R Statistical Tests

How it works

A statistical test evaluates data under a null model and its assumptions. A p-value is not the probability that the null hypothesis is true, and a non-significant result is not proof of no effect. This fictional one-sample t-test compares five observed session durations with a reference of ten minutes. It is arithmetic practice, not operational advice.

Run this R example

These examples run locally with R, not PHP, Python or JavaScript. The reviewed baseline is R 4.5.2 on Windows x64/UCRT, using only packages shipped with R. This is a tested version, not a newest-release claim. Install your own R from the official R project; an IDE is optional. Save the complete source as statistical-tests.R in a separate learning folder and run Rscript --vanilla statistical-tests.R. Keep code and fictional fixtures separate from a real project.

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Example

local({
  previous_options <- options(warn = 2, digits = 8, stringsAsFactors = FALSE)
  on.exit(options(previous_options), add = TRUE)
  minutes <- c(9, 10, 11, 12, 13)
  result <- t.test(minutes, mu = 10)
  cat("estimated mean:", unname(result$estimate), "\n")
  cat("t statistic:", sprintf("%.3f", unname(result$statistic)), "\n")
  cat("degrees of freedom:", unname(result$parameter), "\n")
  cat("interval contains reference:", result$conf.int[1] <= 10 && result$conf.int[2] >= 10, "\n")
  invisible(NULL)
})

minutes <- c(9, 10, 11, 12, 13)
result <- t.test(minutes, mu = 10)
cat("estimated mean:", unname(result$estimate), "\n")
cat("t statistic:", sprintf("%.3f", unname(result$statistic)), "\n")
cat("degrees of freedom:", unname(result$parameter), "\n")
cat("interval contains reference:", result$conf.int[1] <= 10 && result$conf.int[2] >= 10, "\n")

Expected result

estimated mean: 11
t statistic: 1.414
degrees of freedom: 4
interval contains reference: TRUE

The interval includes ten for this constructed sample. Interpretation depends on the sampling process, independence and model assumptions, not just the printed test result. Repeatedly testing many outcomes and reporting only a favourable one undermines the intended error-rate interpretation.