Assumption Checking

Before running a parametric test, it is good practice to verify that the data meets the test’s assumptions. HypoTestX provides standalone functions for the most common checks.

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check_normality()

Test whether a sample comes from a normally distributed population using the Shapiro-Wilk test (n ≤ 5000) or Jarque-Bera (n > 5000).

from hypotestx import check_normality

norm = check_normality(data, alpha=0.05)
print(norm.summary())

Interpreting the result

• norm.is_significant == False → fail to reject H₀ (data is consistent with normality) → assumption met

• norm.is_significant == True → reject H₀ → normality assumption violated

if not norm.is_significant:
    print("Normality assumption met — proceed with t-test")
    result = hx.ttest_2samp(group1, group2)
else:
    print("Non-normal data — use Mann-Whitney U instead")
    result = hx.mannwhitney(group1, group2)

Available tests

n	Test used	Description
≤ 5 000	Shapiro-Wilk	Sensitive power test; exact for small n
> 5 000	Jarque-Bera	Tests skewness and excess kurtosis

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check_equal_variances()

Test whether two or more groups have equal variances.

from hypotestx import check_equal_variances

ev = check_equal_variances(group1, group2, method="levene", alpha=0.05)
print(ev.summary())

Parameter	Type	Description
*groups	list[float]	Two or more data groups
method	str	"levene" (default) or "bartlett"
alpha	float	Significance level

Levene vs Bartlett

Test	When to use
Levene	Recommended when normality cannot be assumed; more robust
Bartlett	More powerful when normality holds

Interpreting the result

• ev.is_significant == False → fail to reject H₀ → variances are equal → use Student’s t-test

• ev.is_significant == True → reject H₀ → variances are unequal → use Welch’s t-test

ev = check_equal_variances(group1, group2)

if not ev.is_significant:
    result = hx.ttest_2samp(group1, group2, equal_var=True)   # Student's t
else:
    result = hx.ttest_2samp(group1, group2, equal_var=False)  # Welch's t

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Individual Tests

Shapiro-Wilk

from hypotestx.core.assumptions import shapiro_wilk

result = shapiro_wilk(data, alpha=0.05)
print(result.statistic)   # W statistic
print(result.p_value)

Levene’s Test

from hypotestx.core.assumptions import levene_test

result = levene_test(group1, group2, group3, alpha=0.05)

Bartlett’s Test

from hypotestx.core.assumptions import bartlett_test

result = bartlett_test(group1, group2, alpha=0.05)

Jarque-Bera

from hypotestx.core.assumptions import jarque_bera

result = jarque_bera(data, alpha=0.05)
print(result.statistic)   # χ² statistic
print(result.data_summary["skewness"])
print(result.data_summary["kurtosis"])

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Full Decision Workflow

import hypotestx as hx
from hypotestx import check_normality, check_equal_variances

# Step 1: check normality for each group
n1 = check_normality(group1, alpha=0.05)
n2 = check_normality(group2, alpha=0.05)

both_normal = (not n1.is_significant) and (not n2.is_significant)

if both_normal:
    # Step 2: check equal variances
    ev = check_equal_variances(group1, group2)
    equal = not ev.is_significant
    result = hx.ttest_2samp(group1, group2, equal_var=equal)
    print(f"Used {'Student' if equal else 'Welch'}'s t-test")
else:
    result = hx.mannwhitney(group1, group2)
    print("Used Mann-Whitney U (non-parametric)")

print(result.summary())