Nothing
R/dataShape.R
In rosetta: Parallel Use of Statistical Packages in Teaching
#' #' @rdname normalityAssessment
#' #' @export
#' dataShape <- function(sampleVector, na.rm=TRUE, type=2, digits=2,
#' conf.level=.95, plots=TRUE, xLabs = NA,
#' yLabs = NA, qqCI=TRUE, labelOutliers = TRUE,
#' sampleSizeOverride = NULL) {
#'
#' ### Note: this is adapted from the 'skewness' and 'kurtosis' functions
#' ### in 'e1071' and the way they're computed in 'describe' in 'psych', and
#' ### for the variances, also based on Stan Browns page at
#' ### https://www.tc3.edu/instruct/sbrown/stat/shape.htm, as well as of course
#' ### on Joanes & Gill (1998)
#'
#' res <- list(input = as.list(environment()),
#' intermediate = list(), output = list());
#'
#' if (any(isNA <- is.na(sampleVector))) {
#' if (na.rm) {
#' res$intermediate$sampleVector <- sampleVector <- sampleVector[!isNA];
#' }
#' else {
#' return(NA);
#' }
#' } else {
#' res$intermediate$sampleVector <- sampleVector;
#' }
#'
#' if (!(type %in% (1:3))) {
#' stop("Invalid 'type' argument. This must be 1, 2 or 3; see ?skewness for more info.");
#' }
#'
#' ### Number of observations
#' res$intermediate$n <- n <- length(sampleVector);
#'
#' if (n < 3) {
#' stop("There are only ", n, " datapoints/observations - this is too few to ",
#' "compute a sensible estimate of the 'shape' of this data.");
#' }
#'
#' ### First moment (mean)
#' res$intermediate$m1 <- sum(sampleVector^1) / n;
#'
#' ### Center the data
#' res$intermediate$centeredVector <- sampleVector <- sampleVector - res$intermediate$m1;
#'
#' ### Second moment (variance)
#' res$intermediate$m2 <- m2 <- sum(sampleVector^2) / n;
#'
#' ### Third moment
#' res$intermediate$m3 <- m3 <- sum(sampleVector^3) / n;
#'
#' ### Fourth moment
#' res$intermediate$m4 <- m4 <- sum(sampleVector^4) / n;
#'
#' ### Sample skewness
#' res$intermediate$g1 <- m3 / (m2 ^ (3/2));
#'
#' ### Sample (excess) kurtosis
#' res$intermediate$g2 <- (m4 / (m2 ^ 2)) - 3;
#'
#' ### Population skewness
#' res$intermediate$G1 <- res$intermediate$g1 *
#' sqrt( n * (n-1) ) /
#' ( n - 2 );
#'
#' ### Population kurtosis
#' res$intermediate$G2 <- (n-1) *
#' ( (n+1) * res$intermediate$g2 + 6 ) /
#' ( (n-2) * (n-3) );
#'
#' ### Type 3 correction for skewness
#' res$intermediate$b1 <- res$intermediate$g1 *
#' (((n-1) / n) ^ (3/2));
#'
#' ### Type 3 correction for kurtosis
#' res$intermediate$b2 <- (res$intermediate$g2 + 3) *
#' (((n-1) / n) ^ 2) - 3;
#'
#' ### Now for the variances. We compute the variance in a normal
#' ### population, because when we want to test the skewness and
#' ### kurtosis, we do so under the assumption that they come from a
#' ### normal distribution. Plus, no idea how to compute the variance
#' ### otherwise :-)
#'
#' ### These formulas come from the Joanes & Gill (1998) article.
#'
#' ### Note that we use the 'overridden sample size' if one was specified.
#' ### We do this because when this function is used
#' if (is.numeric(sampleSizeOverride)) n <- sampleSizeOverride;
#'
#' res$intermediate$var.g1 <- ( 6 * (n-2) ) /
#' ( (n+1) * (n+3) );
#' res$intermediate$var.g2 <- ( 24*n * (n-2) * (n-3) ) /
#' ( (n+1)^2 * (n+3) * (n + 5) );
#' res$intermediate$var.G1 <- res$intermediate$var.g1 *
#' sqrt(n * (n-1)) /
#' (n-2)^2;
#' res$intermediate$var.G2 <- res$intermediate$var.g2 *
#' (((n-1) * (n+1)) /
#' ((n-2) * (n-3))) ^ 2;
#' res$intermediate$var.b1 <- res$intermediate$var.g1 *
#' ((n-1) / n) ^ 3;
#' res$intermediate$var.b2 <- res$intermediate$var.g2 *
#' ((n-1) / n) ^ 4;
#'
#' ### And the standard error for the skewness and the kurtosis,
#' ### based on the formulas on https://www.tc3.edu/instruct/sbrown/stat/shape.htm
#' res$intermediate$se.G1 <- sqrt( ( 6 * n * (n-1) ) /
#' ( (n-2) * (n+1) * (n+3) ) );
#' res$intermediate$se.G2 <- 2 * res$intermediate$se.G1 *
#' sqrt( (n^2 - 1) /
#' ( (n-3) * (n+5) ) );
#'
#' ### Confidence interval for skewness and kurtosis in the population
#' res$intermediate$zMultiplier <- stats::qnorm(1 - (1-conf.level)/2);
#' res$intermediate$ci.G1 <- c(res$intermediate$G1 -
#' res$intermediate$zMultiplier *
#' res$intermediate$se.G1,
#' res$intermediate$G1 +
#' res$intermediate$zMultiplier *
#' res$intermediate$se.G1);
#' res$intermediate$ci.G2 <- c(res$intermediate$G2 -
#' res$intermediate$zMultiplier *
#' res$intermediate$se.G2,
#' res$intermediate$G2 +
#' res$intermediate$zMultiplier *
#' res$intermediate$se.G2);
#'
#' ### Z-test to test against normal distribution
#' res$intermediate$z.G1 <- res$intermediate$G1 / res$intermediate$se.G1;
#' res$intermediate$z.G2 <- res$intermediate$G2 / res$intermediate$se.G2;
#' res$intermediate$p.G1 <- 2*(1-stats::pnorm(abs(res$intermediate$z.G1)));
#' res$intermediate$p.G2 <- 2*(1-stats::pnorm(abs(res$intermediate$z.G2)));
#'
#' ### Hartigans' Dip Test
#' res$output$D.dip.test <- diptest::dip.test(sampleVector)$statistic[[1]];
#' res$output$p.dip.test <- diptest::dip.test(sampleVector)$p[[1]];
#'
#' ### Store requested estimates in output object
#' if (type == 1) {
#' res$output$skewness <- res$intermediate$g1;
#' res$output$kurtosis <- res$intermediate$g2;
#' res$output$type <- "g";
#' }
#' else if (type == 2) {
#' res$output$skewness <- res$intermediate$G1;
#' res$output$kurtosis <- res$intermediate$G2;
#' res$output$type <- "G";
#' }
#' else if (type == 3) {
#' res$output$skewness <- res$intermediate$b1;
#' res$output$kurtosis <- res$intermediate$b2;
#' res$output$type <- "b";
#' }
#'
#' if (plots) {
#' res$intermediate$histogram <-
#' normalHist(res$intermediate$sampleVector)$plot;
#' res$intermediate$qq <-
#' ggqq(res$intermediate$sampleVector, ci=qqCI);
#' res$intermediate$boxplot <-
#' ggBoxplot(res$intermediate$sampleVector, labelOutliers=labelOutliers);
#' if (!is.null(xLabs)) {
#' if (is.na(xLabs)) {
#' res$intermediate$histogram <-
#' res$intermediate$histogram +
#' ggplot2::theme(axis.title.x = ggplot2::element_blank());
#' res$intermediate$qq <-
#' res$intermediate$qq +
#' ggplot2::theme(axis.title.x = ggplot2::element_blank());
#' res$intermediate$boxplot <-
#' res$intermediate$boxplot +
#' ggplot2::theme(axis.title.x = ggplot2::element_blank());
#' } else {
#' res$intermediate$histogram <-
#' res$intermediate$histogram + ggplot2::xlab(xLabs$hist);
#' res$intermediate$qq <-
#' res$intermediate$qq + ggplot2::xlab(xLabs$qq);
#' res$intermediate$boxplot <-
#' res$intermediate$boxplot + ggplot2::xlab(xLabs$box);
#' }
#' }
#'
#' if (!is.null(yLabs)) {
#' if (is.na(yLabs)) {
#' res$intermediate$histogram <-
#' res$intermediate$histogram +
#' ggplot2::theme(axis.title.y = ggplot2::element_blank());
#' res$intermediate$qq <-
#' res$intermediate$qq +
#' ggplot2::theme(axis.title.y = ggplot2::element_blank());
#' res$intermediate$boxplot <-
#' res$intermediate$boxplot +
#' ggplot2::theme(axis.title.y = ggplot2::element_blank());
#' } else {
#' res$intermediate$histogram <-
#' res$intermediate$histogram + ggplot2::ylab(yLabs$hist);
#' res$intermediate$qq <-
#' res$intermediate$qq + ggplot2::ylab(yLabs$qq);
#' res$intermediate$boxplot <-
#' res$intermediate$boxplot + ggplot2::ylab(yLabs$box);
#' }
#' }
#'
#' res$output$plot <-
#' gridExtra::arrangeGrob(res$intermediate$histogram,
#' res$intermediate$qq,
#' res$intermediate$boxplot, ncol=3);
#' }
#'
#' ### Return results object
#' class(res) <- "dataShape";
#' return(res);
#'
#' }
#'
#' #' @method print dataShape
#' #' @rdname normalityAssessment
#' #' @export
#' print.dataShape <- function(x, digits=x$input$digits, extraNotification=TRUE, ...) {
#' if (x$output$type == "G") {
#' skewness.inference <- paste0(" (se = ", format(x$intermediate$se.G1, digits=digits),
#' ", confidence interval = [",
#' paste0(format(x$intermediate$ci.G1, digits=digits), collapse=", "),
#' "], z = ", format(x$intermediate$z.G1, digits=digits),
#' ", ", formatPvalue(x$intermediate$p.G1, digits=digits), ")");
#' kurtosis.inference <- paste0(" (se = ", format(x$intermediate$se.G2, digits=digits),
#' ", confidence interval = [",
#' paste0(format(x$intermediate$ci.G2, digits=digits), collapse=", "),
#' "], z = ", format(x$intermediate$z.G2, digits=digits),
#' ", ", formatPvalue(x$intermediate$p.G2, digits=digits), ")");
#' }
#' else {
#' skewness.inference <- kurtosis.inference <- "";
#' }
#' cat(paste0("Skewness (", x$output$type, "1): ",
#' round(x$output$skewness, digits=digits),
#' skewness.inference, "\n"));
#' cat(paste0("Kurtosis (", x$output$type, "2): ",
#' round(x$output$kurtosis, digits=digits),
#' kurtosis.inference, "\n"));
#' cat(paste0("Hartigans' Dip Test: ",
#' round(x$output$D.dip.test, digits=digits), ", ",
#' formatPvalue(x$output$p.dip.test), "\n"));
#'
#' if (x$input$plots) {
#' grid::grid.draw(x$output$plot);
#' }
#'
#' if (extraNotification && x$output$type == "g") {
#' cat("\nNote: g1 and g2 are biased estimates of the population skewness and kurtosis.",
#' "For unbiased estimates, use 'type=2' or 'type=3'.");
#' }
#' else if (extraNotification && x$output$type == "G") {
#' cat("\nNote: G1 and G2 are the estimates for skewness and kurtosis used by SPSS and SAS,",
#' "and corrected for the bias present in g1 and g2 ('type=1'). Note that b1 and b2 ('type=3')",
#' "may perform better in small samples from a normal distribution.");
#' }
#' else if (extraNotification && x$output$type == "b") {
#' cat("\nNote: b1 and b2 are estimates for skewness and kurtosis that have smaller mean-squared error in small",
#' "samples from a normal distribution than G1 and G2, which are used by SPSS and SAS ('type=2').");
#' }
#' }
#'
#' #' @method pander dataShape
#' #' @rdname normalityAssessment
#' #' @export
#' pander.dataShape <- function(x, digits=x$input$digits, extraNotification=TRUE, ...) {
#' if (x$output$type == "G") {
#' skewness.inference <- paste0(" (se = ", format(x$intermediate$se.G1, digits=digits),
#' ", confidence interval = [",
#' paste0(format(x$intermediate$ci.G1, digits=digits), collapse=", "),
#' "], z = ", format(x$intermediate$z.G1, digits=digits),
#' ", ", formatPvalue(x$intermediate$p.G1, digits=digits), ")");
#' kurtosis.inference <- paste0(" (se = ", format(x$intermediate$se.G2, digits=digits),
#' ", confidence interval = [",
#' paste0(format(x$intermediate$ci.G2, digits=digits), collapse=", "),
#' "], z = ", format(x$intermediate$z.G2, digits=digits),
#' ", ", formatPvalue(x$intermediate$p.G2, digits=digits), ")");
#' }
#' else {
#' skewness.inference <- kurtosis.inference <- "";
#' }
#' cat(paste0("Skewness (", x$output$type, "1): ",
#' round(x$output$skewness, digits=digits),
#' skewness.inference, " \n"));
#' cat(paste0("Kurtosis (", x$output$type, "2): ",
#' round(x$output$kurtosis, digits=digits),
#' kurtosis.inference, " \n"));
#' cat(paste0("Hartigans' Dip Test: ",
#' round(x$output$D.dip.test, digits=digits), ", ",
#' formatPvalue(x$output$p.dip.test), "\n"));
#'
#' if (extraNotification && x$output$type == "g") {
#' cat("\nNote: g1 and g2 are biased estimates of the population skewness and kurtosis.",
#' "For unbiased estimates, use 'type=2' or 'type=3'.\n");
#' }
#' else if (extraNotification && x$output$type == "G") {
#' cat("\nNote: G1 and G2 are the estimates for skewness and kurtosis used by SPSS and SAS,",
#' "and corrected for the bias present in g1 and g2 ('type=1'). Note that b1 and b2 ('type=3')",
#' "may perform better in small samples from a normal distribution.\n");
#' }
#' else if (extraNotification && x$output$type == "b") {
#' cat("\nNote: b1 and b2 are estimates for skewness and kurtosis that have smaller mean-squared error in small",
#' "samples from a normal distribution than G1 and G2, which are used by SPSS and SAS ('type=2').\n");
#' }
#'
#' cat("\n");
#'
#' if (x$input$plots) {
#' grid::grid.draw(x$output$plot);
#' }
#'
#' }
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#' #' @rdname normalityAssessment
#' #' @export
#' dataShape <- function(sampleVector, na.rm=TRUE, type=2, digits=2,
#' conf.level=.95, plots=TRUE, xLabs = NA,
#' yLabs = NA, qqCI=TRUE, labelOutliers = TRUE,
#' sampleSizeOverride = NULL) {
#'
#' ### Note: this is adapted from the 'skewness' and 'kurtosis' functions
#' ### in 'e1071' and the way they're computed in 'describe' in 'psych', and
#' ### for the variances, also based on Stan Browns page at
#' ### https://www.tc3.edu/instruct/sbrown/stat/shape.htm, as well as of course
#' ### on Joanes & Gill (1998)
#'
#' res <- list(input = as.list(environment()),
#' intermediate = list(), output = list());
#'
#' if (any(isNA <- is.na(sampleVector))) {
#' if (na.rm) {
#' res$intermediate$sampleVector <- sampleVector <- sampleVector[!isNA];
#' }
#' else {
#' return(NA);
#' }
#' } else {
#' res$intermediate$sampleVector <- sampleVector;
#' }
#'
#' if (!(type %in% (1:3))) {
#' stop("Invalid 'type' argument. This must be 1, 2 or 3; see ?skewness for more info.");
#' }
#'
#' ### Number of observations
#' res$intermediate$n <- n <- length(sampleVector);
#'
#' if (n < 3) {
#' stop("There are only ", n, " datapoints/observations - this is too few to ",
#' "compute a sensible estimate of the 'shape' of this data.");
#' }
#'
#' ### First moment (mean)
#' res$intermediate$m1 <- sum(sampleVector^1) / n;
#'
#' ### Center the data
#' res$intermediate$centeredVector <- sampleVector <- sampleVector - res$intermediate$m1;
#'
#' ### Second moment (variance)
#' res$intermediate$m2 <- m2 <- sum(sampleVector^2) / n;
#'
#' ### Third moment
#' res$intermediate$m3 <- m3 <- sum(sampleVector^3) / n;
#'
#' ### Fourth moment
#' res$intermediate$m4 <- m4 <- sum(sampleVector^4) / n;
#'
#' ### Sample skewness
#' res$intermediate$g1 <- m3 / (m2 ^ (3/2));
#'
#' ### Sample (excess) kurtosis
#' res$intermediate$g2 <- (m4 / (m2 ^ 2)) - 3;
#'
#' ### Population skewness
#' res$intermediate$G1 <- res$intermediate$g1 *
#' sqrt( n * (n-1) ) /
#' ( n - 2 );
#'
#' ### Population kurtosis
#' res$intermediate$G2 <- (n-1) *
#' ( (n+1) * res$intermediate$g2 + 6 ) /
#' ( (n-2) * (n-3) );
#'
#' ### Type 3 correction for skewness
#' res$intermediate$b1 <- res$intermediate$g1 *
#' (((n-1) / n) ^ (3/2));
#'
#' ### Type 3 correction for kurtosis
#' res$intermediate$b2 <- (res$intermediate$g2 + 3) *
#' (((n-1) / n) ^ 2) - 3;
#'
#' ### Now for the variances. We compute the variance in a normal
#' ### population, because when we want to test the skewness and
#' ### kurtosis, we do so under the assumption that they come from a
#' ### normal distribution. Plus, no idea how to compute the variance
#' ### otherwise :-)
#'
#' ### These formulas come from the Joanes & Gill (1998) article.
#'
#' ### Note that we use the 'overridden sample size' if one was specified.
#' ### We do this because when this function is used
#' if (is.numeric(sampleSizeOverride)) n <- sampleSizeOverride;
#'
#' res$intermediate$var.g1 <- ( 6 * (n-2) ) /
#' ( (n+1) * (n+3) );
#' res$intermediate$var.g2 <- ( 24*n * (n-2) * (n-3) ) /
#' ( (n+1)^2 * (n+3) * (n + 5) );
#' res$intermediate$var.G1 <- res$intermediate$var.g1 *
#' sqrt(n * (n-1)) /
#' (n-2)^2;
#' res$intermediate$var.G2 <- res$intermediate$var.g2 *
#' (((n-1) * (n+1)) /
#' ((n-2) * (n-3))) ^ 2;
#' res$intermediate$var.b1 <- res$intermediate$var.g1 *
#' ((n-1) / n) ^ 3;
#' res$intermediate$var.b2 <- res$intermediate$var.g2 *
#' ((n-1) / n) ^ 4;
#'
#' ### And the standard error for the skewness and the kurtosis,
#' ### based on the formulas on https://www.tc3.edu/instruct/sbrown/stat/shape.htm
#' res$intermediate$se.G1 <- sqrt( ( 6 * n * (n-1) ) /
#' ( (n-2) * (n+1) * (n+3) ) );
#' res$intermediate$se.G2 <- 2 * res$intermediate$se.G1 *
#' sqrt( (n^2 - 1) /
#' ( (n-3) * (n+5) ) );
#'
#' ### Confidence interval for skewness and kurtosis in the population
#' res$intermediate$zMultiplier <- stats::qnorm(1 - (1-conf.level)/2);
#' res$intermediate$ci.G1 <- c(res$intermediate$G1 -
#' res$intermediate$zMultiplier *
#' res$intermediate$se.G1,
#' res$intermediate$G1 +
#' res$intermediate$zMultiplier *
#' res$intermediate$se.G1);
#' res$intermediate$ci.G2 <- c(res$intermediate$G2 -
#' res$intermediate$zMultiplier *
#' res$intermediate$se.G2,
#' res$intermediate$G2 +
#' res$intermediate$zMultiplier *
#' res$intermediate$se.G2);
#'
#' ### Z-test to test against normal distribution
#' res$intermediate$z.G1 <- res$intermediate$G1 / res$intermediate$se.G1;
#' res$intermediate$z.G2 <- res$intermediate$G2 / res$intermediate$se.G2;
#' res$intermediate$p.G1 <- 2*(1-stats::pnorm(abs(res$intermediate$z.G1)));
#' res$intermediate$p.G2 <- 2*(1-stats::pnorm(abs(res$intermediate$z.G2)));
#'
#' ### Hartigans' Dip Test
#' res$output$D.dip.test <- diptest::dip.test(sampleVector)$statistic[[1]];
#' res$output$p.dip.test <- diptest::dip.test(sampleVector)$p[[1]];
#'
#' ### Store requested estimates in output object
#' if (type == 1) {
#' res$output$skewness <- res$intermediate$g1;
#' res$output$kurtosis <- res$intermediate$g2;
#' res$output$type <- "g";
#' }
#' else if (type == 2) {
#' res$output$skewness <- res$intermediate$G1;
#' res$output$kurtosis <- res$intermediate$G2;
#' res$output$type <- "G";
#' }
#' else if (type == 3) {
#' res$output$skewness <- res$intermediate$b1;
#' res$output$kurtosis <- res$intermediate$b2;
#' res$output$type <- "b";
#' }
#'
#' if (plots) {
#' res$intermediate$histogram <-
#' normalHist(res$intermediate$sampleVector)$plot;
#' res$intermediate$qq <-
#' ggqq(res$intermediate$sampleVector, ci=qqCI);
#' res$intermediate$boxplot <-
#' ggBoxplot(res$intermediate$sampleVector, labelOutliers=labelOutliers);
#' if (!is.null(xLabs)) {
#' if (is.na(xLabs)) {
#' res$intermediate$histogram <-
#' res$intermediate$histogram +
#' ggplot2::theme(axis.title.x = ggplot2::element_blank());
#' res$intermediate$qq <-
#' res$intermediate$qq +
#' ggplot2::theme(axis.title.x = ggplot2::element_blank());
#' res$intermediate$boxplot <-
#' res$intermediate$boxplot +
#' ggplot2::theme(axis.title.x = ggplot2::element_blank());
#' } else {
#' res$intermediate$histogram <-
#' res$intermediate$histogram + ggplot2::xlab(xLabs$hist);
#' res$intermediate$qq <-
#' res$intermediate$qq + ggplot2::xlab(xLabs$qq);
#' res$intermediate$boxplot <-
#' res$intermediate$boxplot + ggplot2::xlab(xLabs$box);
#' }
#' }
#'
#' if (!is.null(yLabs)) {
#' if (is.na(yLabs)) {
#' res$intermediate$histogram <-
#' res$intermediate$histogram +
#' ggplot2::theme(axis.title.y = ggplot2::element_blank());
#' res$intermediate$qq <-
#' res$intermediate$qq +
#' ggplot2::theme(axis.title.y = ggplot2::element_blank());
#' res$intermediate$boxplot <-
#' res$intermediate$boxplot +
#' ggplot2::theme(axis.title.y = ggplot2::element_blank());
#' } else {
#' res$intermediate$histogram <-
#' res$intermediate$histogram + ggplot2::ylab(yLabs$hist);
#' res$intermediate$qq <-
#' res$intermediate$qq + ggplot2::ylab(yLabs$qq);
#' res$intermediate$boxplot <-
#' res$intermediate$boxplot + ggplot2::ylab(yLabs$box);
#' }
#' }
#'
#' res$output$plot <-
#' gridExtra::arrangeGrob(res$intermediate$histogram,
#' res$intermediate$qq,
#' res$intermediate$boxplot, ncol=3);
#' }
#'
#' ### Return results object
#' class(res) <- "dataShape";
#' return(res);
#'
#' }
#'
#' #' @method print dataShape
#' #' @rdname normalityAssessment
#' #' @export
#' print.dataShape <- function(x, digits=x$input$digits, extraNotification=TRUE, ...) {
#' if (x$output$type == "G") {
#' skewness.inference <- paste0(" (se = ", format(x$intermediate$se.G1, digits=digits),
#' ", confidence interval = [",
#' paste0(format(x$intermediate$ci.G1, digits=digits), collapse=", "),
#' "], z = ", format(x$intermediate$z.G1, digits=digits),
#' ", ", formatPvalue(x$intermediate$p.G1, digits=digits), ")");
#' kurtosis.inference <- paste0(" (se = ", format(x$intermediate$se.G2, digits=digits),
#' ", confidence interval = [",
#' paste0(format(x$intermediate$ci.G2, digits=digits), collapse=", "),
#' "], z = ", format(x$intermediate$z.G2, digits=digits),
#' ", ", formatPvalue(x$intermediate$p.G2, digits=digits), ")");
#' }
#' else {
#' skewness.inference <- kurtosis.inference <- "";
#' }
#' cat(paste0("Skewness (", x$output$type, "1): ",
#' round(x$output$skewness, digits=digits),
#' skewness.inference, "\n"));
#' cat(paste0("Kurtosis (", x$output$type, "2): ",
#' round(x$output$kurtosis, digits=digits),
#' kurtosis.inference, "\n"));
#' cat(paste0("Hartigans' Dip Test: ",
#' round(x$output$D.dip.test, digits=digits), ", ",
#' formatPvalue(x$output$p.dip.test), "\n"));
#'
#' if (x$input$plots) {
#' grid::grid.draw(x$output$plot);
#' }
#'
#' if (extraNotification && x$output$type == "g") {
#' cat("\nNote: g1 and g2 are biased estimates of the population skewness and kurtosis.",
#' "For unbiased estimates, use 'type=2' or 'type=3'.");
#' }
#' else if (extraNotification && x$output$type == "G") {
#' cat("\nNote: G1 and G2 are the estimates for skewness and kurtosis used by SPSS and SAS,",
#' "and corrected for the bias present in g1 and g2 ('type=1'). Note that b1 and b2 ('type=3')",
#' "may perform better in small samples from a normal distribution.");
#' }
#' else if (extraNotification && x$output$type == "b") {
#' cat("\nNote: b1 and b2 are estimates for skewness and kurtosis that have smaller mean-squared error in small",
#' "samples from a normal distribution than G1 and G2, which are used by SPSS and SAS ('type=2').");
#' }
#' }
#'
#' #' @method pander dataShape
#' #' @rdname normalityAssessment
#' #' @export
#' pander.dataShape <- function(x, digits=x$input$digits, extraNotification=TRUE, ...) {
#' if (x$output$type == "G") {
#' skewness.inference <- paste0(" (se = ", format(x$intermediate$se.G1, digits=digits),
#' ", confidence interval = [",
#' paste0(format(x$intermediate$ci.G1, digits=digits), collapse=", "),
#' "], z = ", format(x$intermediate$z.G1, digits=digits),
#' ", ", formatPvalue(x$intermediate$p.G1, digits=digits), ")");
#' kurtosis.inference <- paste0(" (se = ", format(x$intermediate$se.G2, digits=digits),
#' ", confidence interval = [",
#' paste0(format(x$intermediate$ci.G2, digits=digits), collapse=", "),
#' "], z = ", format(x$intermediate$z.G2, digits=digits),
#' ", ", formatPvalue(x$intermediate$p.G2, digits=digits), ")");
#' }
#' else {
#' skewness.inference <- kurtosis.inference <- "";
#' }
#' cat(paste0("Skewness (", x$output$type, "1): ",
#' round(x$output$skewness, digits=digits),
#' skewness.inference, " \n"));
#' cat(paste0("Kurtosis (", x$output$type, "2): ",
#' round(x$output$kurtosis, digits=digits),
#' kurtosis.inference, " \n"));
#' cat(paste0("Hartigans' Dip Test: ",
#' round(x$output$D.dip.test, digits=digits), ", ",
#' formatPvalue(x$output$p.dip.test), "\n"));
#'
#' if (extraNotification && x$output$type == "g") {
#' cat("\nNote: g1 and g2 are biased estimates of the population skewness and kurtosis.",
#' "For unbiased estimates, use 'type=2' or 'type=3'.\n");
#' }
#' else if (extraNotification && x$output$type == "G") {
#' cat("\nNote: G1 and G2 are the estimates for skewness and kurtosis used by SPSS and SAS,",
#' "and corrected for the bias present in g1 and g2 ('type=1'). Note that b1 and b2 ('type=3')",
#' "may perform better in small samples from a normal distribution.\n");
#' }
#' else if (extraNotification && x$output$type == "b") {
#' cat("\nNote: b1 and b2 are estimates for skewness and kurtosis that have smaller mean-squared error in small",
#' "samples from a normal distribution than G1 and G2, which are used by SPSS and SAS ('type=2').\n");
#' }
#'
#' cat("\n");
#'
#' if (x$input$plots) {
#' grid::grid.draw(x$output$plot);
#' }
#'
#' }
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