Unified Output Format

Every test in SciTeX Stats returns a unified result dictionary with consistent keys. This means you can write generic code that works with any test output.

Result Dictionary

{
  "test_method": "Student's t-test (independent)",
  "statistic": -3.210,
  "stat_symbol": "t",
  "alternative": "two-sided",
  "n_x": 30,
  "n_y": 30,
  "pvalue": 0.0022,
  "stars": "**",
  "alpha": 0.05,
  "significant": true,
  "effect_size": -0.829,
  "effect_size_metric": "Cohen's d",
  "effect_size_interpretation": "large",
  "power": 0.884,
  "H0": "μ(x) = μ(y)",
  "formatted": "t = -3.210, p = 0.0022, Cohen's d = -0.829, **"
}

Key Fields

**Table 1.** Unified result dictionary keys. All 23 tests return these fields (with test-specific additions where appropriate).
Key	Type	Description
`test_method`	str	Human-readable test name
`statistic`	float	Test statistic value
`stat_symbol`	str	Symbol for the statistic (t, F, U, W, χ², r, ρ)
`pvalue`	float	p-value
`stars`	str	Significance stars: `*` (p<0.001), `` (p<0.01), `*` (p<0.05), `ns`
`alpha`	float	Significance level (default 0.05)
`significant`	bool	Whether to reject H0
`effect_size`	float	Effect size value
`effect_size_metric`	str	Which metric (Cohen’s d, eta², Cramér’s V, r, ρ, etc.)
`effect_size_interpretation`	str	Magnitude: negligible, small, medium, or large
`power`	float	Statistical power (when calculable)
`H0`	str	Null hypothesis in plain text
`formatted`	str	APA-style formatted string, ready for publication

Null Hypotheses

Every test now includes H0, the null hypothesis in plain language:

**Table 2.** Null hypotheses for all test families.
Test	H0
t-test (independent)	μ(x) = μ(y)
t-test (paired)	μ(before - after) = 0
t-test (1-sample)	μ(sample) = 0
Mann-Whitney U	Distributions of x and y have equal medians
Wilcoxon signed-rank	median(before - after) = 0
Brunner-Munzel	P(x > y) = 0.5
ANOVA	All groups have equal population means
Kruskal-Wallis	All groups have the same population median
Friedman	All conditions have the same distribution
Pearson	No linear correlation between x and y
Spearman	No monotonic correlation between x and y
Kendall	No monotonic association between x and y
Shapiro-Wilk	Data are normally distributed
Chi-squared	Two variables are independent
Fisher’s exact	Two variables are independent (OR = 1)
McNemar	Marginal proportions are equal (no change)

Significance Stars

The stars field follows the standard convention:

Stars	p-value range	Interpretation
`***`	p < 0.001	Highly significant
`**`	p < 0.01	Very significant
`*`	p < 0.05	Significant
`ns`	p >= 0.05	Not significant

Working with Results

import scitex_stats as ss

result = ss.run_test("ttest_ind", data=group1, data2=group2)

# Quick report
print(result["formatted"])

# Programmatic access
if result["significant"]:
    print(f"Reject H0: {result['H0']}")
    print(f"Effect: {result['effect_size_interpretation']}")

# Convert to significance stars
stars = ss.p_to_stars(0.003)  # "**"