Statistics
Significance and A/B testing, power and sample size, confidence intervals, effect sizes, and a chooser that routes you to the right test.
Statistics is where most quantitative work goes right or quietly wrong, so this section is built to be the deepest of the seven. It covers the everyday decisions: whether a difference is real, how large a sample you actually need, how wide your interval should be, and which test fits your data in the first place. The machinery behind those calls now runs end to end here: distribution tools that turn a raw value into a z-score, a tail probability, or a critical cutoff; the workhorse tests themselves, from the t-test to chi-square to one-way ANOVA; and regression with its correlation coefficient for when two variables move together. Paste a dataset into descriptive statistics to see it summarized, or start from a single question and let the test chooser narrow it down.
Use the causal DAG builder to state an exposure and outcome, inspect backdoor paths, and see which variables to adjust for and which to leave alone.
Meta-analysis takes over where a single study ends, pooling published effects under a fixed-effect or random-effects model and reporting how far the studies disagree. The bootstrap resamples your own data and compares percentile, basic, t with bootstrap standard error, and BCa intervals, while the central limit theorem simulator draws repeated samples from ten populations and prints exact theory beside every simulated value. For many variables at once, principal component analysis reports eigenvalues, explained variance, loadings, scores, a scree plot with parallel analysis, and a labeled biplot.
Every instrument names the test it runs and states its assumptions, so the number you report is one you can defend and show the work behind.
Test chooser
Start with the shape of your data
Pick the closest case. The chooser routes common designs to published calculators only, so every recommendation is a working page.
Compare the two observed groups
This route fits two independent groups with observed counts, conversion rates, or numeric means.
Compare observed conversion rates or two independent means.
Experiment Planning and A/B Testing
Analyze observed experiments, plan sample size, and connect effects to uncertainty.
A/B Test Calculator
Compare two conversion rates or two means with a named frequentist test, effect size, and confidence interval.
Power and Sample Size Calculator
Plan sample size, power, or effect size for two proportions or two independent means.
Minimum Detectable Effect Calculator
Estimate the smallest conversion-rate lift an A/B test plan can reliably detect.
Bayesian A/B Test Calculator
Compare two conversion variants with posterior probability under a visible beta prior.
t-Test Calculator: One-Sample, Two-Sample, Welch, and Paired
Run one-sample, two-sample (Student or Welch), and paired t-tests from raw data or summary stats. Returns the t statistic, df, exact p-value, confidence interval, and Cohen's d.
Fisher's Exact Test
Run an exact fixed-margin 2 by 2 count test with odds ratio, p-value, and support table.
Chi-Square Test Calculator: Independence and Goodness of Fit
Chi-square test of independence or goodness of fit on any size table, with the expected-count table, each cell's contribution, degrees of freedom, the p-value, and Cramér's V.
Mann-Whitney U Test Calculator
Compare two independent samples with ranks, exact or asymptotic p-values, and effect sizes.
Two-Way ANOVA Calculator: Full Table, F, and p-Value
Run a two-way or one-way ANOVA in your browser: sums of squares, df, mean squares, F, and p for every effect, with the balanced-design and interaction conventions stated on the page.
P-value in Excel
Use Excel T.TEST for a two-tailed unequal-variance t-test and compare a worked example to the canonical A/B test logic.
Intervals and Estimation
Estimate proportions, means, and uncertainty with the method stated beside the result.
Confidence Interval Calculator
Calculate Wilson, exact, Wald, and mean confidence intervals with the method and assumptions shown.
Effect Size Calculator
Convert Cohen's d, r, odds ratio, eta-squared, and Cohen's f with assumptions shown.
Error Propagation
Propagate measurement uncertainty for common operations or a typed formula.
Meta-Analysis Calculator and Forest Plot Generator
Combine several studies into one estimate and draw the forest plot.
Cohen's Kappa Calculator
Calculate unweighted Cohen kappa from a square two-rater agreement table.
Cronbach's Alpha Calculator
Estimate raw Cronbach alpha from complete item response data with alpha if item deleted.
Standard Deviation Calculator: Mean, Median, and Five-Number Summary
Paste one list of numbers to compute mean, median, mode, variance, standard deviation, five-number summary, quartiles, IQR, range, and coefficient of variation, with a sample or population toggle.
CSV/JSON Column Stats
Convert CSV and JSON locally, preview rows, and compute descriptive statistics for numeric columns.
Standard Error in Google Sheets
Use the Google Sheets formula for standard error and check a sample through the canonical column-stats logic.
Bootstrap Confidence Interval Calculator: Resampling Simulator
Paste one or two samples, build a bootstrap distribution, and compare percentile, basic, t with bootstrap SE, and BCa intervals.
Probability Paradoxes and Selection Effects
Explore counterintuitive probability, base-rate, and selection effects with exact math and simulations.
Expected Value Calculator: Variance and Standard Deviation
Enter outcomes and probabilities to get the expected value, variance, and standard deviation of a discrete distribution, with a probability check that shows the running sum and one-click normalize.
Monty Hall Simulator
Simulate stay and switch strategies under the classic host-knows Monty Hall rules.
Birthday Paradox Simulator
Birthday paradox calculator: the exact probability of a shared birthday in a group of n, with a repeated simulation that converges on the exact value.
Bayes Theorem Calculator: Base Rates and Diagnostic Testing
Use base rate, sensitivity, and specificity to see posterior probability through natural frequencies.
Simpson's Paradox Simulator
Edit subgroup counts and see how aggregate rates can reverse the within-group pattern.
Berkson's Paradox Simulator
Filter independent traits on a shared selection rule and see the selected-sample association emerge.
Probability Distributions and Critical Values
Compute exact count probabilities, read continuous distribution tables, and find the cutoff a chosen probability implies.
Normal Distribution Calculator: Curve, Area, and Inverse
Draw a normal distribution curve and read the area below, above, between, or outside your values, with an inverse mode that finds x from a probability or percentile.
Z-Score Calculator: Single Value, Data Set, and Percentile
Compute a z-score with z = (x - mu)/sigma for one value or a whole data set, and convert between z-scores and percentiles. Population SD by default, sample SD one toggle away, method shown.
Z Score Table: Positive and Negative
Read positive and negative z score tables where every body value is P(Z ≤ z), the area to the left of z. Type a z to highlight its exact cell or print a clean full page.
Binomial Distribution Calculator: PMF, CDF, Table, and Inverse
Compute binomial probabilities for any comparison, read the complete k table, get the bracketed inverse with both attained probabilities, and see the normal and Poisson approximation error.
Poisson Distribution Calculator: PMF, CDF, Table, and Inverse
Compute Poisson probabilities for any comparison, read the complete k table around lambda, get the bracketed inverse with both attained probabilities, and see the normal approximation error.
T Table: Student's t Distribution Critical Values
The full Student's t table, degrees of freedom 1 to 1000 plus the normal limit, with one-tailed alpha, two-tailed alpha and confidence on every column header.
Chi-Square Table: Critical Values by Degrees of Freedom
The full chi-square table, degrees of freedom 1 to 1000, with both tails printed and every column header showing cumulative probability, right-tail area and left-tail area.
F Table: F Distribution Critical Values
Six complete F tables, one for each significance level from 0.10 down to 0.001, with numerator degrees of freedom to infinity and denominator degrees of freedom to 500 and infinity.
Critical Value Calculator: t, z, F, and Chi-Square
Find the critical value for a t, z, F, or chi-square test at any alpha, with one-tailed and two-tailed handling and the tail probability shown.
Central Limit Theorem Simulator: Sampling Distribution Calculator
Draw repeated samples from ten populations, compare two sample sizes or statistics, and read simulated values beside exact theory.
Correlation and Regression
Measure how strongly two variables move together and fit the line that predicts one from the other.
Coefficient of Correlation Calculator
Paste two columns to get Pearson's r or Spearman's rank correlation, with r-squared, the sample size, and a significance test on r.
Linear Regression Calculator: Line of Best Fit, r, R², Standard Error
Fit a least-squares line to paired data, or run multiple regression on several predictors. Reports the equation, slope, intercept, r, r², the standard error of the estimate, and a scatter plot.
Principal Component Analysis: PCA Calculator
Run PCA on pasted data: eigenvalues, explained variance, eigenvectors and loadings, scores, a scree plot with parallel analysis, and a biplot whose scaling convention is stated on the plot.
Causal Structure
Build a causal DAG, inspect backdoor paths, and see which variables to adjust for or leave alone.