 12.58 is filled as "non-significant",
#' # while the area starting from chi-squared value 12.59 is filled as
#' # "significant"
#' dist_chisq(chi2 = 10, deg.f = 6)
#'
#' # a chi-squared distribution for 6 degrees of freedom,
#' # and a shaded area starting at that chi-squared value, which has
#' # a p-level of about 0.125 (which equals a chi-squared value of about 10).
#' # With a df of 6, a chi-squared value of 12.59 would be "significant",
#' # thus the shaded area from 10 to 12.58 (p-level 0.125 to p-level 0.05)
#' # is filled as "non-significant", while the area starting from chi-squared
#' # value 12.59 (p-level < 0.05) is filled as "significant".
#' dist_chisq(p = 0.125, deg.f = 6)
#'
#' @import ggplot2
#' @export
dist_chisq <- function(chi2 = NULL,
deg.f = NULL,
p = NULL,
xmax = NULL,
geom.colors = NULL,
geom.alpha = 0.7) {
# --------------------------------------
# check parameters
# --------------------------------------
if (is.null(deg.f)) {
warning("Degrees of freedom ('deg.f') needs to be specified.", call. = F)
return(invisible(NULL))
}
# --------------------------------------
# determine maximum range of x-axis. if we have
# p-value but no chi2-value, distribution should range until
# a theoretical p-value of 0.00001 is reached. this should
# cover all possible (and visible) chi2-values
# --------------------------------------
if (is.null(xmax)) {
if (is.null(chi2)) {
chisq.max <- stats::qchisq(0.00001, deg.f, lower.tail = F)
}
# --------------------------------------
# else, if we have a chi2-value, take into
# account all possible chi2-values that would lead
# to a theoretical p-value of 0.00001.
# --------------------------------------
else {
chisq.max <- chi2
while (stats::pchisq(chisq.max, deg.f, lower.tail = F) > 0.00001) {
chisq.max <- chisq.max + 1
}
}
}
else {
chisq.max <- xmax
}
# --------------------------------------
# create data frame
# --------------------------------------
mydat <- data.frame(x = seq(0, chisq.max, length.out = 10 * chisq.max))
# density distribution of chi2
mydat$y <- stats::dchisq(mydat$x, deg.f)
# base plot with chi2-distribution
gp <- ggplot(mydat, aes_string(x = "x", y = "y")) + geom_line()
sub.df <- NULL
if (!is.null(p)) {
# plot area for indicated chi2-value...
sub.df <- mydat[mydat$x > stats::qchisq(p, deg.f, lower.tail = F), ]
}
else if (!is.null(chi2)) {
# resp. for p-value...
sub.df <- mydat[mydat$x > chi2, ]
}
if (!is.null(sub.df)) {
sub.df$p.level <- ifelse(sub.df$x > stats::qchisq(0.05, deg.f, lower.tail = F), "sig", "non-sig")
cs <- stats::qchisq(0.05, deg.f, lower.tail = F)
gp <- gp +
geom_ribbon(data = sub.df,
aes_string(ymax = "y", fill = "p.level"),
ymin = 0,
alpha = geom.alpha) +
annotate("text",
label = as.character(as.expression(substitute(chi^2 == c2, list(c2 = sprintf("%.2f", cs))))),
parse = TRUE,
x = cs,
y = 0,
vjust = 1.2)
# add limit of p-value
if (!is.null(chi2)) {
pv <- stats::pchisq(chi2, deg.f, lower.tail = F)
if (pv >= 0.05) {
gp <- gp +
annotate("text",
label = sprintf("p = %.2f", pv),
x = chi2,
y = 0,
hjust = -0.1,
vjust = -0.5,
angle = 90)
}
}
}
gp <- sj.setGeomColors(gp, geom.colors, pal.len = 2, labels = c("p > 5%", "p < 0.05"))
gp <- gp + ylab(NULL) + xlab("chi-squared value")
print(gp)
}
#' @title Plot F distributions
#' @name dist_f
#'
#' @description This function plots a simple F distribution or an F distribution
#' with shaded areas that indicate at which F value a significant p-level
#' is reached.
#'
#' @param f Numeric, optional. If specified, an F distribution with \code{deg.f1} and \code{deg.f2} degrees
#' of freedom is plotted and a shaded area at \code{f} value position is plotted that
#' indicates whether or not the specified value is significant or not.
#' If both \code{f} and \code{p} are not specified, a distribution without shaded
#' area is plotted.
#' @param deg.f1 Numeric. The first degrees of freedom for the F distribution. Needs to
#' be specified.
#' @param deg.f2 Numeric. The second degrees of freedom for the F distribution. Needs to
#' be specified.
#' @param p Numeric, optional. If specified, a F distribution with \code{deg.f1} and \code{deg.f2} degrees
#' of freedom is plotted and a shaded area at the position where the specified p-level
#' starts is plotted. If both \code{f} and \code{p} are not specified, a distribution
#' without shaded area is plotted.
#' @param xmax Numeric, optional. Specifies the maximum x-axis-value. If not specified, the x-axis
#' ranges to a value where a p-level of 0.00001 is reached.
#'
#' @inheritParams dist_norm
#' @inheritParams plot_grpfrq
#'
#' @examples
#' # a simple F distribution for 6 and 45 degrees of freedom
#' dist_f(deg.f1 = 6, deg.f2 = 45)
#'
#' # F distribution for 6 and 45 degrees of freedom,
#' # and a shaded area starting at F value of two.
#' # F-values equal or greater than 2.31 are "significant"
#' dist_f(f = 2, deg.f1 = 6, deg.f2 = 45)
#'
#' # F distribution for 6 and 45 degrees of freedom,
#' # and a shaded area starting at a p-level of 0.2
#' # (F-Value about 1.5).
#' dist_f(p = 0.2, deg.f1 = 6, deg.f2 = 45)
#'
#' @import ggplot2
#' @export
dist_f <- function(f = NULL,
deg.f1 = NULL,
deg.f2 = NULL,
p = NULL,
xmax = NULL,
geom.colors = NULL,
geom.alpha = 0.7) {
# --------------------------------------
# check parameters
# --------------------------------------
if (is.null(deg.f1) || is.null(deg.f2)) {
warning("Both degrees of freedom ('deg.f1' and 'deg.f2') needs to be specified.", call. = F)
return(invisible(NULL))
}
# --------------------------------------
# determine maximum range of x-axis. if we have
# p-value but no f-value, distribution should range until
# a theoretical p-value of 0.00001 is reached. this should
# cover all possible (and visible) f-values
# --------------------------------------
if (is.null(xmax)) {
if (is.null(f)) {
f.max <- stats::qf(0.00001, deg.f1, deg.f2, lower.tail = F)
# --------------------------------------
# else, if we have a f-value, take into
# account all possible f-values that would lead
# to a theoretical p-value of 0.00001.
# --------------------------------------
} else {
f.max <- f
while (stats::pf(f.max, deg.f1, deg.f2, lower.tail = F) > 0.00001) f.max <- f.max + 1
}
} else {
f.max <- xmax
}
# --------------------------------------
# create data frame
# --------------------------------------
mydat <- data.frame(x = seq(0, f.max, length.out = 30 * f.max))
# density distribution of f
mydat$y <- stats::df(mydat$x, deg.f1, deg.f2)
# base plot with f-distribution
gp <- ggplot(mydat, aes_string(x = "x", y = "y")) + geom_line()
sub.df <- NULL
if (!is.null(p)) {
# plot area for indicated f-value...
sub.df <- mydat[mydat$x > stats::qf(p, deg.f1, deg.f2, lower.tail = F), ]
} else if (!is.null(f)) {
# resp. for p-value...
sub.df <- mydat[mydat$x > f, ]
}
if (!is.null(sub.df)) {
sub.df$p.level <- ifelse(sub.df$x > stats::qf(0.05, deg.f1, deg.f2, lower.tail = F), "sig", "non-sig")
fv <- stats::qf(0.05, deg.f1, deg.f2, lower.tail = F)
gp <- gp +
geom_ribbon(data = sub.df,
aes_string(ymax = "y", fill = "p.level"),
ymin = 0,
alpha = geom.alpha) +
annotate("text",
label = sprintf("F = %.2f", fv),
x = fv,
y = 0,
vjust = 1.3)
# add limit of p-value
if (!is.null(f)) {
pv <- stats::pf(f, deg.f1, deg.f2, lower.tail = F)
if (pv >= 0.05) {
gp <- gp +
annotate("text",
label = sprintf("p = %.2f", pv),
x = f,
y = 0,
hjust = -0.1,
vjust = -0.5,
angle = 90)
}
}
}
gp <- sj.setGeomColors(gp, geom.colors, pal.len = 2, labels = c("p > 5%", "p < 0.05"))
gp <- gp + ylab(NULL) + xlab("F-value")
print(gp)
}
#' @title Plot t-distributions
#' @name dist_t
#'
#' @description This function plots a simple t-distribution or a t-distribution
#' with shaded areas that indicate at which t-value a significant p-level
#' is reached.
#'
#' @param t Numeric, optional. If specified, a t-distribution with \code{deg.f} degrees
#' of freedom is plotted and a shaded area at \code{t} value position is plotted that
#' indicates whether or not the specified value is significant or not.
#' If both \code{t} and \code{p} are not specified, a distribution without shaded
#' area is plotted.
#' @param deg.f Numeric. The degrees of freedom for the t-distribution. Needs to
#' be specified.
#' @param p Numeric, optional. If specified, a t-distribution with \code{deg.f} degrees
#' of freedom is plotted and a shaded area at the position where the specified p-level
#' starts is plotted. If both \code{t} and \code{p} are not specified, a distribution
#' without shaded area is plotted.
#' @param xmax Numeric, optional. Specifies the maximum x-axis-value. If not specified, the x-axis
#' ranges to a value where a p-level of 0.00001 is reached.
#'
#' @inheritParams dist_norm
#' @inheritParams plot_grpfrq
#'
#' @examples
#' # a simple t-distribution
#' # for 6 degrees of freedom
#' dist_t(deg.f = 6)
#'
#' # a t-distribution for 6 degrees of freedom,
#' # and a shaded area starting at t-value of one.
#' # With a df of 6, a t-value of 1.94 would be "significant".
#' dist_t(t = 1, deg.f = 6)
#'
#' # a t-distribution for 6 degrees of freedom,
#' # and a shaded area starting at p-level of 0.4
#' # (t-value of about 0.26).
#' dist_t(p = 0.4, deg.f = 6)
#'
#' @import ggplot2
#' @export
dist_t <- function(t = NULL,
deg.f = NULL,
p = NULL,
xmax = NULL,
geom.colors = NULL,
geom.alpha = 0.7) {
# --------------------------------------
# check parameters
# --------------------------------------
if (is.null(deg.f)) {
warning("Degrees of freedom ('deg.f') needs to be specified.", call. = F)
return(invisible(NULL))
}
# --------------------------------------
# determine maximum range of x-axis. if we have
# p-value but no t-value, distribution should range until
# a theoretical p-value of 0.00001 is reached. this should
# cover all possible (and visible) t-values
# --------------------------------------
if (is.null(xmax)) {
if (is.null(t)) {
t.max <- stats::qt(0.00001, deg.f, lower.tail = F)
}
# --------------------------------------
# else, if we have a t-value, take into
# account all possible t-values that would lead
# to a theoretical p-value of 0.00001.
# --------------------------------------
else {
t.max <- t
while (stats::pt(t.max, deg.f, lower.tail = F) > 0.00001) {
t.max <- t.max + 1
}
}
}
else {
t.max <- xmax
}
# --------------------------------------
# create data frame
# --------------------------------------
mydat <- data.frame(x = seq(-t.max, t.max, length.out = 20 * t.max))
# density distribution of t
mydat$y <- stats::dt(mydat$x, deg.f)
# base plot with t-distribution
gp <- ggplot(mydat, aes_string(x = "x", y = "y")) + geom_line()
sub.df <- NULL
if (!is.null(p)) {
# plot area for indicated t-value...
sub.df <- mydat[mydat$x > stats::qt(p, deg.f, lower.tail = F), ]
}
else if (!is.null(t)) {
# resp. for p-value...
sub.df <- mydat[mydat$x > t, ]
}
if (!is.null(sub.df)) {
sub.df$p.level <- ifelse(sub.df$x > stats::qt(0.05, deg.f, lower.tail = F), "sig", "non-sig")
tv <- stats::qt(0.05, deg.f, lower.tail = F)
gp <- gp +
geom_ribbon(data = sub.df,
aes_string(ymax = "y", fill = "p.level"),
ymin = 0,
alpha = geom.alpha) +
annotate("text",
label = sprintf("t = %.2f", tv),
x = tv,
y = 0,
vjust = 1.3)
# add limit of p-value
if (!is.null(t)) {
pv <- stats::pt(t, deg.f, lower.tail = F)
if (pv >= 0.05) {
gp <- gp +
annotate("text",
label = sprintf("p = %.2f", pv),
x = t,
y = 0,
hjust = -0.1,
vjust = -0.5,
angle = 90)
}
}
}
gp <- sj.setGeomColors(gp, geom.colors, pal.len = 2, labels = c("p > 5%", "p < 0.05"))
gp <- gp + ylab(NULL) + xlab("t-value")
print(gp)
}
|
