Statistical Test Functions

All test functions return a HypoResult object.

Parametric Tests

hypotestx.tests.parametric.one_sample_ttest(data: List[float], mu: float = 0.0, alpha: float = 0.05, alternative: str = 'two-sided') → HypoResult

One-sample t-test implemented from scratch

Parameters:

• data – Sample data

• mu – Hypothesized population mean

• alpha – Significance level

• alternative – “two-sided”, “greater”, or “less”

Returns:

HypoResult object with test results

hypotestx.tests.parametric.two_sample_ttest(group1: List[float], group2: List[float], alpha: float = 0.05, alternative: str = 'two-sided', equal_var: bool = True) → HypoResult

Two-sample t-test (Student’s t-test or Welch’s t-test)

Parameters:

• group1 – First group data

• group2 – Second group data

• alpha – Significance level

• alternative – “two-sided”, “greater”, or “less”

• equal_var – Whether to assume equal variances (Student’s vs Welch’s)

Returns:

HypoResult object with test results

hypotestx.tests.parametric.paired_ttest(before: List[float], after: List[float], alpha: float = 0.05, alternative: str = 'two-sided') → HypoResult

Paired t-test for dependent samples

Parameters:

• before – Before measurements

• after – After measurements

• alpha – Significance level

• alternative – “two-sided”, “greater”, or “less”

Returns:

HypoResult object with test results

hypotestx.tests.parametric.anova_one_way(*groups: List[float], alpha: float = 0.05) → HypoResult

One-way analysis of variance (ANOVA).

Tests whether the population means of three or more independent groups are equal. Assumes normality and homogeneity of variance within groups.

Parameters:

• *groups – Two or more group samples

• alpha – Significance level

Returns:

HypoResult with statistic=F, effect_size=eta-squared

Examples

>>> result = anova_one_way([5, 6, 7], [8, 9, 10], [3, 4, 5])
>>> print(result.summary())

Non-parametric Tests

hypotestx.tests.nonparametric.mann_whitney_u(group1: List[float], group2: List[float], alpha: float = 0.05, alternative: str = 'two-sided') → HypoResult

Mann-Whitney U test for two independent samples.

A non-parametric alternative to the two-sample t-test that tests whether one group tends to have larger values than the other.

Uses a normal approximation (with tie correction) for the p-value.

Parameters:

• group1 – First group sample values

• group2 – Second group sample values

• alpha – Significance level (default 0.05)

• alternative – ‘two-sided’, ‘greater’ (group1 > group2), or ‘less’

Returns:

HypoResult with statistic=U1, effect_size=rank-biserial r

Examples

>>> result = mann_whitney_u([1, 2, 3, 4], [5, 6, 7, 8])
>>> print(result.summary())

hypotestx.tests.nonparametric.wilcoxon_signed_rank(x: List[float], y: List[float] | None = None, mu: float = 0.0, alpha: float = 0.05, alternative: str = 'two-sided') → HypoResult

Wilcoxon signed-rank test.

Tests whether the median of differences (or of a single sample relative to mu) differs from zero. Non-parametric alternative to the one-sample or paired t-test.

Parameters:

• x – Data values (or differences if y is not supplied)

• y – Optional second paired sample; if provided, differences = x - y

• mu – Hypothesised median under H0 (default 0)

• alpha – Significance level

• alternative – ‘two-sided’, ‘greater’, or ‘less’

Returns:

HypoResult with statistic=W+ (sum of positive ranks)

Examples

>>> result = wilcoxon_signed_rank([1, 2, 3, 4, 5], mu=2)
>>> result = wilcoxon_signed_rank(before, after)   # paired

hypotestx.tests.nonparametric.kruskal_wallis(*groups: List[float], alpha: float = 0.05) → HypoResult

Kruskal-Wallis H test for k independent groups.

Non-parametric one-way ANOVA. Tests whether the population medians of all groups are equal. P-value is obtained from the chi-square distribution with k-1 degrees of freedom.

Parameters:

• *groups – Two or more group samples (each a list of floats)

• alpha – Significance level

Returns:

HypoResult with statistic=H, effect_size=eta-squared

Examples

>>> result = kruskal_wallis([1,2,3], [4,5,6], [7,8,9])
>>> print(result.summary())

Categorical Tests

hypotestx.tests.categorical.chi_square_test(observed: List[List[float]] | List[float], expected: List[float] | None = None, alpha: float = 0.05, correction: bool = False) → HypoResult

Chi-square test of independence (2-D table) or goodness-of-fit (1-D).

For a 2-D contingency table the test checks whether row and column variables are independent. For a 1-D array of observed counts it checks whether they follow the specified (or uniform) expected distribution.

Parameters:

• observed – 2-D contingency table or 1-D list of observed counts

• expected – Expected counts for each category (1-D case only). If None, a uniform expected distribution is assumed.

• alpha – Significance level

• correction – Apply Yates’ continuity correction (2×2 tables only)

Returns:

HypoResult with statistic=chi2, effect_size=Cramer’s V (or phi for 2×2)

Examples

>>> # 2-D contingency table
>>> table = [[30, 10], [20, 40]]
>>> result = chi_square_test(table)

>>> # Goodness-of-fit
>>> result = chi_square_test([50, 30, 20], expected=[40, 30, 30])

hypotestx.tests.categorical.fisher_exact_test(table: List[List[float]], alpha: float = 0.05, alternative: str = 'two-sided') → HypoResult

Fisher’s Exact Test for a 2×2 contingency table.

Computes the exact p-value using the hypergeometric distribution. Preferred over the chi-square test when any expected cell count is < 5.

Parameters:

• table – 2×2 contingency table [[a, b], [c, d]]

• alpha – Significance level

• alternative – ‘two-sided’, ‘greater’ (more association than expected), or ‘less’

Returns:

HypoResult with statistic=odds_ratio

Examples

>>> table = [[8, 2], [1, 5]]
>>> result = fisher_exact_test(table)
>>> print(result.p_value)

Correlation Tests

hypotestx.tests.correlation.pearson_correlation(x: List[float], y: List[float], alpha: float = 0.05, alternative: str = 'two-sided') → HypoResult

Pearson product-moment correlation coefficient and test.

Tests whether the linear relationship between x and y is significantly different from zero. Assumes both variables are approximately continuous and bivariate normal.

Parameters:

• x – First variable

• y – Second variable (same length as x)

• alpha – Significance level

• alternative – ‘two-sided’, ‘greater’ (positive correlation), or ‘less’

Returns:

HypoResult with statistic=t, effect_size=r (Pearson r)

Examples

>>> result = pearson_correlation([1,2,3,4,5], [2,4,5,4,5])
>>> print(f"r = {result.effect_size:.3f}, p = {result.p_value:.4f}")

hypotestx.tests.correlation.spearman_correlation(x: List[float], y: List[float], alpha: float = 0.05, alternative: str = 'two-sided') → HypoResult

Spearman rank-order correlation coefficient and test.

A non-parametric measure of monotonic association. Computed by ranking both variables and calculating their Pearson correlation.

Parameters:

• x – First variable

• y – Second variable (same length as x)

• alpha – Significance level

• alternative – ‘two-sided’, ‘greater’, or ‘less’

Returns:

HypoResult with statistic=t, effect_size=rho (Spearman rho)

Examples

>>> result = spearman_correlation([3,1,4,1,5], [9,2,6,5,3])
>>> print(f"rho = {result.effect_size:.3f}")

hypotestx.tests.correlation.point_biserial_correlation(continuous: List[float], binary: List, alpha: float = 0.05, alternative: str = 'two-sided') → HypoResult

Point-biserial correlation between a continuous and a dichotomous variable.

Equivalent to Pearson correlation when one variable is binary (0/1 coded). Tests whether the mean of the continuous variable differs across the two groups.

Parameters:

• continuous – Continuous-scale measurements

• binary – Binary group indicator (must contain exactly 2 unique values)

• alpha – Significance level

• alternative – ‘two-sided’, ‘greater’, or ‘less’

Returns:

HypoResult with statistic=t, effect_size=r_pb

Examples

>>> result = point_biserial_correlation(
...     [5.5, 6.1, 7.2, 4.8, 5.9],
...     [0, 1, 1, 0, 0]
... )

Public Aliases

The following short-form names are exposed at the top-level hypotestx namespace for convenience:

hx.ttest_1samp      # one_sample_ttest
hx.ttest_2samp      # two_sample_ttest
hx.welch_ttest      # two_sample_ttest with equal_var=False
hx.ttest_paired     # paired_ttest
hx.anova_1way       # anova_one_way
hx.mannwhitney      # mann_whitney_u
hx.wilcoxon         # wilcoxon_signed_rank
hx.kruskal          # kruskal_wallis
hx.chi2_test        # chi_square_test
hx.fisher_exact     # fisher_exact_test
hx.pearson          # pearson_correlation
hx.spearman         # spearman_correlation
hx.pointbiserial    # point_biserial_correlation