Comprehensive normality assessment combining multiple approaches.

Returns a map with:

• Shapiro-Wilk test result
• Skewness and kurtosis
• Overall recommendation

Examples

iex> data = [5.0, 5.1, 4.9, 5.2, 4.8, 5.0, 5.1, 4.9, 5.0, 5.1]
iex> assessment = CrucibleBench.Stats.NormalityTests.assess_normality(data)
iex> is_map(assessment)
true

Quick normality check using skewness and kurtosis thresholds.

Faster than Shapiro-Wilk but less reliable. Use for quick screening.

Examples

iex> data = [5.0, 5.1, 4.9, 5.2, 4.8]
iex> result = CrucibleBench.Stats.NormalityTests.quick_check(data)
iex> is_boolean(result.is_normal)
true

Shapiro-Wilk test for normality.

Most powerful omnibus test for normality. Tests null hypothesis that data comes from a normal distribution.

Returns:

• :statistic - W statistic (0 to 1, closer to 1 indicates more normal)
• :p_value - Probability of observing this data if truly normal
• :is_normal - true if p-value > 0.05
• :interpretation - Human-readable result

Limitations:

• Requires 3 ≤ n ≤ 5000
• Sensitive to ties in small samples

Examples

iex> # Approximately normal data
iex> data = [5.0, 5.2, 4.8, 5.1, 4.9, 5.3, 4.7, 5.0, 5.1, 4.9]
iex> result = CrucibleBench.Stats.NormalityTests.shapiro_wilk(data)
iex> result.statistic > 0.3
true

iex> # Clearly non-normal (uniform-like)
iex> data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
iex> result = CrucibleBench.Stats.NormalityTests.shapiro_wilk(data)
iex> is_float(result.statistic)
true