Paired Samples Difference t-Test Calculator
Calculates the t-statistic for a paired t-test from the mean difference, standard deviation of differences, and sample s...
Probability, sampling, and descriptive statistics made readable.
Means, medians, standard deviations, confidence intervals, and sample size planning — with formulas and worked examples for each tool.
Calculates the t-statistic for a paired t-test from the mean difference, standard deviation of differences, and sample s...
Calculates Poisson probabilities: P(X=k) = e^(−λ)·λᵏ/k!, and the cumulative P(X≤k) by summing from 0 to k. Used for coun...
Calculates Poisson probability mass function P(X = k) and cumulative distribution P(X ≤ k) for a given rate λ and event...
Calculates the minimum detectable effect MDE = (z_α + z_β) × √(2σ²/n), where z_α is the critical value and z_β correspon...
Calculates x̄_w = Σ(w_i · x_i) / Σw_i for up to six value/weight pairs. Used in grade calculations, portfolio returns, a...
Calculates Cohen's d standardised effect size between two groups from their means and pooled standard deviation.
Calculates the z-statistic for a one-sample proportion test comparing an observed sample proportion against a known or h...
Calculates IQR = Q3 − Q1. Also computes the lower and upper fences for outlier detection: lower = Q1 − 1.5×IQR, upper =...
Calculates the cumulative area under the normal curve (P(X ≤ x)) and the percentile rank for a value x given mean μ and...
Calculates the sample size per variant needed for an A/B test: n ≈ 2 × [z_α/2 + z_β]² × p̄(1−p̄) / (p₁−p₂)², using the p...
Calculates the PDF, CDF, mean, and variance of an exponential distribution from rate parameter λ at a given value x.
Calculates the multinomial coefficient n!/(n₁!·n₂!·n₃!) and the probability of each outcome when items are drawn from a...
Calculates the minimum sample size needed to estimate a proportion with a specified margin of error and confidence level...
Calculates Weibull reliability R(t), failure probability, hazard rate, and MTTF from shape parameter β and scale paramet...
Calculates the chi-square statistic for a 2×2 contingency table to test for independence between two categorical variabl...
Updates a Beta(α, β) prior with n trials and k successes to get the posterior Beta(α+k, β+n−k). Returns posterior mean,...
Calculates the confidence interval for a population proportion from sample proportion, sample size, and chosen confidenc...
Calculates z-score z = (x − μ)/σ and approximate one-tailed percentile using the rational approximation of the standard...
Calculates χ² = Σ(O−E)²/E from observed and expected frequencies in up to a 4-cell (2×2) contingency table, and indicate...
Calculates the expected value E[X] = Σ xᵢ·P(xᵢ) and variance Var[X] = Σ(xᵢ−μ)²·P(xᵢ) for a discrete probability distribu...
Calculates the Pearson product-moment correlation coefficient r and r² from summary statistics (means, standard deviatio...
Calculates type II error rate β = 1 − power, type I error rate α, and the four outcomes of a hypothesis test with their...
Calculates the Erlang B formula for call blocking probability and Erlang C for probability of queuing in a M/M/c telepho...
Calculates the statistical power of a one-sample z-test from effect size, sample size, and significance level.