Introduction to oneMeanTest

knitr::opts_chunk$set( collapse = TRUE, comment = “#>” )

Overview

The oneMeanTest package provides tools for performing a one-sample t-test for a population mean when the variance is unknown, along with descriptive statistics, assumption checks, bootstrap-based inference, power analysis, and informative plots.

This vignette shows a complete analysis workflow using simulated data that mimics a real application.

Setup

library(oneMeanTest) set.seed(123)

Example data

Suppose we measure a numeric outcome (e.g., exam scores, weights, or waiting times) on $n = 30$ individuals, and we want to test whether the population mean equals a hypothesized value $\mu_0 = 5$.

Here we simulate such a dataset:

x <- rnorm(30, mean = 5, sd = 2) head(x) length(x)

You can replace this simulated data with your own dataset when using the package in practice.

Descriptive statistics

Before running the hypothesis test, we examine the basic descriptive statistics.

ds <- descriptive_stats(x, digits = NULL) ds

The output includes the sample size, mean, median, standard deviation, standard error, variance, range, quartiles, and IQR.

One-sample t-test

We now perform a one-sample t-test of

$$H_0: \mu = 5 \quad \text{vs.} \quad H_a: \mu \neq 5.$$

res <- one_mean_test( x, mu0 = 5, alternative = “two.sided”, alpha = 0.05, conf.level = 0.95, check_assumptions = TRUE )

res

The printed result shows:

• the t statistic and degrees of freedom
  
• the p-value
  
• a confidence interval for the mean
  
• the sample mean
  
• the decision to reject or fail to reject $H_0$
  
• a plain-language interpretation.

Assumption checks

The one-sample t-test assumes that the data are approximately normally distributed (or that the sample size is large enough for the central limit theorem to apply).

The check_assumptions() function, which is called inside one_mean_test() when check_assumptions = TRUE, provides a basic assessment:

assump <- check_assumptions(x, alpha = 0.05, verbose = FALSE) assump

Interpret these results to decide whether the normality assumption is reasonable.

Graphical summaries

The plot() method for oneMeanTest objects provides several useful visualizations.

First, a t-distribution with the observed t statistic and critical values:

plot(res, which = “t”)

Next, a confidence interval plot for the mean:

plot(res, which = “ci”)

If you store the raw data in the result object, you can also draw a histogram, boxplot, and normal Q-Q plot:

attr(res, “data”) <- x

plot(res, which = “hist”) plot(res, which = “box”) plot(res, which = “qq”)

These plots can be used directly as screenshots in your presentation.

Bootstrap-based inference

The bootstrap_ttest() function implements a simple non-parametric bootstrap procedure for the one-sample mean.

boot_res <- bootstrap_ttest( x, mu0 = 5, nboot = 500, conf.level = 0.95, alternative = “two.sided”, seed = 123 )

boot_res

You can compare the bootstrap confidence interval and p-value to the classical t-test results as part of your discussion.

Power analysis

Finally, power_analysis_one_mean() wraps stats::power.t.test() for one-sample t-tests.

For example, to compute the power for detecting a true difference of 1 unit with $n = 30$, $sd = 2$, and $\alpha = 0.05$:

p_res <- power_analysis_one_mean( n = 30, delta = 1, sd = 2, sig.level = 0.05, power = NULL, alternative = “two.sided” )

p_res

To find the required sample size for 80% power:

n_res <- power_analysis_one_mean( n = NULL, delta = 1, sd = 2, sig.level = 0.05, power = 0.8, alternative = “two.sided” )

n_res

Summary

In this vignette, we:

• simulated a numeric dataset;
  
• computed descriptive statistics;
  
• performed a one-sample t-test using one_mean_test();
  
• checked assumptions, created informative plots, and compared bootstrap-based inference;
  
• explored power analysis using power_analysis_one_mean().

You can adapt this workflow to your own data to analyze a single population mean with unknown variance and to create materials for your STAT 181 presentation.