Advanced Statistical Tests

Advanced statistical tests using functions from the DescTools package. Includes effect size calculations (Cohen's D), goodness-of-fit tests (Hosmer-Lemeshow, Anderson-Darling), agreement tests (Barnard, Breslow-Day), and trend tests (Cochran-Armitage). Essential for clinical research, epidemiological studies, and advanced statistical analysis.

Usage

desctools(
  data,
  effect_size_analysis = FALSE,
  group_var = NULL,
  continuous_var = NULL,
  pooled_sd = TRUE,
  hedges_correction = FALSE,
  effect_ci_level = 0.95,
  goodness_of_fit = FALSE,
  fitted_probs = NULL,
  observed_outcomes = NULL,
  hl_groups = 10,
  normality_var = NULL,
  categorical_tests = FALSE,
  cat_var1 = NULL,
  cat_var2 = NULL,
  stratum_var = NULL,
  ordered_exposure = NULL,
  binary_outcome = NULL,
  multiple_testing = "none",
  show_effect_sizes = TRUE,
  show_goodness_tests = TRUE,
  show_categorical_tests = TRUE,
  show_interpretations = TRUE
)

Arguments

data

The data as a data frame for statistical analysis.

effect_size_analysis

Calculate effect sizes including Cohen's D for comparing group means. Essential for determining practical significance in clinical studies.

group_var

Categorical variable defining groups for effect size comparison. Should have exactly 2 levels for Cohen's D calculation.

continuous_var

Continuous variable for effect size calculation (outcome measure).

pooled_sd

Use pooled standard deviation for Cohen's D calculation. Recommended when group variances are similar.

hedges_correction

Apply Hedges correction for small sample bias in effect size calculation.

effect_ci_level

Confidence level for effect size confidence intervals.

goodness_of_fit

Perform goodness of fit tests including Hosmer-Lemeshow test for logistic regression models and normality tests.

fitted_probs

Fitted probabilities from a logistic regression model for Hosmer-Lemeshow goodness of fit test.

observed_outcomes

Observed binary outcomes (0/1) for Hosmer-Lemeshow test.

hl_groups

Number of groups for Hosmer-Lemeshow test. Usually 10 groups provide good balance between power and stability.

normality_var

Continuous variable for normality testing using Anderson-Darling and other goodness of fit tests.

categorical_tests

Perform advanced tests for categorical data including Barnard's test, Breslow-Day test, and Cochran-Armitage trend test.

cat_var1

First categorical variable for contingency table analysis.

cat_var2

Second categorical variable for contingency table analysis.

stratum_var

Stratification variable for Breslow-Day test of homogeneity of odds ratios across strata.

ordered_exposure

Ordered exposure variable for Cochran-Armitage trend test. Should represent ordered dose or exposure levels.

binary_outcome

Binary outcome variable for Cochran-Armitage trend test.

multiple_testing

Method for correcting p-values when multiple tests are performed. FDR (Benjamini-Hochberg) is recommended for most clinical studies.

show_effect_sizes

Display effect size calculations including Cohen's D with confidence intervals and interpretation.

show_goodness_tests

Display goodness of fit test results including Hosmer-Lemeshow and normality tests.

show_categorical_tests

Display results of advanced categorical data tests.

show_interpretations

Provide clinical interpretations and guidelines for statistical results to aid in medical decision making.

Value

A results object containing:

results$instructions					a html
results$effect_size_results					a html
results$goodness_fit_results					a html
results$categorical_results					a html

Examples

# Load example data
data("histopathology")
data("dca_test_data")
data("BreastCancer")

# Example 1: Effect Size Analysis - Compare age between treatment groups
desctools(
    data = histopathology,
    effect_size_analysis = TRUE,
    group_var = "Group",
    continuous_var = "Age",
    pooled_sd = TRUE,
    hedges_correction = FALSE,
    effect_ci_level = 0.95
)
#> 
#>  ADVANCED STATISTICAL TESTS
#> 
#> character(0)
#> 
#>  <div style='font-family: Arial, sans-serif;'>
#> 
#>  Effect Size Analysis
#> 
#>  Group Summary Statistics
#> 
#>  <table border='1' cellpadding='5' cellspacing='0'
#>  style='border-collapse: collapse;'><tr style='background-color:
#>  #f0f0f0; font-weight:
#>  bold;'>GroupNMeanSDMinMaxControl12049.82514.4152673Treatment12848.96913.2562573
#> 
#>  Effect Size Results
#> 
#>  <table border='1' cellpadding='5' cellspacing='0'
#>  style='border-collapse: collapse;'><tr style='background-color:
#>  #f0f0f0; font-weight: bold;'>MeasureValueLower CIUpper
#>  CIMagnitudeCohen's d0.062-0.1870.311Negligible
#> 
#>  Clinical Interpretation
#> 
#>  <div style='background-color: #f9f9f9; padding: 10px; border-left: 4px
#>  solid #007acc;'>
#> 
#>  Effect Size Interpretation: The effect size is negligible, suggesting
#>  minimal practical difference between groups.
#> 
#>  Cohen's Conventions:
#> 
#>  Small effect: d = 0.2Medium effect: d = 0.5Large effect: d = 0.8

# Example 2: Goodness of Fit - Hosmer-Lemeshow test for model validation
desctools(
    data = dca_test_data,
    goodness_of_fit = TRUE,
    fitted_probs = "basic_model",
    observed_outcomes = "cardiac_event_numeric",
    hl_groups = 10
)
#> 
#>  ADVANCED STATISTICAL TESTS
#> 
#> character(0)
#> 
#>  <div style='font-family: Arial, sans-serif;'>
#> 
#>  Goodness of Fit Tests
#> 
#>  Hosmer-Lemeshow Goodness of Fit Test
#> 
#>  <table border='1' cellpadding='5' cellspacing='0'
#>  style='border-collapse: collapse;'><tr style='background-color:
#>  #f0f0f0; font-weight: bold;'>StatisticValuedfp-valueC
#>  Statistic25.582480.0012
#> 
#>  Interpretation: Poor model fit (p ≤ 0.05). Consider model revision or
#>  additional predictors.

# Example 3: Categorical Analysis - Test for trend across tumor grades
desctools(
    data = histopathology,
    categorical_tests = TRUE,
    ordered_exposure = "Grade",
    binary_outcome = "Death"
)
#> 
#>  ADVANCED STATISTICAL TESTS
#> 
#>  <div style='color: red; font-weight: bold;'>Error in statistical
#>  analysis: unused argument (g = exposure_data)
#> 
#>  Please check your variable selections and data format.
#> 
#> character(0)

# Example 4: Comprehensive Analysis - All three analysis types
desctools(
    data = histopathology,
    effect_size_analysis = TRUE,
    group_var = "Group",
    continuous_var = "Age",
    goodness_of_fit = TRUE,
    normality_var = "MeasurementA",
    categorical_tests = TRUE,
    ordered_exposure = "Grade",
    binary_outcome = "Death",
    multiple_testing = "BH",
    show_interpretations = TRUE
)
#> 
#>  ADVANCED STATISTICAL TESTS
#> 
#>  <div style='color: red; font-weight: bold;'>Error in statistical
#>  analysis: unused argument (g = exposure_data)
#> 
#>  Please check your variable selections and data format.
#> 
#>  <div style='font-family: Arial, sans-serif;'>
#> 
#>  Effect Size Analysis
#> 
#>  Group Summary Statistics
#> 
#>  <table border='1' cellpadding='5' cellspacing='0'
#>  style='border-collapse: collapse;'><tr style='background-color:
#>  #f0f0f0; font-weight:
#>  bold;'>GroupNMeanSDMinMaxControl12049.82514.4152673Treatment12848.96913.2562573
#> 
#>  Effect Size Results
#> 
#>  <table border='1' cellpadding='5' cellspacing='0'
#>  style='border-collapse: collapse;'><tr style='background-color:
#>  #f0f0f0; font-weight: bold;'>MeasureValueLower CIUpper
#>  CIMagnitudeCohen's d0.062-0.1870.311Negligible
#> 
#>  Clinical Interpretation
#> 
#>  <div style='background-color: #f9f9f9; padding: 10px; border-left: 4px
#>  solid #007acc;'>
#> 
#>  Effect Size Interpretation: The effect size is negligible, suggesting
#>  minimal practical difference between groups.
#> 
#>  Cohen's Conventions:
#> 
#>  Small effect: d = 0.2Medium effect: d = 0.5Large effect: d = 0.8
#> 
#>  <div style='font-family: Arial, sans-serif;'>
#> 
#>  Goodness of Fit Tests
#> 
#>  Normality Tests
#> 
#>  <table border='1' cellpadding='5' cellspacing='0'
#>  style='border-collapse: collapse;'><tr style='background-color:
#>  #f0f0f0; font-weight:
#>  bold;'>TestStatisticp-valueConclusionAnderson-DarlingInf0Non-normalJarque-Bera0.74330.6896Normal
#> 
#> character(0)

# Example 5: Clinical Application - Biomarker validation
desctools(
    data = BreastCancer,
    effect_size_analysis = TRUE,
    group_var = "Class",
    continuous_var = "Cl.thickness",
    hedges_correction = TRUE,
    goodness_of_fit = TRUE,
    normality_var = "Cell.size",
    multiple_testing = "BH"
)
#> 
#>  ADVANCED STATISTICAL TESTS
#> 
#> character(0)
#> 
#>  <div style='font-family: Arial, sans-serif;'>
#> 
#>  Effect Size Analysis
#> 
#>  Group Summary Statistics
#> 
#>  <table border='1' cellpadding='5' cellspacing='0'
#>  style='border-collapse: collapse;'><tr style='background-color:
#>  #f0f0f0; font-weight:
#>  bold;'>GroupNMeanSDMinMaxbenign4582.9561.67418malignant2417.1952.429110
#> 
#>  Effect Size Results
#> 
#>  <table border='1' cellpadding='5' cellspacing='0'
#>  style='border-collapse: collapse;'><tr style='background-color:
#>  #f0f0f0; font-weight: bold;'>MeasureValueLower CIUpper
#>  CIMagnitudeHedges' g-2.152-2.345-1.959Large
#> 
#>  Clinical Interpretation
#> 
#>  <div style='background-color: #f9f9f9; padding: 10px; border-left: 4px
#>  solid #007acc;'>
#> 
#>  Effect Size Interpretation: The effect size is large and represents a
#>  substantial clinical difference between groups.
#> 
#>  Cohen's Conventions:
#> 
#>  Small effect: d = 0.2Medium effect: d = 0.5Large effect: d = 0.8
#> 
#>  <div style='font-family: Arial, sans-serif;'>
#> 
#>  Goodness of Fit Tests
#> 
#>  Normality Tests
#> 
#>  <table border='1' cellpadding='5' cellspacing='0'
#>  style='border-collapse: collapse;'><tr style='background-color:
#>  #f0f0f0; font-weight:
#>  bold;'>TestStatisticp-valueConclusionAnderson-DarlingInf0Non-normalJarque-Bera440.45380Non-normal