🎲 Probability & Hypothesis Tests

14 calculators in this category.

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Work out probabilities for the normal, binomial and Poisson distributions, z-scores, Bayes’ theorem, expected value, permutations and combinations.

Run t-tests, chi-square tests and one-way ANOVA with p-values, build confidence intervals and find the sample size you need — computed precisely, without table rounding.

Z-Score

Calculate the z-score of a value from the mean and standard deviation, its percentile, the probability below and above it, and the two-tailed p-value.

Normal Distribution

Find normal distribution probabilities — below, above, between or outside values — and inverse values for a given probability, with a shaded bell curve.

Binomial Distribution

Calculate binomial probabilities — exactly, at most, at least or between k successes in n trials — with the mean, variance and the full probability table and chart.

Poisson Distribution

Calculate Poisson probabilities of k events when the average rate is λ — exactly, at most, at least or between — with a probability table and chart.

Probability

Find P(A and B), P(A or B), P(A given B), complements and ‘at least once’ probabilities for independent, mutually exclusive or overlapping events.

Bayes’ Theorem

Apply Bayes’ theorem: find P(A|B) from the prior P(A) and the likelihoods P(B|A) and P(B|not A) — with a medical-test example and counts out of 10,000.

Expected Value

Find the expected value E(X), variance and standard deviation of a discrete probability distribution — and the expected profit of a game, lottery or decision.

nPr & nCr

Calculate permutations nPr and combinations nCr, with or without repetition, exactly even for huge numbers — with the formulas and worked examples.

Chi-Square Test

Run a chi-square goodness-of-fit test or a test of independence on a contingency table — χ², degrees of freedom, p-value, critical value and Cramér’s V.

T-Test

Run a one-sample, two-sample (Welch or pooled) or paired t-test from your data — t statistic, degrees of freedom, p-value, confidence interval and effect size.

Confidence Interval

Calculate a confidence interval for a mean (t or z) or a proportion (Wald and Wilson), with the margin of error and 90%, 95% and 99% intervals.

P-Value

Convert a test statistic into a p-value for the z, t, chi-square or F distribution — one- or two-tailed — with critical values at common significance levels.

Sample Size

Find the sample size needed for a survey or study from the confidence level, margin of error and population size — for proportions or means, with response rate.

ANOVA

Run a one-way ANOVA on 2 to 6 groups — F statistic, p-value, critical F, η² effect size, group means and the full ANOVA table (SS, df, MS).

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