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Comprehensive Hypothesis Testing Calculator Suite

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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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

Frequently Asked Questions

When to use t-test vs z-test?
Use t-test when sample size is small (n<30) or population standard deviation is unknown. Use z-test when sample size is large (n≥30) and population standard deviation is known. T-test accounts for additional uncertainty with smaller samples using the t-distribution.
How to interpret p-values in hypothesis testing?
P-values indicate the probability of obtaining results as extreme as observed, assuming the null hypothesis is true. P < 0.05 typically indicates statistical significance, but consider effect size and practical significance. Lower p-values provide stronger evidence against the null hypothesis.
What is the difference between one-tailed and two-tailed tests?
One-tailed tests examine effects in a specific direction (greater than or less than), while two-tailed tests examine effects in either direction (different from). Use one-tailed when you have a specific directional hypothesis, two-tailed for general difference testing. One-tailed tests have more power but require theoretical justification.
When should I use ANOVA instead of multiple t-tests?
Use ANOVA when comparing means across three or more groups to control Type I error rate. Multiple t-tests inflate the probability of false positives (family-wise error rate). ANOVA provides an overall test, followed by post-hoc tests for specific comparisons when the overall test is significant.

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