One-Sample Statistical Test Tool (Parametric + Nonparametric)

An all-in-one R script for automated one-sample hypothesis testing with assumption checks, optional safe transforms, effect sizes, and APA-style reporting.

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1) Features

• Assumption checks
  • Normality of (x − μ) using Shapiro–Wilk (default) or Anderson–Darling.
• Automatic decision logic
  • One-sample t (raw or transformed scale) if assumptions satisfied.
  • Wilcoxon signed-rank if normality fails and cannot be rescued.
• Safe transformations
  • Log, square root, inverse, Yeo–Johnson (via bestNormalize).
  • Applied with safe shifts/epsilons to avoid invalid values.
  • Transform chosen if it restores normality (p ≥ α).
• Effect sizes
  • Parametric: Cohen’s d (mean difference ÷ SD), Hedges’ g (bias-corrected d), optional 95% CI for g (via MBESS).
  • Nonparametric: r = Z/√n from Wilcoxon statistic.
• Outputs
  • APA-style text (with assumptions + interpretation).
  • Group descriptives (M, SD, Median, n).
  • Tidy tibble with test results & effect sizes.
• Visualization
  • Histograms with normal overlays.
  • Q–Q plots.
  • Transform audit panels (raw vs transforms).

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2) Installation

# R >= 4.1 recommended
required_packages <- c("tidyverse", "broom", "janitor", "ggplot2")
install.packages(setdiff(required_packages, rownames(installed.packages())))

# Optional (extra functionality)
install.packages(c("nortest", "MBESS", "bestNormalize"))

The script includes an install_if_missing() helper to load/install automatically.

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3) Settings (Section 0)

alpha_level   <- 0.05                  # significance threshold
tail_type     <- "two.sided"           # "two.sided", "greater", "less"
metric_label  <- "jump height"         # label for reporting
mu_reference  <- 55                    # reference value (μ)

try_transform <- TRUE                  # attempt transforms if non-normal
allowed_transforms <- c("log","sqrt","inv","yeojohnson")
method_normality   <- "shapiro"        # "shapiro", "ad", or "none"

show_plots             <- TRUE
show_transform_panel   <- TRUE
verbose                <- TRUE
report_cis_effect_size <- FALSE        # 95% CI for g via MBESS
report_transform_normality_table <- TRUE

1. Clone the repository:

   git clone https://github.com/your-username/one-sample-test-tool.git

2. Open the R script (one_sample_test.R) in RStudio or your preferred R environment.
3. Run the script. The first block will automatically install and load all required packages.

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User-Configuration Settings

alpha_level  <- 0.05                 # significance threshold
tail_type    <- "two.sided"          # "two.sided", "greater", "less"
metric_label <- "jump height"        # label used in reporting

try_transform      <- TRUE           # attempt transforms if non-normal
allowed_transforms <- c("log","sqrt","inv")
method_normality   <- "shapiro"      # "shapiro", "ad", or "none"

show_plots                         <- TRUE
verbose                            <- TRUE
report_cis_effect_size             <- FALSE   # CI for g via MBESS if installed
report_transform_normality_table   <- TRUE    # print p-values for raw + transforms
show_transform_panel               <- TRUE    # facet histograms for all transforms

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Dependencies

# The script handles all required packages automatically:
# Required
install.packages(c("tidyverse", "broom", "janitor"))

# Optional (enables Anderson–Darling; CI for Hedges' g)
install.packages(c("nortest", "MBESS"))

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What it produces

• Console output (if verbose=TRUE)
  • Normality p-value and interpretation
  • If transformed: chosen transform + shift/epsilon used
  • APA-style report for t or Wilcoxon
  • Effect sizes
• Plots (if show_plots=TRUE)
  • Raw histogram with density/normal overlay (p_hist_raw)
  • Final-scale histogram (raw or transformed) (p_hist_final)
  • Raw vs Transformed comparison (only if a transform was used) (p_transform_compare)
  • Transform audit panel: raw + each allowed transform (optional) (p_transform_panel)
• Tidy results table (res$tidy)
  • Method, direction, n, mean/SD (on analyzed scale)
  • t(df) & CI (t path) or V (Wilcoxon)
  • Effect sizes (Cohen’s d, Hedges’ g or r)
  • Transform metadata (name, shift, epsilon)

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Example Data Sets - For learning and Testing

Noraml

set.seed(1)
test_data <- tibble(
  subject_id  = 1:40,
  test_metric = rnorm(40, mean = 56, sd = 4)
)
mu_reference <- 55

Transform-rescue

set.seed(2)
test_data <- tibble(
  subject_id  = 1:35,
  test_metric = rgamma(35, shape = 2, scale = 5)  # skewed
)
mu_reference <- 55

Heavy outliers - likely nonparametric - Wilcoxon

set.seed(3)
test_data <- tibble(
  subject_id  = 1:30,
  test_metric = c(rnorm(25, mean = 55, sd = 4), rep(100, 5))
)
mu_reference <- 55

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Output Example

Parametric (Classic, transformed):

A one-sample t-test compared jump height to μ = 55 (α = 0.05). Data were log-transformed to meet normality. M = 4.01, SD = 0.10; t(29) = 2.52, p = .018, 95% CI [3.97, 4.06]. Effect size: Cohen’s d = 0.46; Hedges’ g = 0.45.

Nonparametric (Wilcoxon):

Wilcoxon signed-rank vs μ = 55 (α = 0.05): V = 229, p = .952. Effect size: r = Z/√n.

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Effect Sizes

• Cohen’s d: mean difference in standard deviation units.
• Hedges’ g: small-sample corrected d.
• Both are reported for parametric tests; interpret as:
  • < 0.20 = trivial
  • 0.20–0.49 = small
  • 0.50–0.79 = medium
  • ≥ 0.80 = large

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License

MIT License. Free to use, modify, and share.

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Contributing

Contributions welcome! If you'd like to suggest improvements, fix bugs, feel free to open a pull request or start a discussion.

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Contact

Created and maintained by Troy Wilson with the assistance of OpenAI's ChatGPT to help structure code, explain statistical logic, and improve documentation clarity. For issues or feature requests, please use the GitHub Issues tab.