### Install pwr from source

Source: https://github.com/heliosdrm/pwr/blob/master/README.md

Installs the package from a local source directory without building PDF documentation.

```R
install.packages("pwr", repos=NULL, type="source")
```

--------------------------------

### Execute pwr.r.test examples

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-correlation-anova.md

Examples demonstrating power calculation, sample size estimation, conventional effect sizes, and one-tailed tests for correlation.

```r
# Calculate power for correlation test
pwr.r.test(n = 50, r = 0.3)

# Calculate required sample size
pwr.r.test(r = 0.4, power = 0.80)

# Use conventional effect size
pwr.r.test(n = 85, r = "medium")

# One-tailed test
pwr.r.test(n = 60, r = 0.35, alternative = "greater")
```

--------------------------------

### Execute pwr.anova.test examples

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-correlation-anova.md

Examples demonstrating power calculation, sample size per group, conventional effect sizes, and group count estimation for ANOVA.

```r
# Calculate power for ANOVA
pwr.anova.test(k = 4, n = 30, f = 0.3)

# Calculate required sample size per group
pwr.anova.test(k = 5, f = 0.25, power = 0.80)

# Use conventional effect size
pwr.anova.test(k = 3, n = 50, f = "medium")

# Calculate number of groups
pwr.anova.test(n = 40, f = 0.2, power = 0.85)
```

--------------------------------

### Install pwr from CRAN

Source: https://github.com/heliosdrm/pwr/blob/master/README.md

Installs the official release of the pwr package from the CRAN repository.

```R
install.packages("pwr", repos="http://cran.r-project.org")
```

--------------------------------

### Chi-Square Power Analysis Usage Examples

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-chisq-regression.md

Examples demonstrating how to calculate power, sample size, and use conventional effect sizes for chi-square tests.

```r
# Calculate power for chi-square test
pwr.chisq.test(w = 0.3, N = 200, df = 4)

# Calculate required sample size
pwr.chisq.test(w = 0.25, df = 2, power = 0.80)

# Use conventional effect size
pwr.chisq.test(w = "medium", N = 300, df = 3)

# Goodness-of-fit test with 5 categories
pwr.chisq.test(w = 0.2, N = 150, df = 4)
```

--------------------------------

### Usage Examples for pwr.f2.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-chisq-regression.md

Various examples demonstrating how to solve for different parameters in multiple regression power analysis.

```r
# Power for testing 3 additional predictors
pwr.f2.test(u = 3, v = 100, f2 = 0.1)

# Required sample size for testing 2 predictors
# If u = 2 and we need v, solve for v when df = n - p - 1
pwr.f2.test(u = 2, f2 = 0.15, power = 0.80)

# Use conventional effect size
pwr.f2.test(u = 1, v = 50, f2 = "small")

# Testing 4 predictors in a model
pwr.f2.test(u = 4, v = 80, power = 0.85)
```

--------------------------------

### Execute pwr.t.test examples

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-t-tests.md

Various usage scenarios for calculating power, sample size, and effect size using pwr.t.test.

```r
# Calculate power given sample size
pwr.t.test(n = 50, d = 0.5, sig.level = 0.05, type = "two.sample")

# Calculate required sample size
pwr.t.test(d = 0.5, power = 0.8, sig.level = 0.05, type = "two.sample")

# Use conventional effect size
pwr.t.test(n = 64, d = "medium", type = "two.sample")

# One-sample t-test
pwr.t.test(n = 30, d = 0.3, type = "one.sample")

# Paired t-test
pwr.t.test(n = 25, d = 0.4, type = "paired")

# One-tailed test
pwr.t.test(n = 60, d = 0.4, alternative = "greater")
```

--------------------------------

### Load pwr package

Source: https://github.com/heliosdrm/pwr/blob/master/README.md

Loads the installed pwr package into the current R session.

```R
library(pwr)
```

--------------------------------

### Execute pwr.t2n.test examples

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-t-tests.md

Usage scenarios for calculating power and sample sizes for two-sample tests with unequal group sizes.

```r
# Calculate power with different sample sizes
pwr.t2n.test(n1 = 30, n2 = 50, d = 0.5, sig.level = 0.05)

# Calculate one group size when other is fixed
pwr.t2n.test(n1 = 40, d = 0.4, power = 0.8)

# Calculate effect size
pwr.t2n.test(n1 = 30, n2 = 50, power = 0.8)
```

--------------------------------

### Calculate power and sample sizes with pwr.2p2n.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-proportions.md

Examples demonstrating how to solve for power, sample size, or effect size by leaving one parameter as NULL.

```r
# Calculate power with unequal sample sizes
pwr.2p2n.test(h = 0.4, n1 = 50, n2 = 75, sig.level = 0.05)

# Calculate one group size
pwr.2p2n.test(h = 0.3, n1 = 100, power = 0.80)

# Calculate effect size
pwr.2p2n.test(n1 = 60, n2 = 80, power = 0.85)
```

--------------------------------

### Visualize Power Analysis Results with ggplot2

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Setup for ggplot2 integration and plotting power analysis results.

```r
install.packages(c("ggplot2", "scales"))
library(ggplot2)
library(scales)

result <- pwr.t.test(n = 50, d = 0.5)
plot(result)  # Will use ggplot2 if available
```

--------------------------------

### Perform power analysis examples

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/types.md

Calculate power for various statistical tests and retrieve Cohen's effect sizes.

```r
# T-test power analysis
t_result <- pwr.t.test(n = 60, d = 0.4, type = "two.sample", alternative = "two.sided")
t_result
# Output includes: n, d, sig.level, power, alternative, note, method

# ANOVA power analysis
anova_result <- pwr.anova.test(k = 5, n = 40, f = 0.25)
anova_result
# Output includes: k, n, f, sig.level, power, note, method

# Cohen's conventional effect size
es_result <- cohen.ES(test = "t", size = "medium")
es_result$effect.size  # Returns 0.5
```

--------------------------------

### Usage Examples for pwr.p.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-proportions.md

Common usage patterns for calculating power, sample size, and performing one-tailed hypothesis tests.

```r
# Calculate power
pwr.p.test(h = 0.5, n = 200)

# Calculate required sample size
pwr.p.test(h = 0.3, power = 0.80)

# One-tailed hypothesis test
pwr.p.test(h = 0.4, n = 150, alternative = "greater")
```

--------------------------------

### pwr.2p.test Usage Examples

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-proportions.md

Various usage scenarios for pwr.2p.test, including calculating power, sample size, and using conventional effect sizes.

```r
# Calculate power with equal sample sizes
pwr.2p.test(h = 0.5, n = 100, sig.level = 0.05)

# Calculate required sample size
pwr.2p.test(h = 0.3, power = 0.8, sig.level = 0.05)

# Use conventional effect size
pwr.2p.test(h = "medium", n = 150, alternative = "two.sided")

# One-tailed test
pwr.2p.test(h = 0.4, power = 0.9, alternative = "greater")
```

--------------------------------

### Trigger uniroot Failure

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/errors.md

Example of a parameter combination that causes a root-finding failure in pwr.t.test.

```r
# Trying to solve for impossible combination
pwr.t.test(n = NULL, d = 2, power = 0.999, sig.level = 0.05)
# If the effect size is too large and power target too high
```

--------------------------------

### Usage Examples for pwr.norm.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-chisq-regression.md

Common usage patterns including calculating power, sample size, using conventional effect sizes, and one-tailed tests.

```r
# Calculate power
pwr.norm.test(d = 0.4, n = 100)

# Calculate required sample size
pwr.norm.test(d = 0.3, power = 0.80)

# Use conventional effect size
pwr.norm.test(d = "medium", n = 150)

# One-tailed test
pwr.norm.test(d = 0.5, power = 0.90, alternative = "greater")
```

--------------------------------

### Optional R Packages

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Lists recommended packages for enhanced visualization and labeling.

```text
ggplot2    - For improved power curve plots (recommended)
scales     - For percentage labeling on plots (with ggplot2)
```

--------------------------------

### Display project file structure

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/INDEX.md

Visual representation of the documentation file organization.

```text
output/
├── INDEX.md (this file)
├── overview.md
├── quick-reference.md
├── configuration.md
├── types.md
├── errors.md
├── api-reference-t-tests.md
├── api-reference-proportions.md
├── api-reference-correlation-anova.md
├── api-reference-chisq-regression.md
├── api-reference-effect-sizes.md
└── api-reference-plotting.md
```

--------------------------------

### Configure proportion test parameters

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Defines parameters for pwr.2p.test, pwr.2p2n.test, and pwr.p.test.

```text
sig.level = 0.05, power = NULL
effect size: h (numeric in [-10, 10] or "small"/"medium"/"large")
alternative: "two.sided" | "less" | "greater"
```

--------------------------------

### List R source files for pwr package

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/00-README.md

Displays the directory structure of the R source code files for the pwr package.

```R
R/
├── pwr.t.test.R
├── pwr.t2n.test.R
├── pwr.2p.test.R
├── pwr.2p2n.test.R
├── pwr.p.test.R
├── pwr.r.test.R
├── pwr.anova.test.R
├── pwr.chisq.test.R
├── pwr.f2.test.R
├── pwr.norm.test.R
├── cohen.ES.R
├── ES.h.R
├── ES.w1.R
├── ES.w2.R
└── plot.power.htest.R
```

--------------------------------

### Package Import Specification

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Defines the package dependencies as specified in the DESCRIPTION file.

```text
Imports: stats, graphics
Suggests: ggplot2, scales, knitr, rmarkdown
```

--------------------------------

### Project Directory Structure

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/overview.md

Visual representation of the pwr package file organization.

```text
pwr/
├── R/
│   ├── pwr.t.test.R           # T-tests
│   ├── pwr.t2n.test.R         # T-tests with unequal n
│   ├── pwr.2p.test.R          # Proportion tests (equal n)
│   ├── pwr.2p2n.test.R        # Proportion tests (unequal n)
│   ├── pwr.p.test.R           # Single proportion tests
│   ├── pwr.r.test.R           # Correlation tests
│   ├── pwr.anova.test.R       # ANOVA
│   ├── pwr.chisq.test.R       # Chi-square tests
│   ├── pwr.f2.test.R          # Multiple regression
│   ├── pwr.norm.test.R        # Normal distribution tests
│   ├── cohen.ES.R             # Conventional effect sizes
│   ├── ES.h.R                 # Effect size for proportions
│   ├── ES.w1.R                # Effect size for goodness-of-fit
│   ├── ES.w2.R                # Effect size for independence
│   └── plot.power.htest.R     # Plotting method
└── man/
    └── (Documentation files)
```

--------------------------------

### Dispatch S3 method

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/types.md

Demonstrate S3 method dispatch for the plot function.

```r
plot(x)
```

--------------------------------

### Configure pwr.f2.test parameters

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Defines parameters for multiple regression power analysis.

```text
sig.level = 0.05, power = NULL
effect size: f2 (numeric ≥ 0 or "small"/"medium"/"large")
u: numeric ≥ 1 (numerator degrees of freedom)
v: numeric ≥ 1 (denominator degrees of freedom)
```

--------------------------------

### Required R Packages

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Lists the mandatory packages for statistical distributions and base plotting.

```text
stats      - For statistical distributions and functions
graphics   - For base plotting capabilities
```

--------------------------------

### Explore Power Analysis Trade-offs in R

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Demonstrates how sample size requirements change based on effect size using pwr.t.test.

```r
# Small effect, need large sample
pwr.t.test(d = 0.2, power = 0.80, type = "two.sample")

# Large effect, need smaller sample
pwr.t.test(d = 0.8, power = 0.80, type = "two.sample")
```

--------------------------------

### Configure pwr.r.test parameters

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Defines parameters for correlation power analysis.

```text
sig.level = 0.05, power = NULL
effect size: r (numeric in [-1+ε, 1-ε] or "small"/"medium"/"large")
alternative: "two.sided" | "less" | "greater"
```

--------------------------------

### Configure pwr.chisq.test parameters

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Defines parameters for Chi-Square power analysis, requiring degrees of freedom.

```text
sig.level = 0.05, power = NULL
effect size: w (numeric ≥ 0 or "small"/"medium"/"large")
df: numeric (degrees of freedom, required)
N: numeric ≥ 1 (total sample size)
```

--------------------------------

### plot.power.htest(x, ...)

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-plotting.md

S3 method for plotting power analysis results from power.htest objects.

```APIDOC
## plot.power.htest(x, ...)

### Description
Generates a power curve showing the relationship between sample size and statistical power for power analysis results. The function automatically detects the test type and renders the plot using either ggplot2 (if available) or base R.

### Signature
`plot.power.htest(x, ...)`

### Parameters
- **x** (power.htest) - Required - An object of class power.htest returned from any of the pwr.*.test functions.
- **...** (optional) - Optional - Additional graphical parameters including: main (plot title), xlab (x-axis label), ylab (y-axis label).

### Return Value
Displays a plot of power vs. sample size, including a line showing power changes, a vertical dashed line for the optimal sample size, and relevant annotations.

### Usage Example
```r
# Plot result from t-test power calculation
result <- pwr.t.test(n = 50, d = 0.5, type = "two.sample")
plot(result)

# Plot with custom title
pwr_result <- pwr.anova.test(k = 4, n = 30, f = 0.3)
plot(pwr_result, main = "ANOVA Power Analysis")
```
```

--------------------------------

### Print power.htest results

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/types.md

Display all fields of a power.htest object using the default print method.

```r
# Default print method displays all fields
result <- pwr.t.test(n = 50, d = 0.5)
print(result)
```

--------------------------------

### Triggering Unsupported Method Errors

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/errors.md

Custom power.htest objects with methods not included in the supported list will fail during plotting.

```r
# If a custom power.htest object with unsupported method is created
obj <- structure(list(method = "Unknown method"), class = "power.htest")
plot(obj)
```

--------------------------------

### Numerical Sample Size Bounds

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Defines the lower and upper bounds for sample size calculations in the numerical solver.

```text
Lower: 2 + 1e-10 (or 4 + 1e-10 for correlation)
Upper: 1e+09
```

--------------------------------

### Catch Errors with tryCatch

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/errors.md

Use tryCatch to gracefully handle errors during power analysis function calls.

```r
# Use tryCatch to handle errors
result <- tryCatch({
    pwr.t.test(n = 50, d = 0.5, power = 0.80, sig.level = 0.05)
}, error = function(e) {
    message("Error in power analysis: ", e$message)
    NULL
})
```

--------------------------------

### Define Statistical Parameters

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Standard significance levels, target power, and alternative hypothesis settings.

```r
sig.level  <- 0.01, 0.05, 0.10    # Significance level (alpha)
power      <- 0.80, 0.90           # Target power (1 - beta)
alternative <- "two.sided" | "less" | "greater"
```

--------------------------------

### Configure pwr.t.test parameters

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Defines parameters for one-sample, two-sample, or paired t-tests.

```text
sig.level = 0.05, power = NULL
effect size: d (numeric in [-10, 10] or "small"/"medium"/"large")
type: "one.sample" | "two.sample" | "paired"
alternative: "two.sided" | "less" | "greater"
```

--------------------------------

### Configure pwr.t2n.test parameters

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Defines parameters for t-tests with unequal sample sizes.

```text
sig.level = 0.05, power = NULL
effect size: d (numeric in [-10, 10] or "small"/"medium"/"large")
alternative: "two.sided" | "less" | "greater"
```

--------------------------------

### Troubleshoot NULL parameter errors in pwr.t.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Ensure exactly one parameter is set to NULL to solve for the desired variable.

```r
# Wrong
pwr.t.test(n = 50, d = 0.5, power = NULL, sig.level = 0.05)

# Correct - one NULL
pwr.t.test(n = 50, d = 0.5, power = NULL, sig.level = 0.05)
```

--------------------------------

### Function Signature for pwr.p.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-proportions.md

The formal definition of the pwr.p.test function in R.

```r
pwr.p.test(h = NULL, n = NULL, sig.level = 0.05, power = NULL,
    alternative = c("two.sided", "less", "greater"))
```

--------------------------------

### Configure pwr.anova.test parameters

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Defines parameters for ANOVA power analysis, requiring group count and per-group sample size.

```text
sig.level = 0.05, power = NULL
effect size: f (numeric ≥ 0 or "small"/"medium"/"large")
k: numeric ≥ 2 (number of groups)
n: numeric ≥ 2 (per-group sample size)
```

--------------------------------

### Solve for sample size using pwr.t.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/INDEX.md

Calculate the required sample size by setting n to NULL while providing other test parameters.

```r
pwr.t.test(n = NULL, d = 0.5, sig.level = 0.05, power = 0.80, type = "two.sample")
# Solves for n (sample size)
```

--------------------------------

### Function Signature for pwr.f2.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-chisq-regression.md

The standard signature for the pwr.f2.test function.

```r
pwr.f2.test(u = NULL, v = NULL, f2 = NULL, sig.level = 0.05, power = NULL)
```

--------------------------------

### Validate Inputs Before Function Calls

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/errors.md

Check parameter constraints and numeric ranges before executing power analysis functions.

```r
# Check that exactly one parameter is NULL
params <- list(n = 50, d = NULL, power = 0.80, sig.level = 0.05)
null_count <- sum(sapply(params, is.null))
if (null_count != 1) {
    stop("Exactly one parameter must be NULL")
}

# Validate numeric ranges
if (!is.numeric(sig.level) || sig.level < 0 || sig.level > 1) {
    stop("sig.level must be numeric in [0, 1]")
}
```

--------------------------------

### Use conventional effect sizes

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/overview.md

Demonstrates using Cohen's conventional effect size categories in power calculations.

```r
# Use "medium" effect size for t-test
pwr.t.test(n = 64, d = "medium", type = "two.sample")

# Equivalent to:
es <- cohen.ES(test = "t", size = "medium")
pwr.t.test(n = 64, d = es$effect.size, type = "two.sample")
```

--------------------------------

### Plot power.htest object

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/types.md

Generate a power curve plot for a power.htest object.

```r
result <- pwr.r.test(n = 50, r = 0.3)
plot(result)
```

--------------------------------

### Define power.htest class

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/types.md

Assign the power.htest class to an object.

```r
class(obj) <- "power.htest"
```

--------------------------------

### plot.power.htest()

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Plots the power curve for a test result.

```APIDOC
## plot.power.htest()

### Description
Generates a power curve plot for a given test result object.

### Parameters
- **x** (object) - The result object from a power test
```

--------------------------------

### Extract and visualize results from pwr.t.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Access individual result components, print the full object, or generate a power curve plot.

```r
result <- pwr.t.test(n = 50, d = 0.5)

# Get specific values
result$n              # 50
result$d              # 0.5
result$power          # Calculated power
result$sig.level      # 0.05
result$method         # Method description

# Print all results
print(result)

# Plot power curve
plot(result)
```

--------------------------------

### Calculate Power or Sample Size in R

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Perform power analysis to find either the power for a given sample size or the required sample size for a target power.

```r
# Find power given n
result <- pwr.t.test(n = 50, d = 0.5, type = "two.sample")
result$power

# Find n given power
result <- pwr.t.test(d = 0.5, power = 0.80, type = "two.sample")
result$n
```

--------------------------------

### Define pwr.2p2n.test signature

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-proportions.md

The function signature for pwr.2p2n.test, which requires exactly one parameter to be NULL to solve for it.

```r
pwr.2p2n.test(h = NULL, n1 = NULL, n2 = NULL, sig.level = 0.05, power = NULL,
    alternative = c("two.sided", "less", "greater"))
```

--------------------------------

### pwr.p.test()

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Performs power analysis for a single proportion.

```APIDOC
## pwr.p.test()

### Description
Calculates power or sample size for a single proportion.

### Parameters
- **n** (numeric) - Sample size
- **h** (numeric) - Effect size
- **alternative** (string) - Alternative hypothesis
```

--------------------------------

### Plotting power analysis results in R

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-plotting.md

Visualizes power vs. sample size for various statistical tests. Supports custom titles and axis labels via standard graphical parameters.

```r
# Plot result from t-test power calculation
result <- pwr.t.test(n = 50, d = 0.5, type = "two.sample")
plot(result)

# Plot with custom title
pwr_result <- pwr.anova.test(k = 4, n = 30, f = 0.3)
plot(pwr_result, main = "ANOVA Power Analysis")

# Plot correlation test result
corr_result <- pwr.r.test(n = 60, r = 0.3)
plot(corr_result, 
     main = "Pearson Correlation Power Analysis",
     xlab = "Sample Size",
     ylab = "Statistical Power")

# Plot proportions test
prop_result <- pwr.2p.test(h = 0.4, n = 100)
plot(prop_result)

# Plot chi-square test
chi_result <- pwr.chisq.test(w = 0.3, N = 200, df = 4)
plot(chi_result)
```

--------------------------------

### Visualize power analysis results

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/overview.md

Generates a plot for the power analysis result object.

```r
# Plot power curve
result <- pwr.anova.test(k = 4, n = 30, f = 0.25)
plot(result)
```

--------------------------------

### pwr.2p.test, pwr.2p2n.test, pwr.p.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Performs power analysis for proportions.

```APIDOC
## pwr.2p.test, pwr.2p2n.test, pwr.p.test

### Parameters
- **sig.level** (numeric) - Default 0.05
- **power** (numeric) - Default NULL
- **h** (numeric or string) - Effect size (numeric in [-10, 10] or "small"/"medium"/"large")
- **alternative** (string) - "two.sided", "less", or "greater"
```

--------------------------------

### pwr.2p2n.test()

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Performs power analysis for proportion differences with unequal sample sizes.

```APIDOC
## pwr.2p2n.test()

### Description
Calculates power or sample size for proportion differences with unequal sample sizes.

### Parameters
- **n1** (numeric) - Sample size 1
- **n2** (numeric) - Sample size 2
- **h** (numeric) - Effect size
- **alternative** (string) - Alternative hypothesis
```

--------------------------------

### pwr.2p2n.test(h, n1, n2, sig.level, power, alternative)

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-proportions.md

Calculates power analysis for differences between two proportions with unequal sample sizes. Exactly one of the parameters must be NULL to be solved for.

```APIDOC
## pwr.2p2n.test

### Description
Performs power analysis for differences between two proportions with unequal sample sizes using arcsine transformation.

### Signature
pwr.2p2n.test(h = NULL, n1 = NULL, n2 = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided", "less", "greater"))

### Parameters
- **h** (numeric, character, or NULL) - Optional - Effect size (Cohen's h). Pass "small", "medium", or "large" for conventional values.
- **n1** (numeric or NULL) - Optional - Sample size for first group. Must be at least 2.
- **n2** (numeric or NULL) - Optional - Sample size for second group. Must be at least 2.
- **sig.level** (numeric) - Optional - Significance level (alpha). Must be in [0, 1]. Default is 0.05.
- **power** (numeric or NULL) - Optional - Statistical power (1 - beta). Must be in [0, 1].
- **alternative** (character) - Optional - Alternative hypothesis: "two.sided", "less", or "greater". Default is "two.sided".

### Return Value
Returns an object of class `power.htest` containing the calculated parameter, effect size, sample sizes, significance level, power, alternative hypothesis, and method details.

### Usage Examples
# Calculate power with unequal sample sizes
pwr.2p2n.test(h = 0.4, n1 = 50, n2 = 75, sig.level = 0.05)

# Calculate one group size
pwr.2p2n.test(h = 0.3, n1 = 100, power = 0.80)

# Calculate effect size
pwr.2p2n.test(n1 = 60, n2 = 80, power = 0.85)
```

--------------------------------

### Retrieve Cohen's Effect Size

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-effect-sizes.md

Retrieves standardized Cohen's effect size benchmarks for various statistical tests.

```r
cohen.ES(test = c("p", "t", "r", "anov", "chisq", "f2"),
          size = c("small", "medium", "large"))
```

```r
# Get conventional effect size for t-test
cohen.ES(test = "t", size = "medium")
# Returns effect.size = 0.5

# Get small effect size for ANOVA
cohen.ES(test = "anov", size = "small")
# Returns effect.size = 0.1

# Get large effect size for correlation
cohen.ES(test = "r", size = "large")
# Returns effect.size = 0.5

# Use in power analysis
library(pwr)
es <- cohen.ES(test = "chisq", size = "medium")
pwr.chisq.test(w = es$effect.size, N = 200, df = 4)
```

--------------------------------

### Validate NULL Parameter Constraint in pwr

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/errors.md

Functions require exactly one parameter to be set to NULL for solving. Providing multiple or zero NULL values triggers an error.

```r
pwr.t.test(n = 50, d = 0.5, power = 0.80, sig.level = 0.05)
# More than one parameter specified
pwr.t.test(n = NULL, d = NULL, power = NULL, sig.level = 0.05)
# All parameters NULL
```

--------------------------------

### Index power.htest fields

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/types.md

Access specific statistical fields within a power.htest object.

```r
# Extract specific fields
result <- pwr.anova.test(k = 4, n = 30, f = 0.25)
result$n        # Sample size per group: 30
result$k        # Number of groups: 4
result$power    # Calculated power
result$method   # "Balanced one-way analysis of variance power calculation"
```

--------------------------------

### ES.w1

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-effect-sizes.md

Calculate effect size w for chi-square goodness-of-fit test.

```APIDOC
## ES.w1(P0, P1)

### Description
Calculate effect size w for chi-square goodness-of-fit test.

### Signature
ES.w1(P0, P1)

### Parameters
- **P0** (numeric vector) - Required - Null hypothesis expected proportions per category. Sum should equal 1.
- **P1** (numeric vector) - Required - Alternative hypothesis proportions per category. Sum should equal 1. Must have same length as P0.

### Return Value
Numeric scalar. The effect size w computed as: w = sqrt(sum((P1 - P0)² / P0))
```

--------------------------------

### Define Sample Size Ranges

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Valid ranges for per-group and total sample sizes.

```r
n       <- 2 to 1e9        # Per-group sample size
n1, n2  <- 2 to 1e9        # Separate group sizes
N       <- 1 to 1e9        # Total sample size
```

--------------------------------

### cohen.ES

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-effect-sizes.md

Retrieve conventional (Cohen's) effect size values for different statistical tests.

```APIDOC
## cohen.ES(test, size)

### Description
Retrieve conventional (Cohen's) effect size values for different statistical tests.

### Signature
cohen.ES(test = c("p", "t", "r", "anov", "chisq", "f2"), size = c("small", "medium", "large"))

### Parameters
- **test** (character) - Required - Type of test: "p" (proportion), "t" (t-test), "r" (correlation), "anov" (ANOVA), "chisq" (chi-square), or "f2" (multiple regression).
- **size** (character) - Required - Effect size magnitude: "small", "medium", or "large".

### Return Value
Returns an object of class `power.htest` containing:
- `test` - type of test
- `size` - size category
- `effect.size` - the corresponding Cohen's conventional effect size value
- `method` - "Conventional effect size from Cohen (1982)"
```

--------------------------------

### Define Effect Size Parameters

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Standard effect size ranges for various statistical tests.

```r
d       <- 0.2 to 0.8      # T-tests, normal tests (or "small", "medium", "large")
h       <- 0.2 to 0.8      # Proportions (or "small", "medium", "large")
r       <- 0.1 to 0.5      # Correlation (or "small", "medium", "large")
f       <- 0.1 to 0.4      # ANOVA (or "small", "medium", "large")
w       <- 0.1 to 0.5      # Chi-square (or "small", "medium", "large")
f2      <- 0.02 to 0.35    # Regression (or "small", "medium", "large")
```

--------------------------------

### Perform Proportion Power Analysis

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Calculate power or sample size for two-proportion tests with equal group sizes.

```r
# Find required n for h=0.4, power=0.80
pwr.2p.test(h = 0.4, power = 0.80)

# Find power for n=100, h=0.3
pwr.2p.test(n = 100, h = 0.3)
```

--------------------------------

### pwr.f2.test(u, v, f2, sig.level, power)

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-chisq-regression.md

Calculates power analysis for multiple regression with linear model F-tests. Exactly one parameter must be NULL to solve for that value.

```APIDOC
## pwr.f2.test

### Description
Performs power analysis for multiple regression using linear model F-tests. It supports calculating one of the parameters (u, v, f2, power, or sig.level) given the others.

### Signature
`pwr.f2.test(u = NULL, v = NULL, f2 = NULL, sig.level = 0.05, power = NULL)`

### Parameters
- **u** (numeric or NULL) - Optional - Numerator degrees of freedom (number of predictors being tested). Must be at least 1.
- **v** (numeric or NULL) - Optional - Denominator degrees of freedom (n - p - 1). Must be at least 1.
- **f2** (numeric, character, or NULL) - Optional - Effect size (Cohen's f²). Can be "small", "medium", or "large".
- **sig.level** (numeric) - Optional - Significance level (alpha). Default is 0.05.
- **power** (numeric or NULL) - Optional - Statistical power (1 - beta).

### Return Value
Returns an object of class `power.htest` containing the calculated parameter, degrees of freedom, effect size, significance level, and power.

### Usage Example
```r
# Power for testing 3 additional predictors
pwr.f2.test(u = 3, v = 100, f2 = 0.1)

# Required sample size for testing 2 predictors
pwr.f2.test(u = 2, f2 = 0.15, power = 0.80)
```
```

--------------------------------

### Perform Correlation Power Analysis

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Calculate power or sample size for correlation tests.

```r
# Find required n for r=0.3, power=0.80
pwr.r.test(r = 0.3, power = 0.80)

# Find power for n=100, r=0.25
pwr.r.test(n = 100, r = 0.25)
```

--------------------------------

### pwr.p.test(h, n, sig.level, power, alternative)

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-proportions.md

Calculates power, sample size, or effect size for a single proportion test. Exactly one parameter must be NULL to be solved for.

```APIDOC
## pwr.p.test

### Description
Performs power analysis for a proportion test against a fixed null hypothesis value. The function solves for the parameter set to NULL based on the provided inputs.

### Signature
pwr.p.test(h = NULL, n = NULL, sig.level = 0.05, power = NULL, alternative = c("two.sided", "less", "greater"))

### Parameters
- **h** (numeric/character) - Optional - Effect size (Cohen's h). Can be "small", "medium", or "large".
- **n** (numeric) - Optional - Sample size. Must be at least 1.
- **sig.level** (numeric) - Optional - Significance level (alpha). Default is 0.05.
- **power** (numeric) - Optional - Statistical power (1 - beta).
- **alternative** (character) - Optional - Alternative hypothesis: "two.sided", "less", or "greater". Default is "two.sided".

### Return Value
Returns an object of class `power.htest` containing:
- **h** (numeric) - Effect size
- **n** (numeric) - Sample size
- **sig.level** (numeric) - Significance level
- **power** (numeric) - Statistical power
- **alternative** (character) - Direction of test
- **method** (character) - "proportion power calculation for binomial distribution (arcsine transformation)"

### Usage Examples
# Calculate power
pwr.p.test(h = 0.5, n = 200)

# Calculate required sample size
pwr.p.test(h = 0.3, power = 0.80)

# One-tailed hypothesis test
pwr.p.test(h = 0.4, n = 150, alternative = "greater")
```

--------------------------------

### Perform Multiple Regression Power Analysis

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Calculate power or sample size for multiple regression models.

```r
# Find required denominator df for u=2, f2=0.15, power=0.80
pwr.f2.test(u = 2, f2 = 0.15, power = 0.80)

# Find power for u=3, v=50, f2=0.1
pwr.f2.test(u = 3, v = 50, f2 = 0.1)
```

--------------------------------

### Perform Chi-square Power Analysis

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Calculate power or sample size for chi-square tests.

```r
# Find required N for w=0.3, df=4, power=0.80
pwr.chisq.test(w = 0.3, df = 4, power = 0.80)

# Find power for N=200, w=0.25, df=2
pwr.chisq.test(N = 200, w = 0.25, df = 2)
```

--------------------------------

### Calculate Effect Size w for Goodness-of-Fit

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-effect-sizes.md

Calculates effect size w for chi-square goodness-of-fit tests by comparing observed and expected proportions.

```r
ES.w1(P0, P1)
```

```r
# Uniform null hypothesis (equal proportions) vs alternative
P0 <- c(0.25, 0.25, 0.25, 0.25)
P1 <- c(0.2, 0.3, 0.25, 0.25)
w <- ES.w1(P0, P1)
pwr.chisq.test(w = w, N = 200, df = 3)

# Three-category example
P0 <- c(0.5, 0.3, 0.2)
P1 <- c(0.4, 0.4, 0.2)
ES.w1(P0, P1)
```

--------------------------------

### ES.w2

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-effect-sizes.md

Calculate effect size w for chi-square test of independence.

```APIDOC
## ES.w2(P)

### Description
Calculate effect size w for chi-square test of independence.

### Signature
ES.w2(P)

### Parameters
- **P** (matrix) - Required - Contingency table with proportions or frequencies. Rows represent one variable, columns represent another.

### Return Value
Numeric scalar. The effect size w computed as: w = sqrt(sum((P - P0)² / P0)) where P0 is the expected frequencies under independence.
```

--------------------------------

### Triggering Effect Size Coercion Errors

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/errors.md

Passing invalid character strings to effect size parameters triggers a match.arg error.

```r
pwr.t.test(n = 50, d = "tiny", type = "two.sample")
pwr.r.test(n = 50, r = "huge")
```

--------------------------------

### Chi-Square Power Analysis Function Signature

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-chisq-regression.md

The function signature for pwr.chisq.test in R.

```r
pwr.chisq.test(w = NULL, N = NULL, df = NULL, sig.level = 0.05, power = NULL)
```

--------------------------------

### Validate Sample Size Requirements

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/errors.md

Different statistical tests have specific minimum sample size requirements for groups or total observations.

```r
pwr.t.test(n = 1, d = 0.5)  # Minimum is implicitly 1 or 2
pwr.t2n.test(n1 = 1, n2 = 50, d = 0.5)  # n1 and n2 must be >= 2
```

```r
pwr.r.test(n = 3, r = 0.3)  # Minimum for correlation is 4
```

```r
pwr.anova.test(k = 1, n = 20, f = 0.25)  # k must be >= 2
pwr.anova.test(k = 4, n = 1, f = 0.25)   # n must be >= 2
```

```r
pwr.2p.test(h = 0.5, n = 0)  # n must be >= 1
```

--------------------------------

### ES.h

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-effect-sizes.md

Calculate effect size h for proportions using arcsine transformation.

```APIDOC
## ES.h(p1, p2)

### Description
Calculate effect size h for proportions using arcsine transformation.

### Signature
ES.h(p1, p2)

### Parameters
- **p1** (numeric) - Required - First proportion. Must be in [0, 1].
- **p2** (numeric) - Required - Second proportion. Must be in [0, 1].

### Return Value
Numeric scalar or vector. The effect size h computed as: h = 2 * arcsin(sqrt(p1)) - 2 * arcsin(sqrt(p2))
```

--------------------------------

### Numerical Effect Size Bounds for Two-Sided Tests

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Specifies the numerical bounds for effect size parameters in two-sided statistical tests.

```text
d, h: c(1e-10, 10)
r: c(1e-10, 1 - 1e-10)
f, w, f2: c(1e-07, 1e+07)
```

--------------------------------

### Numerical Effect Size Bounds for One-Sided Tests (less)

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/configuration.md

Specifies the numerical bounds for effect size parameters in one-sided 'less' tests.

```text
d, h: c(-10, 5)
r: c(-1+1e-10, 1 - 1e-10)
```

--------------------------------

### Perform ANOVA Power Analysis

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Calculate power or sample size for one-way ANOVA.

```r
# Find required n per group for k=4 groups, f=0.25, power=0.80
pwr.anova.test(k = 4, f = 0.25, power = 0.80)

# Find power for k=3, n=30, f=0.2
pwr.anova.test(k = 3, n = 30, f = 0.2)
```

--------------------------------

### Function Signature for pwr.norm.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-chisq-regression.md

The function signature defining parameters for normal distribution power analysis.

```r
pwr.norm.test(d = NULL, n = NULL, sig.level = 0.05, power = NULL,
    alternative = c("two.sided", "less", "greater"))
```

--------------------------------

### Calculate effect sizes

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/overview.md

Computes effect sizes from proportions or contingency tables for use in power tests.

```r
# Calculate effect size from proportions
h <- ES.h(p1 = 0.3, p2 = 0.5)
pwr.2p.test(h = h, n = 100)

# Chi-square effect size from contingency table
P <- matrix(c(0.1, 0.05, 0.05, 0.2), nrow = 2)
w <- ES.w2(P)
pwr.chisq.test(w = w, N = 300, df = 1)
```

--------------------------------

### pwr.2p.test Function Signature

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/api-reference-proportions.md

The function signature for pwr.2p.test, defining the parameters for power analysis.

```r
pwr.2p.test(h = NULL, n = NULL, sig.level = 0.05, power = NULL,
    alternative = c("two.sided", "less", "greater"))
```

--------------------------------

### Use character effect sizes in pwr.t.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/quick-reference.md

Effect sizes can be specified as character strings like 'medium' or their numeric equivalents.

```r
# Both equivalent:
pwr.t.test(n = 64, d = "medium")
pwr.t.test(n = 64, d = 0.5)  # 0.5 is the "medium" value for t-tests
```

--------------------------------

### Calculate power with pwr.t.test

Source: https://github.com/heliosdrm/pwr/blob/master/_autodocs/overview.md

Computes statistical power based on sample size and effect size.

```r
library(pwr)

# Calculate power given sample size and effect size
pwr.t.test(n = 50, d = 0.5, type = "two.sample")
```