Statistics & Probability Calculators
Perform rigorous statistical analysis and hypothesis testing. Calnora’s 16 statistical calculators evaluate central tendency, standard deviation, sample size requirements, probability distributions (Normal, Binomial, Poisson), linear regressions, and inferential tests (t-tests, Chi-square, Cohen’s d effect size) for researchers, data scientists, and students.
Available calculators in Statistics & Probability (16)
Probability & Bayes Calculator
Calculate single event odds, union (A or B), intersection (A and B), and conditional Bayesian probabilities.
Normal Distribution (Z-Score)
Compute standard normal distribution Z-scores, percentiles, left/right tail probabilities, and P-values.
Descriptive Statistics
Compute mean, median, mode, sample/population standard deviation, variance, range, and IQR.
Permutations & Combinations (nPr & nCr)
Calculate permutations (order matters) and combinations (order does not matter) with step formulas.
Sample Size Calculator
Determine statistically representative sample sizes for surveys based on confidence level and margin of error.
Pearson Correlation Coefficient
Calculate Pearson's r, covariance, and linear relationship strength between paired datasets.
Confidence Interval
Mean confidence interval from sample size, standard deviation, and z critical value.
Linear Regression
Least-squares slope, intercept, r, and R² from paired X/Y lists.
Margin of Error
Survey margin of error for a sample proportion at 90/95/99% confidence.
P-Value Calculator
Calculate one-tailed and two-tailed p-values for Z, t, and Chi-Square tests.
Two-Sample T-Test
Compare two independent sample groups, calculate t-statistic, df, and p-value.
Chi-Square Test
Chi-square goodness-of-fit test comparing observed versus expected counts.
Binomial Distribution
Exact probability P(X=k), cumulative CDF P(X≤k), mean, and variance for n trials.
Poisson Distribution
Calculate Poisson probability P(X=k) and cumulative CDF for average rate λ.
Percentile & Quartile Calculator
Find custom percentiles, quartiles Q1/Q2/Q3, and interquartile range (IQR).
Cohen's d Effect Size
Calculate standardized mean difference effect size between two groups.
Frequently Asked Questions — Statistics & Probability
What is the difference between sample and population standard deviation?
Sample standard deviation divides the sum of squared differences by (n - 1) using Bessel’s correction, while population standard deviation divides by N.
When should I use a two-sample t-test versus a z-test?
Use a two-sample t-test when population standard deviations are unknown and sample sizes are small to moderate; use a z-test when population variances are known or sample sizes are very large.