Nothing
## ---- include = FALSE---------------------------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
message = FALSE,
warning = FALSE
)
## -----------------------------------------------------------------------------
library(distributions3)
# read in the data
x <- c(3, 7, 11, 0, 7, 0, 4, 5, 6, 2)
n <- length(x)
# make T_9 random variable
T_9 <- StudentsT(df = 9)
# first approach
mean(x) + quantile(T_9, 0.12 / 2) * sd(x) / sqrt(n)
mean(x) + quantile(T_9, 1 - 0.12 / 2) * sd(x) / sqrt(n)
## -----------------------------------------------------------------------------
# second approach
mean(x) - quantile(T_9, 1 - 0.12 / 2) * sd(x) / sqrt(n)
mean(x) + quantile(T_9, 1 - 0.12 / 2) * sd(x) / sqrt(n)
## ---- echo = FALSE------------------------------------------------------------
got_ggplot2 <- requireNamespace("ggplot2", quietly = TRUE)
got_cowplot <- requireNamespace("cowplot", quietly = TRUE)
got_ggplot2_and_cowplot <- got_ggplot2 * got_cowplot
## ---- echo = FALSE, eval = got_ggplot2_and_cowplot----------------------------
library(ggplot2)
library(cowplot)
grid <- seq(-4, 4, length.out = 300)
density <- pdf(T_9, grid)
lower_trunc <- ifelse(grid <= 1.83, density, 0)
upper_trunc <- ifelse(grid >= 1.83, density, 0)
lower_quantile_plot <- ggplot(data = NULL) +
geom_area(aes(grid, lower_trunc, alpha = 0.2), fill = "steelblue") +
geom_line(aes(grid, density), size = 1, color = "grey") +
geom_vline(xintercept = 1.83, size = 1, color = "darkgrey") +
geom_text(
aes(x = 3.2, y = 0.3, label = "t[0.975] == 1.83"),
parse = TRUE,
size = 4
) +
labs(
title = "Lower tail quantile of a T (df = 9)",
subtitle = "Integral of shaded region is 0.975",
y = "Density",
x = "Support"
) +
theme_minimal() +
theme(legend.position = "none")
upper_quantile_plot <- ggplot(data = NULL) +
geom_area(aes(grid, upper_trunc, alpha = 0.2), fill = "steelblue") +
geom_line(aes(grid, density), size = 1, color = "grey") +
geom_vline(xintercept = 1.83, size = 1, color = "darkgrey") +
geom_text(
aes(x = 3.2, y = 0.3, label = "t[0.025] == 1.83"),
parse = TRUE,
size = 4
) +
labs(
title = "Upper tail quantile of a T (df = 9)",
subtitle = "Integral of shaded region is 0.025",
y = "Density",
x = "Support"
) +
theme_minimal() +
theme(legend.position = "none")
cowplot::plot_grid(lower_quantile_plot, upper_quantile_plot)
## -----------------------------------------------------------------------------
t.test(x, conf.level = 0.88)
## -----------------------------------------------------------------------------
t.test(x)
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