All Statistical Calculators
Explore our complete library of free online statistical tools. Perform hypothesis testing, compute exact p-values, estimate confidence intervals, determine sample sizes, and analyze probability distributions with step-by-step mathematical solutions.
Z Test Calculator
Perform one-sample, two-sample, and proportion z-tests with step-by-step normal distribution derivations and p-values.
- One-sample & two-sample mean tests
- One-proportion & two-proportion tests
- Z-score & two-tailed p-values
T Test Calculator
Calculate Student’s t-tests, Welch’s unequal variance t-tests, and paired repeated measures t-tests with Cohen’s d effect sizes.
- Independent & paired sample designs
- Welch–Satterthwaite df correction
- Cohen's d standardized effect size
Binomial Test Calculator
Exact one-sample binomial test evaluating binary success counts against a hypothesized probability without approximation.
- Exact binomial distribution p-values
- Clopper-Pearson & Wilson score CIs
- Sign test and coin-toss modeling
Fisher's Exact Test Calculator
Exact test of independence for 2×2 contingency tables using the hypergeometric distribution. Ideal for cell counts < 5.
- Exact two-tailed & one-tailed p-values
- Sample Odds Ratio & Relative Risk with CIs
- Lancaster's mid-p value adjustment
McNemar Test Calculator
Test marginal homogeneity for paired dichotomous data in repeated-measures and matched case-control research designs.
- Exact binomial & Edwards corrected χ²
- Discordant odds ratio & marginal risk difference
- Cohen's g paired effect size metric
ANOVA Calculator
One-way Analysis of Variance testing whether population means differ significantly across 3 or more independent groups.
- Between-group & within-group sum of squares
- F-statistic & exact F-distribution p-value
- Eta-squared (η²) variance explained
Chi-Square Calculator
Perform Chi-Square goodness-of-fit and tests of independence across multi-category frequency tables.
- Observed vs. expected frequency tables
- Pearson χ² test statistic & p-value
- Cramér’s V strength of association
F-Test Calculator
Compare the variances of two independent normal populations to verify homoscedasticity assumptions.
- Variance ratio test statistic
- One-tailed & two-tailed F p-values
- Validates t-test and ANOVA assumptions
P-Value Calculator
Instantly calculate exact one-tailed and two-tailed p-values from Z-scores, t-values, F-statistics, r correlations, and χ² values.
- Supports Z, t, F, χ², and Pearson r
- Interactive probability density curves
- Significance interpretation against α
Critical Value Calculator
Determine exact critical value cutoffs for Z, t, Chi-Square, and F distributions given your significance level α and degrees of freedom.
- One-tailed & two-tailed critical bounds
- Rejection region visual highlighting
- Custom α levels (0.001 to 0.20)
Confidence Interval Calculator
Calculate lower and upper bounds for sample means using Z and Student’s t distributions across standard confidence levels.
- 90%, 95%, 99% confidence levels
- Margin of error decomposition
- Known vs. unknown standard deviation
Effect Size Calculator
Compute Cohen’s d, Hedges’ g bias-corrected metric, Glass’s delta, and eta-squared (η²) from summary statistics or group means.
- Standardized mean differences
- Hedges’ small-sample correction
- Cohen benchmark interpretation (0.2, 0.5, 0.8)
Margin of Error Calculator
Find the margin of error for survey proportions or sample means with optional Finite Population Correction (FPC).
- Survey percentage precision
- Finite population correction adjustment
- Custom confidence level inputs
Sample Size Calculator
Determine the exact sample size needed to achieve a target margin of error, statistical power (1 - β), and significance level.
- Proportion & mean sample sizing
- Statistical power requirements
- Finite population downsizing
Z Score Calculator
Convert any raw data score into its standard normal score (Z) and calculate percentiles, tail areas, and probabilities between limits.
- Instant percentile ranking
- Probability area P(Z < z) & P(Z > z)
- Two-point boundary calculations
Standard Deviation Calculator
Calculate sample standard deviation (s), population standard deviation (σ), variance, sum of squares, and mean absolute deviation.
- Sample (n - 1) & population (N) modes
- Full deviation table step-by-step
- Interactive raw dataset pasting
Sample Mean Calculator
Calculate the arithmetic mean, median, mode, geometric mean, and trimmed average for numerical data arrays.
- Step-by-step summation and division
- Median, mode & range summary
- Comma, space, or newline list parsing
Probability Calculator
Calculate single-event, joint independent, mutually exclusive, conditional (Bayes’ theorem), and binomial event probabilities.
- Single, multiple, and conditional events
- Interactive Venn diagram visualizations
- Odds for, odds against, and percentage formats
Not Sure Which Calculator You Need?
Filter our calculator suite by your primary statistical research objective:
Comprehensive Hypothesis Testing Guide
Quick reference guide to understand when and why to apply each major statistical test:
| Statistical Test | Data Type | Sample Structure | Key Assumption | Test Statistic |
|---|---|---|---|---|
| Z-Test | Continuous or Proportions | 1 or 2 Independent groups | Population σ known, or n ≥ 30 | Z = (x̄ - μ) / (σ/√n) |
| Student's T-Test | Continuous (Scale) | 1, 2 Independent or Paired | Population σ unknown, normal data | t = (x̄ - μ) / (s/√n) |
| Exact Binomial Test | Binary (Dichotomous) | 1 Sample (n trials) | Independent Bernoulli trials | k successes ~ B(n, p₀) |
| Fisher's Exact Test | Categorical (2×2 table) | 2 Independent groups | Small samples (any E < 5) | Hypergeometric PMF |
| McNemar's Test | Binary (2×2 table) | Paired / Repeated Measures | Matched pairs, discordant shifts | χ² = (|b - c| - 1)² / (b + c) |
| One-Way ANOVA | Continuous (Scale) | 3 or more Independent groups | Equal variances & normality | F = MS_between / MS_within |
| Chi-Square Test | Categorical (r × c table) | Independent observations | Expected counts E ≥ 5 | χ² = Σ (O - E)² / E |
Created by William Davis
Last updated: October 14, 2026