Perform distribution-free statistical tests including sign tests, rank-based comparisons, goodness-of-fit tests, and independence analysis with step-by-step solutions.
Or enter summary statistics:
Sign Test: Uses only the sign (positive/negative) of differences or deviations
Test Statistic: under H₀
Advantages: Distribution-free, robust to outliers, handles ordinal data
Understanding the statistical principles behind distribution-free testing
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
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
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
• 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)
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Theory & Concepts