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Free Hypothesis Testing Calculator

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Complete hypothesis testing tools: t-test, z-test, chi-square, ANOVA with p-values, effect sizes, and step-by-step interpretations. Free statistical significance calculator for research and education.

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Answer Summary

This free hypothesis testing calculator performs t-tests (one-sample, independent, paired), one-way ANOVA, Chi-Square, and non-parametric alternatives. Enter your data to calculate test statistics, p-values, effect sizes, and confidence intervals — with APA-formatted output ready for academic publication.

Tests: T-Test, ANOVA, Chi-Sq
Output: P-Values & Effect Sizes
Reporting: APA Table Ready
Cost: Free Guest Access; plan options

Author/Reviewer: Prof. Dr. NSB, Professor

[REVIEWED_BY_BIO]

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T-Test Calculator with Effect Size

Comprehensive t-test suite including one-sample, two-sample (independent), and paired t-tests. Calculate t-statistics, p-values, confidence intervals, and Cohen's d effect size with detailed interpretations.

  • One-sample t-test calculator
  • Independent samples t-test
  • Paired samples t-test
  • Welch's t-test for unequal variances
  • Cohen's d effect size calculation

Z-Test Calculator for Large Samples

Z-test calculator for means and proportions with known population parameters. Includes one-sample and two-sample z-tests with confidence intervals and power analysis capabilities.

  • One-sample z-test for means
  • Two-sample z-test comparison
  • Z-test for proportions
  • Two-proportion z-test
  • Critical value calculator

Chi-Square Test of Independence

Chi-square test calculator for categorical data analysis. Test independence in contingency tables, goodness of fit, and homogeneity with Cramér's V effect size and residual analysis.

  • Chi-square test of independence
  • Goodness of fit test
  • Test of homogeneity
  • Cramér's V effect size
  • Standardized residuals

ANOVA Calculator with Post-Hoc Tests

One-way and two-way ANOVA calculator with comprehensive post-hoc testing. Includes Tukey HSD, Bonferroni correction, and effect size measures (eta-squared, omega-squared).

  • One-way ANOVA calculator
  • Two-way ANOVA with interaction
  • Tukey HSD post-hoc tests
  • Bonferroni correction
  • Effect size calculations

Which Statistical Test Should I Use?

Choose the right hypothesis test based on your data type, sample size, and research question:

Continuous Data

Normal Distribution:
• 1 group: One-sample t-test
• 2 groups: Independent t-test
• 3+ groups: One-way ANOVA

Categorical Data

Frequency Counts:
• Independence: Chi-square test
• Goodness of fit: Chi-square
• Small samples: Fisher's exact

Paired/Related Data

Before/After Design:
• Continuous: Paired t-test
• Ordinal: Wilcoxon signed-rank
• Categorical: McNemar's test

Non-Normal Data

Non-Parametric Tests:
• 2 groups: Mann-Whitney U
• 3+ groups: Kruskal-Wallis
• Paired: Wilcoxon signed-rank

Hypothesis Testing: Test Selection Guide

Research Question Data Type Sample Size Recommended Test
Compare mean to known value Continuous, Normal Any size One-sample t-test
Compare two group means Continuous, Normal n ≥ 30 each group Independent samples t-test
Compare before/after Continuous, Normal Any size Paired samples t-test
Compare 3+ group means Continuous, Normal n ≥ 30 per group One-way ANOVA
Test independence Categorical Expected count ≥ 5 Chi-square test
Compare proportions Binary Large samples Two-proportion z-test

How to Report T-Test & ANOVA Results in APA Style

APA 7th Edition Template (Independent T-Test):

"An independent-samples t-test was conducted to compare [Variable] in [Group A] and [Group B]. There was a significant difference in scores for [Group A] (M = [Mean], SD = [SD]) and [Group B] (M = [Mean], SD = [SD]); t([df]) = [t-value], p = [p-value], d = [Cohen's d]."

APA 7th Edition Template (One-Way ANOVA):

"A one-way ANOVA revealed a statistically significant difference in [Variable] between at least two groups (F([df1], [df2]) = [F-value], p = [p-value], η² = [Effect Size])."

Copy and paste these templates into your results section and replace the placeholders with your calculated values.

Frequently Asked Questions

How do I choose between a t-test and ANOVA?
Use a t-test when comparing means between two groups (e.g., treatment vs. control). Use one-way ANOVA when comparing means across three or more groups. ANOVA controls the Type I error rate that would inflate if you ran multiple t-tests. If ANOVA is significant, post-hoc tests (Tukey, Bonferroni) identify which groups differ.
What p-value is considered statistically significant?
The conventional threshold for statistical significance is p < 0.05, meaning there is less than a 5% probability of observing the result by chance alone. For stricter standards (e.g., clinical trials or multiple comparisons), p < 0.01 or p < 0.001 is used. Always report the exact p-value rather than just whether it crossed a threshold.
What is the difference between a one-tailed and two-tailed test?
A two-tailed test detects differences in either direction (Group A > Group B or Group A < Group B). A one-tailed test only tests in one direction and should be chosen before data collection based on a specific directional hypothesis. Two-tailed tests are standard in most research unless a directional hypothesis was pre-registered.

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