Categorical Tests

Tests for categorical and count data.

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Independence Tests

Chi-Square Test of Independence

Parameters

Parameter	Type	Required	Default	Description
row_var	INTEGER	Yes	-	Row category
col_var	INTEGER	Yes	-	Column category
options	MAP	No	-	yates_correction (default: false)

Output

Field	Type	Description
chi2	DOUBLE	Chi-square statistic
p_value	DOUBLE	p-value
df	BIGINT	Degrees of freedom
cramers_v	DOUBLE	Effect size

Example

SELECT anofox_stats_chisq_test_agg(
    row_var,
    col_var
) as result
FROM contingency_data;

Chi-Square Goodness of Fit

Parameters

Parameter	Type	Required	Default	Description
observed	INTEGER	Yes	-	Observed counts
expected	DOUBLE	Yes	-	Expected counts

Example

SELECT anofox_stats_chisq_gof_agg(
    observed,
    expected
) as result
FROM frequency_data;

G-Test (Log-Likelihood Ratio)

Alternative to chi-square, better for small samples.

Parameters

Parameter	Type	Required	Default	Description
row_var	INTEGER	Yes	-	Row category
col_var	INTEGER	Yes	-	Column category

Example

SELECT anofox_stats_g_test_agg(
    row_var,
    col_var
) as result
FROM data;

Fisher's Exact Test

Exact test for 2x2 tables.

Parameters

Parameter	Type	Required	Default	Description
row_var	INTEGER	Yes	-	Row category
col_var	INTEGER	Yes	-	Column category
options	MAP	No	-	alternative setting

Example

SELECT anofox_stats_fisher_exact_agg(
    row_var,
    col_var
) as result
FROM data;

McNemar's Test

Paired categorical data (before/after).

Parameters

Parameter	Type	Required	Default	Description
var1	INTEGER	Yes	-	Before measurement
var2	INTEGER	Yes	-	After measurement
options	MAP	No	-	Configuration options

Example

SELECT anofox_stats_mcnemar_agg(
    var1,
    var2
) as result
FROM paired_categorical;

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Effect Size Measures

Quantify the magnitude of associations.

Cramér's V

Effect size for chi-square test.

SELECT anofox_stats_cramers_v_agg(row_var, col_var) as v
FROM data;

Interpretation:

V value	Effect Size
0.0 - 0.1	Negligible
0.1 - 0.3	Small
0.3 - 0.5	Medium
> 0.5	Large

Phi Coefficient

Effect size for 2x2 tables.

SELECT anofox_stats_phi_coefficient_agg(row_var, col_var) as phi
FROM data;

Contingency Coefficient

Normalized association measure.

SELECT anofox_stats_contingency_coef_agg(row_var, col_var) as c
FROM data;

Cohen's Kappa

Inter-rater agreement.

Parameters

Parameter	Type	Required	Default	Description
rater1	INTEGER	Yes	-	First rater's classification
rater2	INTEGER	Yes	-	Second rater's classification

Output

Field	Type	Description
kappa	DOUBLE	Cohen's kappa (-1 to 1)
p_value	DOUBLE	p-value
se	DOUBLE	Standard error
ci_lower	DOUBLE	CI lower
ci_upper	DOUBLE	CI upper

Example

SELECT anofox_stats_cohen_kappa_agg(
    rater1,
    rater2
) as result
FROM rating_data;

Interpretation:

Kappa	Agreement
< 0	Less than chance
0.0 - 0.2	Slight
0.2 - 0.4	Fair
0.4 - 0.6	Moderate
0.6 - 0.8	Substantial
0.8 - 1.0	Almost perfect

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Choosing a Test

Scenario	Recommended
2+ categories, large samples	Chi-Square
2x2 table, small samples	Fisher's Exact
Before/after paired data	McNemar's
Prefer likelihood-based	G-Test
Quantify association	Cramér's V
Rater agreement	Cohen's Kappa

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