Statistics Calculators

Statistics is the math of uncertainty — how to summarize messy data, how to decide whether a pattern is real or noise, and how to make decisions when you can't observe everything. Our statistics calculators cover the introductory and intermediate territory: descriptive statistics, probability distributions, hypothesis testing, and the core regression and correlation tools.

Start with the descriptive tools: mean/median/mode, standard deviation, variance, interquartile range, percentiles, outliers, box plots, and histograms. These let you summarize a dataset and identify whether it's roughly normal, skewed, multi-modal, or contains anomalies that need investigation before any inferential analysis.

For probability, we cover the discrete distributions (binomial, Poisson), the continuous normal distribution (including z-scores and area-under-the-curve calculations), expected value for random variables, and the combinatorial counting tools (combinations and permutations). The probability calculator handles the basic union/intersection/conditional probability questions.

Hypothesis testing coverage includes one- and two-sample t-tests, chi-square tests for independence and goodness-of-fit, one-way ANOVA, and the general hypothesis testing framework with effect size and power calculations. The confidence interval and margin-of-error calculators support the estimation side. The Bayes theorem calculator handles posterior probability updates given new evidence.

For regression and association, we have linear regression (least squares with R², residuals, and prediction intervals) and the Pearson correlation coefficient. The sample size calculator handles the planning question: how many observations do you need to detect an effect of a given size at a given power?

Formulas follow standard textbook conventions (NIST/SEMATECH e-Handbook, Wasserman's "All of Statistics," or equivalent). Significance levels default to α = 0.05 with two-tailed tests where applicable; power defaults to 80%. For specific clinical, manufacturing-QA, or research applications where assumptions matter critically (e.g., normality, homoscedasticity, independence), validate the assumptions before relying on test results. Statistical significance is not the same as practical significance — a p-value tells you about your data, not about what to do next.