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Explore the CalcArena Statistics Suite
From classroom-friendly descriptive stats to advanced probability distributions, this section aggregates every statistics calculator in CalcArena. Navigate by sub-category to find the tool you need, whether you are analysing data, solving combinatorics, or running Monte Carlo experiments. The hub now features 44 calculators across descriptive, inferential, probability, and effect-size workflows.
𧎠Descriptive Statistics
Data SummaryDescriptive Statistics Toolkit
Mean, median, quartiles, skewness, and variance for any dataset.
Mean Calculator
Arithmetic mean, sum, count, and trimmed mean preview.
Median Calculator
Median, quartiles, percentile lookup, and sorted preview.
Mode Calculator
Dominant values with frequency tables and multimodal detection.
Range Calculator
Minimum, maximum, range, midrange, and trimmed range insights.
Quartile Calculator
Q1, Q2, Q3 with Tukey or inclusive methods, plus five-number summary.
Percentile Calculator
Inclusive vs exclusive percentiles with interpolation details.
Interquartile Range Calculator
IQR, quartile fences, and outlier counts using Tukey or inclusive quartiles.
Variance Calculator
Sample & population variance, standard deviation, and sum of squares.
Standard Deviation Calculator
Sample & population standard deviation with variance context.
Coefficient of Variation Calculator
Relative variability percentages for sample and population scenarios.
Skewness Calculator
Fisher-Pearson skewness with direction and magnitude interpretation.
Kurtosis Calculator
Excess kurtosis for detecting heavy or light tails.
Weighted Mean Calculator
Pair values and weights to compute weighted averages and contributions.
Geometric Mean Calculator
Log-safe multiplicative averages for growth rates and ratios.
Harmonic Mean Calculator
Rate-based average with reciprocal insights.
Sum & Count Calculator
Quick totals: sum, count, average, min, max, and range.
Outlier Detector
Identify low/high outliers using IQR or z-score rules.
Descriptive Summary Report
Generate narrative summaries with key descriptive statistics.
đ˛ Probability & Combinatorics
FoundationsBasic Probability Calculator
Single event probability, complements, unions, and independence checks.
Bayesâ Theorem & Diagnostic Tests
Compute PPV/NPV from prevalence, sensitivity, and specificity.
Permutations & Arrangements
nPr, repeated characters, and circular permutations.
Combinations & Binomial Coefficients
nCr, stars-and-bars, and lottery odds with large-number support.
Counting Principles & InclusionâExclusion
Product rule and union sizes for two or three overlapping sets.
Probability Experiment Simulators
Monte Carlo coin toss, dice rolls, birthday paradox, and Monty Hall.
đ˛ Probability & Combinatorics
Counting & LogicPrefer a curated tour? Visit the Probability & Combinatorics hub.
Basic Probability Calculator
Complements, unions, intersections, and independence checks for single or paired events.
Bayes' Theorem & Diagnostic Tests
Prevalence, sensitivity, specificity, and posterior probabilities with natural-frequency explanations.
Probability & Counting Toolkit
Guided workflows for unions, complements, and conditional probability scenarios.
Counting Principles & InclusionâExclusion
Product rule, union sizes, and inclusionâexclusion templates for overlapping sets.
Combinations & Lottery Odds
Binomial coefficients, stars-and-bars setups, and hypergeometric probability calculations.
Permutations & Arrangements
Linear, repeated, circular, and constrained permutations with inclusionâexclusion support.
Probability Experiment Simulators
Monte Carlo coin toss, dice rolls, birthday paradox, and Monty Hall scenarios with visual summaries.
đ Probability Distributions
Continuous & Discrete𧪠Inferential Statistics
Samples â DecisionsConfidence Intervals & Margin of Error
Hypothesis Tests
One-sample z-Test
Compute z statistics, p-values, and critical regions when population Ď is known. Includes workflow narration and references.
t-Test Suite
Run one-sample, paired, and independent (pooled/Welch) t-tests with effect sizes, assumptions, and confidence intervals.
Proportion & Variance Tests
One-/two-proportion z-tests, chi-square variance checks, and F variance ratios with assumptions and effect sizes.
Chi-Square Goodness-of-Fit
Compare observed versus expected categorical counts with residual analysis and optional custom expectations.
Nonparametric Tests
MannâWhitney, Wilcoxon signed-rank, KruskalâWallis, and ShapiroâWilk with tie corrections and effect sizes.
EDF Tests (KS & AD)
KolmogorovâSmirnov and AndersonâDarling (one-/two-sample) with Lilliefors correction and diagnostic insights.
Fisher's Exact Test
2x2 exact p-values with mid-p adjustments, odds ratios, effect metrics, and workflow narration for small samples.
Exact Binomial Test
Exact two-/one-sided p-values, mid-p adjustment, and Clopper-Pearson intervals for single proportions.
McNemar Test
Paired nominal comparisons with asymptotic, continuity-corrected, and exact binomial options plus effect sizes.
Cochran Q Test
Analyze matched binary outcomes across multiple treatments with Q statistic, chi-square p-value, and Kendall's W.
ANOVA & Advanced Designs
One-Way ANOVA
Construct ANOVA tables from raw data, report F statistic, eta/omega squared, and diagnostic reminders.
Two-Way ANOVA & Post-hoc
Factorial designs with interaction, Tukey HSD, Dunnett corrections, and diagnostics (coming soon).
Effect Sizes & Practical Significance
Cohen's d
Pooled SD, standardized mean difference, confidence intervals, overlap metrics, and r conversions.
Hedges' g
Small-sample corrected effect size with bias factor, confidence intervals, and qualitative labels.
Glass's Delta
Standardize treatment-control differences using control SD with overlap metrics and r equivalents.
ANOVA Effect Sizes
Compute eta^2, omega^2, and partial eta^2 directly from ANOVA sums of squares.
Rank-Biserial Correlation
Convert Mann-Whitney U into correlation, probability of superiority, and confidence intervals.