Nonparametric Tests

Distribution-free tests with no normality assumptions.

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Group Comparison Tests

Mann-Whitney U Test

Test for stochastic superiority between two groups.

Parameters

Parameter	Type	Required	Default	Description
value	DOUBLE	Yes	-	Measurement values
group_id	INTEGER	Yes	-	Group identifier (0 or 1)
options	MAP	No	-	Configuration options

Options MAP:

Option	Type	Default	Description
alternative	VARCHAR	two_sided	two_sided, less, greater
correction	BOOLEAN	true	Apply continuity correction
confidence_level	DOUBLE	0.95	Confidence level

Output

Field	Type	Description
u_statistic	DOUBLE	U statistic
p_value	DOUBLE	p-value
z_score	DOUBLE	z approximation
effect_size	DOUBLE	Rank-biserial correlation

Example

SELECT anofox_stats_mann_whitney_u_agg(
    value,
    group_id
) as result
FROM data;

Kruskal-Wallis Test

Test whether samples originate from the same distribution across 3+ groups.

Parameters

Parameter	Type	Required	Default	Description
value	DOUBLE	Yes	-	Measurement values
group_id	INTEGER	Yes	-	Group identifier

Output

Field	Type	Description
h_statistic	DOUBLE	H statistic
p_value	DOUBLE	p-value
df	BIGINT	Degrees of freedom
epsilon_squared	DOUBLE	Effect size

Example

SELECT anofox_stats_kruskal_wallis_agg(
    value,
    group_id
) as result
FROM data;

Wilcoxon Signed-Rank Test

Paired samples comparison.

Parameters

Parameter	Type	Required	Default	Description
value1	DOUBLE	Yes	-	First measurement
value2	DOUBLE	Yes	-	Paired measurement
options	MAP	No	-	Configuration options

Example

SELECT anofox_stats_wilcoxon_signed_rank_agg(
    value1,
    value2
) as result
FROM paired_data;

Brunner-Munzel Test

Robust comparison without equal variance assumption.

Parameters

Parameter	Type	Required	Default	Description
value	DOUBLE	Yes	-	Measurement values
group_id	INTEGER	Yes	-	Group identifier
options	MAP	No	-	Configuration options

Example

SELECT anofox_stats_brunner_munzel_agg(
    value,
    group_id
) as result
FROM data;

Permutation t-Test

Exact test using permutation distribution.

Parameters

Parameter	Type	Required	Default	Description
value	DOUBLE	Yes	-	Measurement values
group_id	INTEGER	Yes	-	Group identifier
options	MAP	No	-	n_permutations (default: 10000)

Example

SELECT anofox_stats_permutation_t_test_agg(
    value,
    group_id,
    MAP {'n_permutations': '10000'}
) as result
FROM data;

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Distribution Comparison

Compare entire distributions.

Energy Distance

Parameters

Parameter	Type	Required	Default	Description
value	DOUBLE	Yes	-	Values
group_id	INTEGER	Yes	-	Group identifier

Example

SELECT anofox_stats_energy_distance_agg(
    value,
    group_id
) as result
FROM data;

Maximum Mean Discrepancy (MMD)

Parameters

Parameter	Type	Required	Default	Description
value	DOUBLE	Yes	-	Values
group_id	INTEGER	Yes	-	Group identifier
options	MAP	No	-	Kernel settings

Example

SELECT anofox_stats_mmd_agg(
    value,
    group_id
) as result
FROM data;

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