MathIsimple
Interactive Calculator

Nonparametric Testing Calculator

Perform distribution-free statistical tests including sign tests, rank-based comparisons, goodness-of-fit tests, and independence analysis with step-by-step solutions.

Test Selection
Choose the nonparametric test type for your analysis
Sign Test Configuration
Test median values using sign information only

Or enter summary statistics:

Testing Method

Sign Test: Uses only the sign (positive/negative) of differences or deviations

Test Statistic: N+B(n,0.5)N^+ \sim B(n, 0.5) under H₀

Advantages: Distribution-free, robust to outliers, handles ordinal data

📊 Nonparametric Testing Theory

Understanding the statistical principles behind distribution-free testing

Distribution-Free Advantages

No Distributional Assumptions: Tests work without requiring specific population distributions

Robust to Outliers: Rank-based methods are less sensitive to extreme values

Small Sample Friendly: Effective even with limited data where normality may not hold

Test Selection Guide

Sign Test: Use for median testing when only sign information is reliable

Rank Sum Test: Compare two independent samples when distributions may differ

Goodness-of-Fit: Test if data follows a theoretical distribution

Independence Test: Analyze relationships between categorical variables

Power Considerations

Efficiency: Nonparametric tests typically have 85-95% efficiency compared to parametric tests when assumptions are met

Robustness Trade-off: Lower power but much greater robustness when assumptions are violated

Important Assumptions

Independence: Observations must be independent

Random Sampling: Data should come from random samples

Adequate Sample Size: Some tests require minimum sample sizes for validity

Measurement Scale: Tests require appropriate data types (ordinal, interval, ratio)