Free Statistics Calculators

Describe Your Data and Work With Distributions

Every analysis starts by describing the data. The Descriptive Statistics Calculator gives the mean, median, standard deviation and more; the Quartile & IQR Calculator, Percentile, Outlier and Skewness and Kurtosis calculators check shape and spread, and the Standard Error, Z-Score and Coefficient of Variation calculators standardize it.

For probability, pick the distribution that matches how the data arose: Normal for measurements, Binomial for successes in a fixed number of trials, Poisson for events per interval, Hypergeometric for sampling without replacement, and the Exponential, Geometric, Uniform and Negative Binomial calculators for waiting times. The Central Limit Theorem Simulator shows why sample means look normal. For exams that allow tables there are the Z-Table, T-Table, Chi-Square Table and F-Table. Counting problems go to the Permutation & Combination Calculator, and conditional probability to the Bayes' Theorem and Expected Value calculators.

Choosing a Hypothesis Test

Start from two questions: what kind of outcome you measured, and how the groups relate to each other. The Statistical Test Selector walks through them. The table pairs the common designs with a parametric test and its rank-based or exact alternative — use the alternative when the data are ordinal, heavily skewed, or the samples are small.

Assumptions, Effect Sizes and Reporting

Check the assumptions before you report. The Shapiro-Wilk and Kolmogorov–Smirnov calculators test normality, and the Statistical Power & Sample Size Calculator tells you whether a non-significant result could have detected the effect you cared about. Plan a study with the Sample Size and Margin of Error calculators; run many tests at once and adjust with the Multiple Comparisons Correction Calculator.

Report the size of the effect as well as the p-value: the Effect Size Calculator gives Cohen's d and related measures, and the Confidence Interval and Bootstrap Confidence Interval calculators give the range. The APA Statistics Formatter writes the result line: the statistic, its degrees of freedom, the exact p-value and an effect size, with statistical symbols italicized and the leading zero dropped from values that cannot exceed 1 (p = .032, r = .41).

Measurement quality has its own calculators. Internal consistency: Cronbach's Alpha. Agreement between raters: Cohen's Kappa, Fleiss' Kappa, Krippendorff's Alpha and the Intraclass Correlation. Health and diagnostic studies: Odds Ratio & Relative Risk, Sensitivity & Specificity, the ROC Curve, Kaplan–Meier survival curves and the Meta-Analysis Calculator. The dosage and IV drip calculators are practice tools for nursing-math coursework, not for clinical use.

Frequently Asked Questions

Which statistical test should I use?

Decide the type of outcome (numeric, ordinal or categorical), the number of groups, and whether the groups are independent or the same people measured repeatedly. Two independent groups with a numeric outcome call for a t-test; three or more call for ANOVA; two categorical variables call for chi-square. The Statistical Test Selector asks these questions and points to the matching calculator.

Should I use a t-test or a Mann-Whitney U test?

Use the independent t-test when the outcome is numeric and roughly normal in each group, or when both groups are large enough for the central limit theorem to carry it. Use the Mann-Whitney U test when the outcome is ordinal, clearly skewed in small samples, or has extreme outliers. The two test different things — means versus the tendency of one group's values to exceed the other's — so state which one you ran.

What does a p-value of 0.05 mean?

It is the probability of seeing a result at least this extreme if the null hypothesis were true. It is not the probability that the null hypothesis is true, and 0.05 is a convention, not a law. Report the exact p-value with an effect size and a confidence interval, so the reader can judge the evidence for themselves.

How big a sample do I need?

It depends on the effect you want to detect, the variability of the outcome, the significance level and the power you want — usually 80%. A smaller expected effect needs a much larger sample. Enter those four values in the power analysis calculator; for a survey, the sample size calculator works from the margin of error you will accept.

What is the difference between statistical significance and effect size?

A p-value says how surprising your data would be if there were no effect. An effect size says how large the effect is. With a big enough sample a trivial difference becomes significant, and with a small sample a large one may not, which is why APA style asks for both.

Are these calculators accurate enough for a thesis, and is my data uploaded?

They compute exact p-values from the t, F, chi-square and normal distributions rather than reading them from a table, and show each step so you can check the result against R, SPSS or Stata, which your committee may still expect. The calculators run in your browser; the numbers you paste are not sent to CitationEasy or anyone else.