Test Dataset for Chi-Square Post-Hoc Analysis
chisqposttest_test_data.RdA comprehensive test dataset specifically designed for testing the chisqposttest function. Contains multiple categorical variables with known associations of different strengths, edge cases, and missing data patterns.
Usage
data("chisqposttest_test_data")Format
A data frame with 300 observations and 14 variables:
- PatientID
Patient identifier (1-300)
- Treatment
Treatment group: "Standard", "Experimental"
- Response
Treatment response: "No Response", "Response" (strongly associated with Treatment)
- Sex
Patient sex: "Male", "Female" (balanced)
- TumorGrade
Tumor grade: "Grade 1", "Grade 2", "Grade 3"
- TumorStage
Tumor stage: "Stage I", "Stage II", "Stage III" (moderately associated with TumorGrade)
- Institution
Hospital: "Hospital A", "Hospital B", "Hospital C", "Hospital D"
- QualityScore
Quality rating: "High", "Low" (weakly associated with Institution)
- RandomVar1
Random variable: "Group A", "Group B", "Group C" (no associations)
- RandomVar2
Random variable: "Type X", "Type Y" (no associations)
- RareCategory
Frequency category: "Common", "Uncommon", "Rare" (unbalanced)
- BinaryOutcome
Binary outcome: "Negative", "Positive" (associated with RareCategory)
- AgeGroup
Age category: "Young", "Middle", "Elderly"
- BiomarkerStatus
Biomarker status: "Negative", "Positive" (moderately associated with AgeGroup)
Details
This dataset contains several types of associations designed to test different aspects of chi-square post-hoc analysis:
Strong Associations:
Treatment -> Response: Clear treatment effect with odds ratio ~5
Moderate Associations:
TumorGrade -> TumorStage: Higher grades associated with advanced stages
AgeGroup -> BiomarkerStatus: Age-related biomarker expression pattern
Weak Associations:
Institution -> QualityScore: Institutional quality differences
RareCategory -> BinaryOutcome: Effect in rare category with small cell counts
No Associations:
RandomVar1 ⊥ RandomVar2: Independent random variables for null hypothesis testing
The dataset includes approximately 5% missing data in Treatment, Sex, and TumorGrade variables to test missing data handling options.
Source
Simulated data created for testing purposes. Associations are based on realistic clinical scenarios but data is artificially generated.
See also
chisqposttest, histopathology
Examples
# Load the dataset
data(chisqposttest_test_data)
# Examine structure
str(chisqposttest_test_data)
#> 'data.frame': 300 obs. of 14 variables:
#> $ PatientID : int 1 2 3 4 5 6 7 8 9 10 ...
#> $ Treatment : Factor w/ 2 levels "Standard","Experimental": 1 1 2 1 1 2 1 2 1 1 ...
#> $ Response : Factor w/ 2 levels "No Response",..: 1 1 1 1 1 2 1 2 1 1 ...
#> $ Sex : Factor w/ 2 levels "Male","Female": 2 2 2 2 1 1 2 2 2 2 ...
#> $ TumorGrade : Factor w/ 3 levels "Grade 1","Grade 2",..: 3 2 1 2 3 3 1 2 NA 3 ...
#> $ TumorStage : Factor w/ 3 levels "Stage I","Stage II",..: 3 3 1 2 2 3 2 2 3 3 ...
#> $ Institution : Factor w/ 4 levels "Hospital A","Hospital B",..: 1 1 3 1 3 4 1 1 3 1 ...
#> $ QualityScore : Factor w/ 2 levels "High","Low": 1 2 2 1 1 1 1 1 2 1 ...
#> $ RandomVar1 : Factor w/ 3 levels "Group A","Group B",..: 2 2 2 2 1 2 1 1 1 2 ...
#> $ RandomVar2 : Factor w/ 2 levels "Type X","Type Y": 1 2 2 1 2 2 1 2 1 1 ...
#> $ RareCategory : Factor w/ 3 levels "Common","Uncommon",..: 2 2 1 1 1 1 2 1 1 1 ...
#> $ BinaryOutcome : Factor w/ 2 levels "Negative","Positive": 1 2 1 1 2 1 2 1 1 1 ...
#> $ AgeGroup : Factor w/ 3 levels "Young","Middle",..: 3 2 1 1 3 2 2 2 1 2 ...
#> $ BiomarkerStatus: Factor w/ 2 levels "Negative","Positive": 2 1 2 1 2 2 2 1 1 1 ...
#> - attr(*, "description")= chr "Test dataset for chisqposttest function with known associations"
#> - attr(*, "associations")=List of 4
#> ..$ strong : chr "Treatment -> Response"
#> ..$ moderate: chr [1:2] "TumorGrade -> TumorStage" "AgeGroup -> BiomarkerStatus"
#> ..$ weak : chr [1:2] "Institution -> QualityScore" "RareCategory -> BinaryOutcome"
#> ..$ none : chr "RandomVar1 ⊥ RandomVar2"
#> - attr(*, "created")= Date[1:1], format: "2025-07-02"
#> - attr(*, "sample_size")= num 300
# Example 1: Strong association (should be highly significant)
chisqposttest(
data = chisqposttest_test_data,
rows = "Treatment",
cols = "Response",
posthoc = "bonferroni"
)
#> Warning: Chi-squared approximation may be incorrect
#> Warning: Chi-squared approximation may be incorrect
#> Warning: Chi-squared approximation may be incorrect
#>
#> CHI-SQUARE POST-HOC TESTS
#>
#> character(0)
#>
#> Chi-Square Test Results
#> ──────────────────────────────────────────────
#> Statistic Value df p-value
#> ──────────────────────────────────────────────
#> Chi-Square 66.63312 2 < .0000001
#> ──────────────────────────────────────────────
#>
#>
#> <div style="padding: 15px; background-color: #f8f9fa; border-left: 4px
#> solid #1976d2; margin: 10px 0;">
#> <h4 style="color: #1976d2; margin-top: 0;">Chi-Square Post-Hoc
#> Analysis Guide
#>
#> Three-Step Comprehensive Analysis:
#>
#>
#>
#> 1.
#> Overall Chi-Square Test:
#> Tests if there's any association between variables
#> <br/>
#> 2.
#> Residuals Analysis:
#> Identifies which specific cells contribute to significance
#> <br/>
#> 3.
#> Pairwise Comparisons:
#> Formal hypothesis testing between group pairs
#>
#>
#>
#> *Recommended approach: Start with residuals analysis for pattern
#> identification, then use pairwise tests for formal hypothesis
#> testing.*
#>
#>
#> <table border='1' style='border-collapse: collapse;'>No
#> ResponseResponseStandard8828Experimental49130NA23
#>
#> <div style='margin: 15px 0;'><div style="padding: 15px;
#> background-color: #e8f5e8; border-left: 4px solid #4caf50; margin:
#> 10px 0;">
#> <h4 style="color: #2e7d32; margin-top: 0;">Standardized Residuals
#> Interpretation
#>
#> What are standardized residuals?
#>
#>
#> Standardized residuals measure how much each cell deviates from what
#> we'd expect if there was no association. They're calculated as
#> (Observed - Expected) / √Expected, then adjusted for multiple
#> comparisons.
#>
#> <div style="background-color: #f1f8e9; padding: 10px; border-radius:
#> 3px;">
#> Interpretation Guidelines:
#> <br/>
#> • |Residual| > 2.0: Suggests meaningful deviation
#> <br/>
#> • |Residual| > 3.0: Strong evidence of deviation
#> <br/>
#> • Positive values: Over-represented (more than expected)
#> <br/>
#> • Negative values: Under-represented (fewer than expected)
#>
#> <table style='border-collapse: collapse; width: 100%; margin: 15px
#> 0;'><tr style='background-color: #e8f5e8;'><th style='border: 1px
#> solid #666; padding: 8px;'><th style='border: 1px solid #666; padding:
#> 8px; text-align: center;'>No Response<th style='border: 1px solid
#> #666; padding: 8px; text-align: center;'>Response<td style='border:
#> 1px solid #666; padding: 8px; font-weight: bold; background-color:
#> #f5f5f5;'>Standard<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #ffebee; color: #c62828;
#> font-weight: bold;'>8.144
#> Over-represented<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #e3f2fd; color: #1565c0;
#> font-weight: bold;'>-8.144
#> Under-represented<td style='border: 1px solid #666; padding: 8px;
#> font-weight: bold; background-color: #f5f5f5;'>Experimental<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;
#> background-color: #e3f2fd; color: #1565c0; font-weight: bold;'>-8.01
#> Under-represented<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #ffebee; color: #c62828;
#> font-weight: bold;'>8.01
#> Over-represented<td style='border: 1px solid #666; padding: 8px;
#> font-weight: bold; background-color: #f5f5f5;'>NA<td style='border:
#> 1px solid #666; padding: 8px; text-align: center; background-color:
#> #f9f9f9;'>-0.286
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>0.286
#> As expected
#>
#> Critical value for significance: ±2.638
#>
#> <div style="padding: 15px; background-color: #fff3e0; border-left: 4px
#> solid #ff9800; margin: 10px 0;">
#> <h4 style="color: #e65100; margin-top: 0;">Multiple Testing Correction
#>
#> Why correction is needed:
#>
#>
#> When performing multiple tests, the probability of finding at least
#> one false positive increases. With
#> 3
#> comparisons, there's a
#> 14.3
#> % chance of a false positive without correction.
#>
#>
#> <div style="background-color: #fce4ec; padding: 10px; border-radius:
#> 3px;">
#> Correction Applied:
#> <br/>
#> • Number of comparisons:
#> 3
#> <br/>
#> • Adjusted significance level: α =
#> 0.0167
#> <br/>
#> • Use adjusted p-values for significance decisions
#>
#>
#> Pairwise Comparison Results
#> ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Comparison Test Method Chi-Square p-value Adj. p-value Effect Size (Phi) Significant
#> ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Standard vs Experimental Chi-square 66.5303419 < .0000001 < .0000001 0.47500000 Yes
#> Standard vs NA Fisher's exact 3.2350414 0.1056590 0.2113181 0.16400000 No
#> Experimental vs NA Fisher's exact 0.3870168 0.6181533 1.0000000 0.04600000 No
#> ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#>
#>
#> <div style='margin: 20px 0;'><h3 style='color: #1976d2;'>Detailed
#> Pairwise Comparison Tables
#>
#> <div style='margin: 20px 0; padding: 15px; border: 1px solid #ddd;
#> border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Standard vs Experimental
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Chi-square test (standard approach)
#> Chi-square = 66.53, p = 3.45e-16, Adjusted p = 1.03e-15
#> Effect size (Phi) = 0.475
#> <span style='color: #d32f2f; font-weight: bold;'>✓ Significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>No Response<th style='border: 1px
#> solid #666; padding: 8px; text-align: center;'>Response<th
#> style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>Total<td style='border: 1px solid #666; padding: 8px;
#> background-color: #e3f2fd; font-weight: bold;'>Standard<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>88
#> (75.9%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>28
#> (24.1%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>116<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight:
#> bold;'>Experimental<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>49
#> (27.4%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>130
#> (72.6%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>179<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>137
#> (46.4%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>158
#> (53.6%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>295<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Standard vs NA
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Fisher's exact test (used due to low expected frequencies)
#> Chi-square = 3.235, p = 0.106, Adjusted p = 0.211
#> Effect size (Phi) = 0.164
#> <span style='color: #666;'>Not significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>No Response<th style='border: 1px
#> solid #666; padding: 8px; text-align: center;'>Response<th
#> style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>Total<td style='border: 1px solid #666; padding: 8px;
#> background-color: #e3f2fd; font-weight: bold;'>Standard<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>88
#> (75.9%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>28
#> (24.1%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>116<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>NA<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>2
#> (40%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>3
#> (60%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>5<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>90
#> (74.4%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>31
#> (25.6%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>121<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Experimental vs NA
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Fisher's exact test (used due to low expected frequencies)
#> Chi-square = 0.387, p = 0.618, Adjusted p = 1
#> Effect size (Phi) = 0.046
#> <span style='color: #666;'>Not significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>No Response<th style='border: 1px
#> solid #666; padding: 8px; text-align: center;'>Response<th
#> style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>Total<td style='border: 1px solid #666; padding: 8px;
#> background-color: #e3f2fd; font-weight: bold;'>Experimental<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>49
#> (27.4%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>130
#> (72.6%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>179<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>NA<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>2
#> (40%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>3
#> (60%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>5<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>51
#> (27.7%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>133
#> (72.3%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>184
# Example 2: Moderate association (should be significant with post-hoc differences)
chisqposttest(
data = chisqposttest_test_data,
rows = "TumorGrade",
cols = "TumorStage",
posthoc = "fdr"
)
#> Warning: Chi-squared approximation may be incorrect
#> Warning: Chi-squared approximation may be incorrect
#> Warning: Chi-squared approximation may be incorrect
#> Warning: Chi-squared approximation may be incorrect
#>
#> CHI-SQUARE POST-HOC TESTS
#>
#> character(0)
#>
#> Chi-Square Test Results
#> ──────────────────────────────────────────────
#> Statistic Value df p-value
#> ──────────────────────────────────────────────
#> Chi-Square 109.4691 6 < .0000001
#> ──────────────────────────────────────────────
#>
#>
#> <div style="padding: 15px; background-color: #f8f9fa; border-left: 4px
#> solid #1976d2; margin: 10px 0;">
#> <h4 style="color: #1976d2; margin-top: 0;">Chi-Square Post-Hoc
#> Analysis Guide
#>
#> Three-Step Comprehensive Analysis:
#>
#>
#>
#> 1.
#> Overall Chi-Square Test:
#> Tests if there's any association between variables
#> <br/>
#> 2.
#> Residuals Analysis:
#> Identifies which specific cells contribute to significance
#> <br/>
#> 3.
#> Pairwise Comparisons:
#> Formal hypothesis testing between group pairs
#>
#>
#>
#> *Recommended approach: Start with residuals analysis for pattern
#> identification, then use pairwise tests for formal hypothesis
#> testing.*
#>
#>
#> <table border='1' style='border-collapse: collapse;'>Stage IStage
#> IIStage IIIGrade 156247Grade 2287122Grade 363249NA032
#>
#> <div style='margin: 15px 0;'><div style="padding: 15px;
#> background-color: #e8f5e8; border-left: 4px solid #4caf50; margin:
#> 10px 0;">
#> <h4 style="color: #2e7d32; margin-top: 0;">Standardized Residuals
#> Interpretation
#>
#> What are standardized residuals?
#>
#>
#> Standardized residuals measure how much each cell deviates from what
#> we'd expect if there was no association. They're calculated as
#> (Observed - Expected) / √Expected, then adjusted for multiple
#> comparisons.
#>
#> <div style="background-color: #f1f8e9; padding: 10px; border-radius:
#> 3px;">
#> Interpretation Guidelines:
#> <br/>
#> • |Residual| > 2.0: Suggests meaningful deviation
#> <br/>
#> • |Residual| > 3.0: Strong evidence of deviation
#> <br/>
#> • Positive values: Over-represented (more than expected)
#> <br/>
#> • Negative values: Under-represented (fewer than expected)
#>
#> <table style='border-collapse: collapse; width: 100%; margin: 15px
#> 0;'><tr style='background-color: #e8f5e8;'><th style='border: 1px
#> solid #666; padding: 8px;'><th style='border: 1px solid #666; padding:
#> 8px; text-align: center;'>Stage I<th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Stage II<th style='border: 1px
#> solid #666; padding: 8px; text-align: center;'>Stage III<td
#> style='border: 1px solid #666; padding: 8px; font-weight: bold;
#> background-color: #f5f5f5;'>Grade 1<td style='border: 1px solid #666;
#> padding: 8px; text-align: center; background-color: #ffebee; color:
#> #c62828; font-weight: bold;'>8.302
#> Over-represented<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #e3f2fd; color: #1565c0;
#> font-weight: bold;'>-3.518
#> Under-represented<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #e3f2fd; color: #1565c0;
#> font-weight: bold;'>-4.661
#> Under-represented<td style='border: 1px solid #666; padding: 8px;
#> font-weight: bold; background-color: #f5f5f5;'>Grade 2<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;
#> background-color: #f9f9f9;'>-2.132
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #ffebee; color: #c62828;
#> font-weight: bold;'>4.41
#> Over-represented<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>-2.732
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> font-weight: bold; background-color: #f5f5f5;'>Grade 3<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;
#> background-color: #e3f2fd; color: #1565c0; font-weight: bold;'>-5.581
#> Under-represented<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>-1.464
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #ffebee; color: #c62828;
#> font-weight: bold;'>7.423
#> Over-represented<td style='border: 1px solid #666; padding: 8px;
#> font-weight: bold; background-color: #f5f5f5;'>NA<td style='border:
#> 1px solid #666; padding: 8px; text-align: center; background-color:
#> #f9f9f9;'>-1.476
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>0.758
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>0.68
#> As expected
#>
#> Critical value for significance: ±2.865
#>
#> <div style="padding: 15px; background-color: #fff3e0; border-left: 4px
#> solid #ff9800; margin: 10px 0;">
#> <h4 style="color: #e65100; margin-top: 0;">Multiple Testing Correction
#>
#> Why correction is needed:
#>
#>
#> When performing multiple tests, the probability of finding at least
#> one false positive increases. With
#> 6
#> comparisons, there's a
#> 26.5
#> % chance of a false positive without correction.
#>
#>
#> <div style="background-color: #fce4ec; padding: 10px; border-radius:
#> 3px;">
#> Correction Applied:
#> <br/>
#> • Number of comparisons:
#> 6
#> <br/>
#> • Adjusted significance level: α =
#> 0.0083
#> <br/>
#> • Use adjusted p-values for significance decisions
#>
#>
#> Pairwise Comparison Results
#> ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Comparison Test Method Chi-Square p-value Adj. p-value Effect Size (Phi) Significant
#> ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Grade 1 vs Grade 2 Chi-square 35.741905 < .0000001 < .0000001 0.4150000 Yes
#> Grade 1 vs Grade 3 Chi-square 72.965438 < .0000001 < .0000001 0.6480000 Yes
#> Grade 1 vs NA Fisher's exact 9.846232 0.0045976 0.0137929 0.3270000 Yes
#> Grade 2 vs Grade 3 Chi-square 34.637706 < .0000001 < .0000001 0.4080000 Yes
#> Grade 2 vs NA Fisher's exact 2.358454 0.2905058 0.4357587 0.1370000 No
#> Grade 3 vs NA Fisher's exact 1.242070 0.5701787 0.5701787 0.1160000 No
#> ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#>
#>
#> <div style='margin: 20px 0;'><h3 style='color: #1976d2;'>Detailed
#> Pairwise Comparison Tables
#>
#> <div style='margin: 20px 0; padding: 15px; border: 1px solid #ddd;
#> border-radius: 5px;'><h4 style='margin-top: 0; color: #1976d2;'>Grade
#> 1 vs Grade 2
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Chi-square test (standard approach)
#> Chi-square = 35.742, p = 1.73e-08, Adjusted p = 5.2e-08
#> Effect size (Phi) = 0.415
#> <span style='color: #d32f2f; font-weight: bold;'>✓ Significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Stage I<th style='border: 1px solid
#> #666; padding: 8px; text-align: center;'>Stage II<th style='border:
#> 1px solid #666; padding: 8px; text-align: center;'>Total<td
#> style='border: 1px solid #666; padding: 8px; background-color:
#> #e3f2fd; font-weight: bold;'>Grade 1<td style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>56
#> (64.4%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>24
#> (27.6%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>87<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>Grade
#> 2<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>28
#> (23.1%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>71
#> (58.7%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>121<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>84
#> (40.4%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>95
#> (45.7%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>208<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Grade 1 vs Grade 3
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Chi-square test (standard approach)
#> Chi-square = 72.965, p = <2e-16, Adjusted p = 8.59e-16
#> Effect size (Phi) = 0.648
#> <span style='color: #d32f2f; font-weight: bold;'>✓ Significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Stage I<th style='border: 1px solid
#> #666; padding: 8px; text-align: center;'>Stage II<th style='border:
#> 1px solid #666; padding: 8px; text-align: center;'>Total<td
#> style='border: 1px solid #666; padding: 8px; background-color:
#> #e3f2fd; font-weight: bold;'>Grade 1<td style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>56
#> (64.4%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>24
#> (27.6%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>87<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>Grade
#> 3<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>6
#> (6.9%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>32
#> (36.8%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>87<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>62
#> (35.6%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>56
#> (32.2%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>174<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Grade 1 vs NA
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Fisher's exact test (used due to low expected frequencies)
#> Chi-square = 9.846, p = 0.0046, Adjusted p = 0.0138
#> Effect size (Phi) = 0.327
#> <span style='color: #d32f2f; font-weight: bold;'>✓ Significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Stage I<th style='border: 1px solid
#> #666; padding: 8px; text-align: center;'>Stage II<th style='border:
#> 1px solid #666; padding: 8px; text-align: center;'>Total<td
#> style='border: 1px solid #666; padding: 8px; background-color:
#> #e3f2fd; font-weight: bold;'>Grade 1<td style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>56
#> (64.4%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>24
#> (27.6%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>87<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>NA<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>0
#> (0%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>3
#> (60%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>5<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>56
#> (60.9%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>27
#> (29.3%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>92<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Grade 2 vs Grade 3
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Chi-square test (standard approach)
#> Chi-square = 34.638, p = 3.01e-08, Adjusted p = 6.02e-08
#> Effect size (Phi) = 0.408
#> <span style='color: #d32f2f; font-weight: bold;'>✓ Significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Stage I<th style='border: 1px solid
#> #666; padding: 8px; text-align: center;'>Stage II<th style='border:
#> 1px solid #666; padding: 8px; text-align: center;'>Total<td
#> style='border: 1px solid #666; padding: 8px; background-color:
#> #e3f2fd; font-weight: bold;'>Grade 2<td style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>28
#> (23.1%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>71
#> (58.7%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>121<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>Grade
#> 3<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>6
#> (6.9%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>32
#> (36.8%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>87<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>34
#> (16.3%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>103
#> (49.5%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>208<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Grade 2 vs NA
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Fisher's exact test (used due to low expected frequencies)
#> Chi-square = 2.358, p = 0.291, Adjusted p = 0.436
#> Effect size (Phi) = 0.137
#> <span style='color: #666;'>Not significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Stage I<th style='border: 1px solid
#> #666; padding: 8px; text-align: center;'>Stage II<th style='border:
#> 1px solid #666; padding: 8px; text-align: center;'>Total<td
#> style='border: 1px solid #666; padding: 8px; background-color:
#> #e3f2fd; font-weight: bold;'>Grade 2<td style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>28
#> (23.1%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>71
#> (58.7%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>121<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>NA<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>0
#> (0%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>3
#> (60%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>5<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>28
#> (22.2%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>74
#> (58.7%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>126<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Grade 3 vs NA
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Fisher's exact test (used due to low expected frequencies)
#> Chi-square = 1.242, p = 0.57, Adjusted p = 0.57
#> Effect size (Phi) = 0.116
#> <span style='color: #666;'>Not significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Stage I<th style='border: 1px solid
#> #666; padding: 8px; text-align: center;'>Stage II<th style='border:
#> 1px solid #666; padding: 8px; text-align: center;'>Total<td
#> style='border: 1px solid #666; padding: 8px; background-color:
#> #e3f2fd; font-weight: bold;'>Grade 3<td style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>6
#> (6.9%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>32
#> (36.8%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>87<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>NA<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>0
#> (0%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>3
#> (60%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>5<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>6
#> (6.5%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>35
#> (38%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>92
# Example 3: No association (should be non-significant)
chisqposttest(
data = chisqposttest_test_data,
rows = "RandomVar1",
cols = "RandomVar2",
posthoc = "bonferroni"
)
#>
#> CHI-SQUARE POST-HOC TESTS
#>
#> character(0)
#>
#> Chi-Square Test Results
#> ─────────────────────────────────────────────
#> Statistic Value df p-value
#> ─────────────────────────────────────────────
#> Chi-Square 6.359561 2 0.0415948
#> ─────────────────────────────────────────────
#>
#>
#> <div style="padding: 15px; background-color: #f8f9fa; border-left: 4px
#> solid #1976d2; margin: 10px 0;">
#> <h4 style="color: #1976d2; margin-top: 0;">Chi-Square Post-Hoc
#> Analysis Guide
#>
#> Three-Step Comprehensive Analysis:
#>
#>
#>
#> 1.
#> Overall Chi-Square Test:
#> Tests if there's any association between variables
#> <br/>
#> 2.
#> Residuals Analysis:
#> Identifies which specific cells contribute to significance
#> <br/>
#> 3.
#> Pairwise Comparisons:
#> Formal hypothesis testing between group pairs
#>
#>
#>
#> *Recommended approach: Start with residuals analysis for pattern
#> identification, then use pairwise tests for formal hypothesis
#> testing.*
#>
#>
#> <table border='1' style='border-collapse: collapse;'>Type XType YGroup
#> A4749Group B5157Group C6135
#>
#> <div style='margin: 15px 0;'><div style="padding: 15px;
#> background-color: #e8f5e8; border-left: 4px solid #4caf50; margin:
#> 10px 0;">
#> <h4 style="color: #2e7d32; margin-top: 0;">Standardized Residuals
#> Interpretation
#>
#> What are standardized residuals?
#>
#>
#> Standardized residuals measure how much each cell deviates from what
#> we'd expect if there was no association. They're calculated as
#> (Observed - Expected) / √Expected, then adjusted for multiple
#> comparisons.
#>
#> <div style="background-color: #f1f8e9; padding: 10px; border-radius:
#> 3px;">
#> Interpretation Guidelines:
#> <br/>
#> • |Residual| > 2.0: Suggests meaningful deviation
#> <br/>
#> • |Residual| > 3.0: Strong evidence of deviation
#> <br/>
#> • Positive values: Over-represented (more than expected)
#> <br/>
#> • Negative values: Under-represented (fewer than expected)
#>
#> <table style='border-collapse: collapse; width: 100%; margin: 15px
#> 0;'><tr style='background-color: #e8f5e8;'><th style='border: 1px
#> solid #666; padding: 8px;'><th style='border: 1px solid #666; padding:
#> 8px; text-align: center;'>Type X<th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Type Y<td style='border: 1px solid
#> #666; padding: 8px; font-weight: bold; background-color:
#> #f5f5f5;'>Group A<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>-0.962
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>0.962
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> font-weight: bold; background-color: #f5f5f5;'>Group B<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;
#> background-color: #f9f9f9;'>-1.504
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>1.504
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> font-weight: bold; background-color: #f5f5f5;'>Group C<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;
#> background-color: #f9f9f9;'>2.51
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>-2.51
#> As expected
#>
#> Critical value for significance: ±2.638
#>
#> <div style="padding: 15px; background-color: #fff3e0; border-left: 4px
#> solid #ff9800; margin: 10px 0;">
#> <h4 style="color: #e65100; margin-top: 0;">Multiple Testing Correction
#>
#> Why correction is needed:
#>
#>
#> When performing multiple tests, the probability of finding at least
#> one false positive increases. With
#> 3
#> comparisons, there's a
#> 14.3
#> % chance of a false positive without correction.
#>
#>
#> <div style="background-color: #fce4ec; padding: 10px; border-radius:
#> 3px;">
#> Correction Applied:
#> <br/>
#> • Number of comparisons:
#> 3
#> <br/>
#> • Adjusted significance level: α =
#> 0.0167
#> <br/>
#> • Use adjusted p-values for significance decisions
#>
#>
#> Pairwise Comparison Results
#> ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Comparison Test Method Chi-Square p-value Adj. p-value Effect Size (Phi) Significant
#> ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Group A vs Group B Chi-square 0.06136889 0.8043453 1.0000000 0.01700000 No
#> Group A vs Group C Chi-square 4.14814815 0.0416801 0.1250403 0.14700000 No
#> Group B vs Group C Chi-square 5.46676048 0.0193815 0.0581446 0.16400000 No
#> ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#>
#>
#> <div style='margin: 20px 0;'><h3 style='color: #1976d2;'>Detailed
#> Pairwise Comparison Tables
#>
#> <div style='margin: 20px 0; padding: 15px; border: 1px solid #ddd;
#> border-radius: 5px;'><h4 style='margin-top: 0; color: #1976d2;'>Group
#> A vs Group B
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Chi-square test (standard approach)
#> Chi-square = 0.061, p = 0.804, Adjusted p = 1
#> Effect size (Phi) = 0.017
#> <span style='color: #666;'>Not significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Type X<th style='border: 1px solid
#> #666; padding: 8px; text-align: center;'>Type Y<th style='border: 1px
#> solid #666; padding: 8px; text-align: center;'>Total<td style='border:
#> 1px solid #666; padding: 8px; background-color: #e3f2fd; font-weight:
#> bold;'>Group A<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>47
#> (49%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>49
#> (51%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>96<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>Group
#> B<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>51
#> (47.2%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>57
#> (52.8%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>108<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>98
#> (48%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>106
#> (52%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>204<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Group A vs Group C
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Chi-square test (standard approach)
#> Chi-square = 4.148, p = 0.0417, Adjusted p = 0.125
#> Effect size (Phi) = 0.147
#> <span style='color: #666;'>Not significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Type X<th style='border: 1px solid
#> #666; padding: 8px; text-align: center;'>Type Y<th style='border: 1px
#> solid #666; padding: 8px; text-align: center;'>Total<td style='border:
#> 1px solid #666; padding: 8px; background-color: #e3f2fd; font-weight:
#> bold;'>Group A<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>47
#> (49%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>49
#> (51%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>96<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>Group
#> C<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>61
#> (63.5%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>35
#> (36.5%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>96<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>108
#> (56.2%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>84
#> (43.8%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>192<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Group B vs Group C
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Chi-square test (standard approach)
#> Chi-square = 5.467, p = 0.0194, Adjusted p = 0.0581
#> Effect size (Phi) = 0.164
#> <span style='color: #666;'>Not significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Type X<th style='border: 1px solid
#> #666; padding: 8px; text-align: center;'>Type Y<th style='border: 1px
#> solid #666; padding: 8px; text-align: center;'>Total<td style='border:
#> 1px solid #666; padding: 8px; background-color: #e3f2fd; font-weight:
#> bold;'>Group B<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>51
#> (47.2%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>57
#> (52.8%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>108<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>Group
#> C<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>61
#> (63.5%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>35
#> (36.5%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>96<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>112
#> (54.9%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>92
#> (45.1%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>204
# Example 4: Edge case with rare categories
chisqposttest(
data = chisqposttest_test_data,
rows = "RareCategory",
cols = "BinaryOutcome",
posthoc = "fdr"
)
#>
#> CHI-SQUARE POST-HOC TESTS
#>
#> character(0)
#>
#> Chi-Square Test Results
#> ─────────────────────────────────────────────
#> Statistic Value df p-value
#> ─────────────────────────────────────────────
#> Chi-Square 24.74713 2 0.0000042
#> ─────────────────────────────────────────────
#>
#>
#> <div style="padding: 15px; background-color: #f8f9fa; border-left: 4px
#> solid #1976d2; margin: 10px 0;">
#> <h4 style="color: #1976d2; margin-top: 0;">Chi-Square Post-Hoc
#> Analysis Guide
#>
#> Three-Step Comprehensive Analysis:
#>
#>
#>
#> 1.
#> Overall Chi-Square Test:
#> Tests if there's any association between variables
#> <br/>
#> 2.
#> Residuals Analysis:
#> Identifies which specific cells contribute to significance
#> <br/>
#> 3.
#> Pairwise Comparisons:
#> Formal hypothesis testing between group pairs
#>
#>
#>
#> *Recommended approach: Start with residuals analysis for pattern
#> identification, then use pairwise tests for formal hypothesis
#> testing.*
#>
#>
#> <table border='1' style='border-collapse:
#> collapse;'>NegativePositiveCommon14456Uncommon5328Rare316
#>
#> <div style='margin: 15px 0;'><div style="padding: 15px;
#> background-color: #e8f5e8; border-left: 4px solid #4caf50; margin:
#> 10px 0;">
#> <h4 style="color: #2e7d32; margin-top: 0;">Standardized Residuals
#> Interpretation
#>
#> What are standardized residuals?
#>
#>
#> Standardized residuals measure how much each cell deviates from what
#> we'd expect if there was no association. They're calculated as
#> (Observed - Expected) / √Expected, then adjusted for multiple
#> comparisons.
#>
#> <div style="background-color: #f1f8e9; padding: 10px; border-radius:
#> 3px;">
#> Interpretation Guidelines:
#> <br/>
#> • |Residual| > 2.0: Suggests meaningful deviation
#> <br/>
#> • |Residual| > 3.0: Strong evidence of deviation
#> <br/>
#> • Positive values: Over-represented (more than expected)
#> <br/>
#> • Negative values: Under-represented (fewer than expected)
#>
#> <table style='border-collapse: collapse; width: 100%; margin: 15px
#> 0;'><tr style='background-color: #e8f5e8;'><th style='border: 1px
#> solid #666; padding: 8px;'><th style='border: 1px solid #666; padding:
#> 8px; text-align: center;'>Negative<th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Positive<td style='border: 1px
#> solid #666; padding: 8px; font-weight: bold; background-color:
#> #f5f5f5;'>Common<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #ffebee; color: #c62828;
#> font-weight: bold;'>2.771
#> Over-represented<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #e3f2fd; color: #1565c0;
#> font-weight: bold;'>-2.771
#> Under-represented<td style='border: 1px solid #666; padding: 8px;
#> font-weight: bold; background-color: #f5f5f5;'>Uncommon<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;
#> background-color: #f9f9f9;'>-0.276
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>0.276
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> font-weight: bold; background-color: #f5f5f5;'>Rare<td style='border:
#> 1px solid #666; padding: 8px; text-align: center; background-color:
#> #e3f2fd; color: #1565c0; font-weight: bold;'>-4.861
#> Under-represented<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #ffebee; color: #c62828;
#> font-weight: bold;'>4.861
#> Over-represented
#>
#> Critical value for significance: ±2.638
#>
#> <div style="padding: 15px; background-color: #fff3e0; border-left: 4px
#> solid #ff9800; margin: 10px 0;">
#> <h4 style="color: #e65100; margin-top: 0;">Multiple Testing Correction
#>
#> Why correction is needed:
#>
#>
#> When performing multiple tests, the probability of finding at least
#> one false positive increases. With
#> 3
#> comparisons, there's a
#> 14.3
#> % chance of a false positive without correction.
#>
#>
#> <div style="background-color: #fce4ec; padding: 10px; border-radius:
#> 3px;">
#> Correction Applied:
#> <br/>
#> • Number of comparisons:
#> 3
#> <br/>
#> • Adjusted significance level: α =
#> 0.0167
#> <br/>
#> • Use adjusted p-values for significance decisions
#>
#>
#> Pairwise Comparison Results
#> ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Comparison Test Method Chi-Square p-value Adj. p-value Effect Size (Phi) Significant
#> ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Common vs Uncommon Chi-square 1.186668 0.2760028 0.2760028 0.06500000 No
#> Common vs Rare Fisher's exact 24.843523 0.0000021 0.0000042 0.33700000 Yes
#> Uncommon vs Rare Fisher's exact 15.392437 0.0001695 0.0001695 0.39200000 Yes
#> ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#>
#>
#> <div style='margin: 20px 0;'><h3 style='color: #1976d2;'>Detailed
#> Pairwise Comparison Tables
#>
#> <div style='margin: 20px 0; padding: 15px; border: 1px solid #ddd;
#> border-radius: 5px;'><h4 style='margin-top: 0; color: #1976d2;'>Common
#> vs Uncommon
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Chi-square test (standard approach)
#> Chi-square = 1.187, p = 0.276, Adjusted p = 0.276
#> Effect size (Phi) = 0.065
#> <span style='color: #666;'>Not significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Negative<th style='border: 1px
#> solid #666; padding: 8px; text-align: center;'>Positive<th
#> style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>Total<td style='border: 1px solid #666; padding: 8px;
#> background-color: #e3f2fd; font-weight: bold;'>Common<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>144
#> (72%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>56
#> (28%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>200<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight:
#> bold;'>Uncommon<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>53
#> (65.4%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>28
#> (34.6%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>81<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>197
#> (70.1%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>84
#> (29.9%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>281<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Common vs Rare
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Fisher's exact test (used due to low expected frequencies)
#> Chi-square = 24.844, p = 2.11e-06, Adjusted p = 4.23e-06
#> Effect size (Phi) = 0.337
#> <span style='color: #d32f2f; font-weight: bold;'>✓ Significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Negative<th style='border: 1px
#> solid #666; padding: 8px; text-align: center;'>Positive<th
#> style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>Total<td style='border: 1px solid #666; padding: 8px;
#> background-color: #e3f2fd; font-weight: bold;'>Common<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>144
#> (72%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>56
#> (28%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>200<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>Rare<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>3
#> (15.8%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>16
#> (84.2%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>19<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>147
#> (67.1%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>72
#> (32.9%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>219<div style='margin: 20px 0; padding: 15px; border: 1px
#> solid #ddd; border-radius: 5px;'><h4 style='margin-top: 0; color:
#> #1976d2;'>Uncommon vs Rare
#>
#> <div style='margin-bottom: 15px; padding: 10px; background-color:
#> #f5f5f5; border-radius: 3px;'>Test Results:
#> Method: Fisher's exact test (used due to low expected frequencies)
#> Chi-square = 15.392, p = 0.00017, Adjusted p = 0.00017
#> Effect size (Phi) = 0.392
#> <span style='color: #d32f2f; font-weight: bold;'>✓ Significant<table
#> style='border-collapse: collapse; width: 100%; margin: 10px 0;'><tr
#> style='background-color: #e3f2fd;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'><th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Negative<th style='border: 1px
#> solid #666; padding: 8px; text-align: center;'>Positive<th
#> style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>Total<td style='border: 1px solid #666; padding: 8px;
#> background-color: #e3f2fd; font-weight: bold;'>Uncommon<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>53
#> (65.4%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>28
#> (34.6%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>81<td style='border: 1px solid #666;
#> padding: 8px; background-color: #e3f2fd; font-weight: bold;'>Rare<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;'>3
#> (15.8%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>16
#> (84.2%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center; font-weight: bold;'>19<tr style='background-color: #f5f5f5;
#> font-weight: bold;'><td style='border: 1px solid #666; padding:
#> 8px;'>Total<td style='border: 1px solid #666; padding: 8px;
#> text-align: center;'>56
#> (56%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>44
#> (44%)<td style='border: 1px solid #666; padding: 8px; text-align:
#> center;'>100
# Example 5: Missing data handling
chisqposttest(
data = chisqposttest_test_data,
rows = "Treatment",
cols = "Sex",
excl = TRUE # Exclude missing values
)
#>
#> CHI-SQUARE POST-HOC TESTS
#>
#> character(0)
#>
#> Chi-Square Test Results
#> ───────────────────────────────────────────────
#> Statistic Value df p-value
#> ───────────────────────────────────────────────
#> Chi-Square 0.02066086 1 0.8857067
#> ───────────────────────────────────────────────
#>
#>
#> <div style="padding: 15px; background-color: #f8f9fa; border-left: 4px
#> solid #1976d2; margin: 10px 0;">
#> <h4 style="color: #1976d2; margin-top: 0;">Chi-Square Post-Hoc
#> Analysis Guide
#>
#> Three-Step Comprehensive Analysis:
#>
#>
#>
#> 1.
#> Overall Chi-Square Test:
#> Tests if there's any association between variables
#> <br/>
#> 2.
#> Residuals Analysis:
#> Identifies which specific cells contribute to significance
#> <br/>
#> 3.
#> Pairwise Comparisons:
#> Formal hypothesis testing between group pairs
#>
#>
#>
#> *Recommended approach: Start with residuals analysis for pattern
#> identification, then use pairwise tests for formal hypothesis
#> testing.*
#>
#>
#> <table border='1' style='border-collapse:
#> collapse;'>MaleFemaleStandard5062Experimental8197
#>
#> <div style='margin: 15px 0;'><div style="padding: 15px;
#> background-color: #e8f5e8; border-left: 4px solid #4caf50; margin:
#> 10px 0;">
#> <h4 style="color: #2e7d32; margin-top: 0;">Standardized Residuals
#> Interpretation
#>
#> What are standardized residuals?
#>
#>
#> Standardized residuals measure how much each cell deviates from what
#> we'd expect if there was no association. They're calculated as
#> (Observed - Expected) / √Expected, then adjusted for multiple
#> comparisons.
#>
#> <div style="background-color: #f1f8e9; padding: 10px; border-radius:
#> 3px;">
#> Interpretation Guidelines:
#> <br/>
#> • |Residual| > 2.0: Suggests meaningful deviation
#> <br/>
#> • |Residual| > 3.0: Strong evidence of deviation
#> <br/>
#> • Positive values: Over-represented (more than expected)
#> <br/>
#> • Negative values: Under-represented (fewer than expected)
#>
#> <table style='border-collapse: collapse; width: 100%; margin: 15px
#> 0;'><tr style='background-color: #e8f5e8;'><th style='border: 1px
#> solid #666; padding: 8px;'><th style='border: 1px solid #666; padding:
#> 8px; text-align: center;'>Male<th style='border: 1px solid #666;
#> padding: 8px; text-align: center;'>Female<td style='border: 1px solid
#> #666; padding: 8px; font-weight: bold; background-color:
#> #f5f5f5;'>Standard<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>-0.144
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>0.144
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> font-weight: bold; background-color: #f5f5f5;'>Experimental<td
#> style='border: 1px solid #666; padding: 8px; text-align: center;
#> background-color: #f9f9f9;'>0.144
#> As expected<td style='border: 1px solid #666; padding: 8px;
#> text-align: center; background-color: #f9f9f9;'>-0.144
#> As expected
#>
#> Critical value for significance: ±2.498
#>
#> <div style='padding: 15px; background-color: #d4edda; border: 1px
#> solid #c3e6cb;'>Note: Overall chi-square test is not significant (p ≥
#> 0.05). Post-hoc pairwise comparisons are not recommended when the
#> overall test is non-significant.
#>
#> Pairwise Comparison Results
#> ────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> Comparison Test Method Chi-Square p-value Adj. p-value Effect Size (Phi) Significant
#> ────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> ────────────────────────────────────────────────────────────────────────────────────────────────────────────
#>
#>
#> character(0)