# 13.1: Sampling Error (Section @ref{samplingerror})

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$

( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\id}{\mathrm{id}}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\kernel}{\mathrm{null}\,}$$

$$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$

$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$

$$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$

$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$

$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vectorC}[1]{\textbf{#1}}$$

$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$

$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$

$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

Here we will repeatedly sample from the NHANES Height variable in order to obtain the sampling distribution of the mean.

sampSize <- 50 # size of sample
nsamps <- 5000 # number of samples we will take

# set up variable to store all of the results
sampMeans <- tibble(meanHeight=rep(NA,nsamps))

# Loop through and repeatedly sample and compute the mean
for (i in 1:nsamps) {
sampMeans$meanHeight[i] <- NHANES_adult %>% sample_n(sampSize) %>% summarize(meanHeight=mean(Height)) %>% pull(meanHeight) } Now let’s plot the sampling distribution. We will also overlay the sampling distribution of the mean predicted on the basis of the population mean and standard deviation, to show that it properly describes the actual sampling distribution. # pipe the sampMeans data frame into ggplot sampMeans %>% ggplot(aes(meanHeight)) + # create histogram using density rather than count geom_histogram( aes(y = ..density..), bins = 50, col = "gray", fill = "gray" ) + # add a vertical line for the population mean geom_vline(xintercept = mean(NHANES_adult$Height),
size=1.5) +
# add a label for the line
annotate(
"text",
x = 169.6,
y = .4,
label = "Population mean",
size=6
) +
# label the x axis
labs(x = "Height (inches)") +
# add normal based on population mean/sd
stat_function(
fun = dnorm, n = sampSize,
args = list(
mean = mean(NHANES_adult$Height), sd = sd(NHANES_adult$Height)/sqrt(sampSize)
),
size = 1.5,
color = "black",
linetype='dotted'
) 

This page titled 13.1: Sampling Error (Section @ref{samplingerror}) is shared under a not declared license and was authored, remixed, and/or curated by Russell A. Poldrack via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.