Hypothesis Tests

January 29, 2026 · View on GitHub

Comprehensive statistical hypothesis testing functions for comparing groups and distributions.

Parametric Tests

t_test_agg

Two-sample t-test comparing means of two groups. Supports both Welch's (default) and Student's t-test.

Signature:

t_test_agg(value DOUBLE, group_id INTEGER, [options MAP]) -> STRUCT

Options:

Key	Type	Default	Description
alternative	VARCHAR	'two_sided'	'two_sided', 'less', 'greater'
confidence_level	DOUBLE	0.95	Confidence level for CI
kind	VARCHAR	'welch'	'welch' (default) or 'student'
mu	DOUBLE	0.0	Hypothesized mean difference

Returns:

STRUCT(
    statistic DOUBLE,     -- t-statistic
    p_value DOUBLE,       -- p-value
    df DOUBLE,            -- Degrees of freedom
    effect_size DOUBLE,   -- Cohen's d
    ci_lower DOUBLE,      -- CI lower bound
    ci_upper DOUBLE,      -- CI upper bound
    n1 BIGINT,            -- Group 1 sample size
    n2 BIGINT,            -- Group 2 sample size
    method VARCHAR        -- "Welch's t-test" or "Student's t-test"
)

Example:

-- Compare treatment vs control (group_id: 0 = control, 1 = treatment)
SELECT (t_test_agg(outcome, treatment_group)).*
FROM experiment;

-- One-sided test (treatment > control)
SELECT t_test_agg(score, group, {'alternative': 'greater'})
FROM test_results;

one_way_anova_agg

One-way Analysis of Variance for comparing means across multiple groups.

Signature:

one_way_anova_agg(value DOUBLE, group_id INTEGER) -> STRUCT

Returns:

STRUCT(
    f_statistic DOUBLE,   -- F-statistic
    p_value DOUBLE,       -- p-value
    df_between BIGINT,    -- Between-groups degrees of freedom
    df_within BIGINT,     -- Within-groups degrees of freedom
    ss_between DOUBLE,    -- Between-groups sum of squares
    ss_within DOUBLE,     -- Within-groups sum of squares
    n_groups BIGINT,      -- Number of groups
    n BIGINT,             -- Total sample size
    method VARCHAR        -- "One-Way ANOVA"
)

Example:

-- Compare means across treatment groups
SELECT (one_way_anova_agg(response, treatment_group)).*
FROM clinical_trial;

yuen_agg

Yuen's trimmed mean test - robust alternative to t-test.

Signature:

yuen_agg(value DOUBLE, group_id INTEGER, [options MAP]) -> STRUCT

Options:

Key	Type	Default	Description
trim	DOUBLE	0.2	Proportion to trim from each tail

brown_forsythe_agg

Brown-Forsythe test for equality of variances.

Signature:

brown_forsythe_agg(value DOUBLE, group_id INTEGER) -> STRUCT

Nonparametric Tests

mann_whitney_u_agg

Mann-Whitney U test (Wilcoxon rank-sum). Non-parametric alternative to t-test.

Signature:

mann_whitney_u_agg(value DOUBLE, group_id INTEGER, [options MAP]) -> STRUCT

Options:

Key	Type	Default	Description
alternative	VARCHAR	'two_sided'	'two_sided', 'less', 'greater'
confidence_level	DOUBLE	0.95	Confidence level for CI
correction	BOOLEAN	true	Apply continuity correction

Returns:

STRUCT(
    statistic DOUBLE,     -- U statistic
    p_value DOUBLE,       -- p-value
    effect_size DOUBLE,   -- Rank-biserial correlation
    ci_lower DOUBLE,      -- CI lower bound
    ci_upper DOUBLE,      -- CI upper bound
    n1 BIGINT,            -- Group 1 sample size
    n2 BIGINT,            -- Group 2 sample size
    method VARCHAR        -- "Mann-Whitney U"
)

kruskal_wallis_agg

Kruskal-Wallis H test. Non-parametric alternative to ANOVA.

Signature:

kruskal_wallis_agg(value DOUBLE, group_id INTEGER) -> STRUCT

wilcoxon_signed_rank_agg

Wilcoxon signed-rank test for paired samples.

Signature:

wilcoxon_signed_rank_agg(x DOUBLE, y DOUBLE, [options MAP]) -> STRUCT

brunner_munzel_agg

Brunner-Munzel test - robust to unequal variances and non-normality.

Signature:

brunner_munzel_agg(value DOUBLE, group_id INTEGER, [options MAP]) -> STRUCT

permutation_t_test_agg

Permutation t-test - exact test without distributional assumptions.

Signature:

permutation_t_test_agg(value DOUBLE, group_id INTEGER, [options MAP]) -> STRUCT

Options:

Key	Type	Default	Description
n_permutations	INTEGER	10000	Number of permutations

Normality Tests

shapiro_wilk_agg

Shapiro-Wilk test for normality.

Signature:

shapiro_wilk_agg(value DOUBLE) -> STRUCT

Returns:

STRUCT(
    statistic DOUBLE,    -- W statistic (closer to 1 = more normal)
    p_value DOUBLE,      -- p-value (low = reject normality)
    n BIGINT,            -- Sample size
    method VARCHAR       -- "Shapiro-Wilk"
)

jarque_bera_agg

Jarque-Bera test for normality based on skewness and kurtosis.

Signature:

jarque_bera_agg(value DOUBLE) -> STRUCT

dagostino_k2_agg

D'Agostino K² test for normality.

Signature:

dagostino_k2_agg(value DOUBLE) -> STRUCT

Equivalence Tests (TOST)

tost_t_test_agg

Two One-Sided Tests (TOST) for equivalence.

Signature:

tost_t_test_agg(value DOUBLE, group_id INTEGER, [options MAP]) -> STRUCT

Options:

Key	Type	Default	Description
equivalence_margin	DOUBLE	0.5	Equivalence margin
confidence_level	DOUBLE	0.95	Confidence level

tost_paired_agg

TOST for paired samples.

tost_correlation_agg

TOST for correlation equivalence.

Distribution Comparison

energy_distance_agg

Energy distance between two distributions.

Signature:

energy_distance_agg(value DOUBLE, group_id INTEGER) -> STRUCT

mmd_agg

Maximum Mean Discrepancy test.

Signature:

mmd_agg(value DOUBLE, group_id INTEGER, [options MAP]) -> STRUCT

Forecast Evaluation

diebold_mariano_agg

Diebold-Mariano test for comparing forecast accuracy.

Signature:

diebold_mariano_agg(actual DOUBLE, forecast1 DOUBLE, forecast2 DOUBLE, [options MAP]) -> STRUCT

clark_west_agg

Clark-West test for nested forecast models.

Signature:

clark_west_agg(actual DOUBLE, forecast1 DOUBLE, forecast2 DOUBLE) -> STRUCT