Statistics online

Statistical tests, charts, probabilities and clear results. Automatically checks assumptions, interprets results and outputs graphs, histograms and other charts.
The statistics online calculators support not only the test statistic and the p-value but more results like effect size, test power, and the normality level.
If one of the validations fails, the tool recommends a solution.
What statistical test should you use? the following link will help you choose: choose a statistical test - decision questionnaire (Tutorial).

Test statistic calculators

Find the test statistic calculator

Test				Assumptions						Required sample data
#	Test name	Check	Statistic		Ind	σ	σ1=σ2	d	μ/p	x̄/p̂;	n	S
1	One Sample Z-Test	Mean	$z=\frac{\overline{x}-{\mu }_0}{\mathrm{\sigma }/\sqrt{n}}$	✔	✔	✔			✔	✔	✔
2	One Sample T-Test	Mean	$t=\frac{\overline{x}-{\mu }_0}{S/\sqrt{n}}$	✔	✔	✘			✔	✔	✔	✔
3	Two Sample Z-Test	Mean	$z=\frac{x_1-x_2-d}{\sqrt{\frac{{\sigma }^2}{n_1}+\frac{{\sigma }^2}{n_2}}}$	✔	✔	✔		✔		✔	✔
4	Two Sample T-Test (Pooled variance)	Mean	$t=\frac{{\overline{x}}_1-{\overline{x}}_2-d}{s\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$	✔	✔	✘	✔	✔		✔	✔	✔
5	Two Sample T-Test (Welch's)	Mean	$t=\frac{{\overline{x}}_1-{\overline{x}}_2-d}{\sqrt{\frac{{s_1}^2}{n_1}+\frac{{s_2}^2}{n_2}}}$	✔	✔	✘	✘	✔		✔	✔	✔
6	Two Sample Mann-Whitney U Test	Rank	$z=\frac{U-\mu +c}{\sigma }$		✔			✔					✔
7	Paired T-Test	Mean	$t=\frac{{\overline{x}}_d-{\mu }_0}{{\mathrm{S}}_d/\sqrt{n}}$	✔	Paired								✔
8	Paired Wilcoxon Sign Rank Test	Rank	$z=\frac{W-\mu +c}{\sigma }$		Paired								✔
9	One Way ANOVA Test	Mean	$F=\frac{{\mathrm{MS}}_{\text{Between}}}{{\mathrm{MS}}_{\text{Within}}}$	✔	✔		✔						✔
10	Repeated Measures ANOVA Test	Mean	$F=\frac{{\mathrm{MS}}_{\text{Between}}}{{\mathrm{MS}}_{\text{Within}}}$	✔	Dependent groups		Sphericity						✔
11	Friedman Test	Mean	$\mathrm{\chi ²(df)}=\frac{12\sum _{j=1}^k{R_j}^2-3n^{2}k{(k+1)}^2}{nk(k+1)-C_{ties}}$		Dependent groups								✔
12	Kruskal-Wallis Test	Mean	$F=\frac{{\mathrm{MS}}_{\text{Between}}}{{\mathrm{MS}}_{\text{Within}}}$		✔								✔
13	Two Way ANOVA Test Fixed model, Mixed model, Random mode, Mixed model with repeats	Mean	$F=\frac{{\mathrm{MS}}_{\text{Between}}}{{\mathrm{MS}}_{\text{Within}}}$	✔	✔		✔						✔
14	One Way MANOVA Test	Mean	$F=\frac{V}{s-V}.\frac{d{f}_2}{d{f}_1}$	✔	✔		✔						✔
15	One Sample Proportion Test	Proportion	$z=\frac{(\hat{p}-p_0)+c}{\sqrt{\frac{p_0(1-p_0)}{n}}}\text{or}\mathrm{X~}\mathrm{B(}n,p_0\mathrm{)}$	Binomial	✔				✔	✔	✔
16	Two Sample Proportion Test	Proportion	$z=\frac{{\hat{p}}_1-{\hat{p}}_2+\mathrm{Cont}}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1}+\frac{1}{n_2})}}$	Binomial	✔					✔	✔
17	Chi-Squared Test For Variance	σ	${\chi }^2=\frac{(n-1)S^2}{{{\sigma }_0}^2}$	✔	✔						✔	✔
18	F Test For Variances	σ	$F=\frac{{S_1}^2}{{S_2}^2}$	✔	✔						✔	✔
19	Levene's Test For Variances	σ	$F=\frac{{\mathrm{MS}}_{\text{Between}}}{{\mathrm{MS}}_{\text{Within}}}$	✘	✔								✔
20	Chi-Squared Test For Goodness Of Fit McNemar test, Chi-squared test for association, Fisher test, Binomial test	Fit	${\chi }^2=\sum _{i=1}^n\frac{{(o_i-e_i)}^2}{e_i}$		✔								✔
21	Shapiro-Wilk Test	Fit	$W=\frac{{\left(\sum _{i=1}^{\lfloor n/2\rfloor }\left(a_i(x_{\mathrm{n+1-i}}-x_i)\right)\right)}^2}{\sum _{i=1}^n{\left((x_i-\overline{x})\right)}^2}$	✔	✔								✔
22	Kolmogorov Smirnov Test	Fit	D = Max1≤i≤n(Di+,Di-)		✔								✔
23	Two-Sample Kolmogorov Smirnov Test	Fit	D = Max1≤i≤n(Di+,Di-)		✔								✔
24	Kaplan Meier Survival Analysis	Survival	${\chi }^2=\sum _{i=1}^n\frac{{(o_i-e_i)}^2}{e_i}$		✔								✔
25	DeLong test - Independent curves Compares the AUCs of two independent ROC curves	AUC	$D=\frac{{\mathrm{AUC}}_1-{\mathrm{AUC}}_2}{\sqrt{{\mathrm{Var}}_1+{\mathrm{Var}}_1}}$		✔								✔
26	DeLong test - Paired curves Compares the AUCs of two dependent ROC curves	AUC	$Z=\frac{{\mathrm{AUC}}_1-{\mathrm{AUC}}_2}{\sqrt{\mathrm{Var}\mathrm{₁}+\mathrm{Var}\mathrm{₂}-2*\mathrm{Cov}(\mathrm{AUC}\mathrm{₁},\mathrm{AUC}\mathrm{₂})}}$		Paired								✔

Regression calculator

#	Regression	Statistic
1	Simple Linear Regression	$F=\frac{{\mathrm{MS}}_{\text{Regression}}}{{\mathrm{MS}}_{\text{Error}}}$
2	Multiple Linear Regression	$F=\frac{{\mathrm{MS}}_{\text{Regression}}}{{\mathrm{MS}}_{\text{Error}}}$
3	*Bulk Linear Regression	$F=\frac{{\mathrm{MS}}_{\text{Regression}}}{{\mathrm{MS}}_{\text{Error}}}$
4	Binary Logistic Regression	χ2 = 2(LL1-LL0)
5	Multinomial Logistic Regression	χ2 = 2(LL1-LL0)
6	Propensity Score Matching

*Bulk linear regression calculator for several dependent variables with the same predictors.

Confidence interval, Sample size, Effect Size

#	Calculator	Image
	Sample size calculators
	Test power calculators
	Effect size calculators
	Confidence intervals calculators

Distribution calculators

#	Distribution	Image
	P-value
	Distributions
	Normal Distribution
	Binomial Distribution
	T Distribution (Student's)
	Chi-Squared Distribution
	F Distribution (Fisher-Snedecor)
	Poisson Distribution
	Weibull Distribution
	Exponential Distribution

Statistical tables

Basic statistics calculators

Each statistics calculator contains step by step calculation.

Calculator	Statistic calculator	Image
Statistics calculator	The calculator computes statistics such as count, average and standard deviation for each combination of the categorical variables.
Descriptive statistics calculator	The calculator computes statistics such as count, average, and standard deviation for each variable.
Percentile calculator	A percentile tells you the percentage of values below a given value in a data set. For example, a value at the 75th percentile means that 75% of the data lies below that value.
Mean Median Mode calculator	Q1, Q3, IRQ, Range
Measures Of Dispersion calculator	Mean, sample size, APA style
Standard Deviation calculator	Mean, sample size, APA style	$S=\sqrt{\frac{\sum _{i=1}^n{(x_i-\mathrm{x̄})}^2}{n-1}}$
Variance calculator	Variance, Mean, SEM, MAD	$S^2=\frac{\sum _{i=1}^n{(x_i-\mathrm{x̄})}^2}{n-1}$
Coefficient of Variation calculator		$\mathrm{CV}=\frac{s}{\overline{x}}$
Average calculator	Average, Sum, Count	$\overline{x}=\frac{x_1+x_2+\cdots +x_n}{n}$
Sample Mean calculator	Sample mean, Sum, Count	$\overline{x}=\frac{x_1+x_2+\cdots +x_n}{n}$
Geometric Mean calculator	Product, n-th root	$GM=\sqrt[n]{x_1{x}_2\dots x_n}$
Harmonic Mean calculator	The harmonic mean is a type of average used for rates, for example average speed. It is found by dividing n by the sum of the reciprocals of the values.	$H_n=\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+\cdots +\frac{1}{x_n}}$
Probability calculator	Probability formula, Dependent events, Bayes' Theorem, Independent events	P(A), P(A|B), P(A∩B), P(A∪B)
Combinations calculator	With/Without Repetitions	$C_r^n=\frac{n!}{r!(n-r)!}$ , $C_r^{\mathrm{n\; +\; r\; -\; 1}}=\frac{\mathrm{n\; +\; r\; -\; 1}!}{r!(n-1)!}$
Permutation calculator	With/Without Repetitions	$P_r^n=\frac{n!}{(n-r)!}$ , nr
Correlation calculator	Pearson correlation, Spearman's rank correlation	$r=\frac{\sum _{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum _{i=1}^n{(x-\overline{x})}^2}\sqrt{\sum _{i=1}^n{(y_i-\overline{y})}^2}}$
Outliers	Tukey's Fences (Boxplot), Z-Score
Markov chain calculator	nth step probability vector, steady-state vector
Odds calculator	Odds to probability, probability to odds
Betting odds calculator	Fractional odds, decimal odds, American odds
Mean absolute deviation calculator	MAD calculator	μ
Median absolute deviation calculator	MAD calculator	Mdn

Visualization

#	Chart	Image
1	Principal component analysis
2	Cluster analysis
3	Histogram maker
4	Box plot maker
5	Bar graph maker
6	Pie chart maker
7	Line chart maker
8	Scatter chart maker
9	Area chart maker
10	Violin plot maker
11	Venn diagram maker
12	Venn diagram calculator
13	Stem and Leaf plot
14	ROC Calculator

Guide

• Guide
• Bonferroni correction
• Central Limit Theorem
• Confidence interval
• Linear regression
• Logistic regression
• Outliers
• P-value
• Skewness and kurtosis
• Standard deviation
• Test power

Exams

Free statistics exams with solution.

Statistical Tests

• Chi-squared test
• Levene's test
• Mann-Whitney U Rank test
• One Way ANOVA test
• Proportion test
• Shapiro Wilk test
• T-test
• T-test vs Z-Test
• Tukey HSD test
• Wilcoxon Sign Rank test

Goal

The goal of this website is to make statistics accessible to anyone, converting complex statistical jargon into common everyday language.
We help everybody to calculate statistics.
The calculators also provide R codes for your convenience.
We started adding a step-by-step work-through for education purposes, an easy guide on how to calculate test statistics.

Terms

We put in a lot of effort to provide accurate results and we automatically test every new page, The older pages were tested manually, but we slowly also automate the old pages.
We usually compare the results to the R results.
The information and tools on this website are given AS IS WITHOUT ANY WARRANTY OF ANY KIND.

Calculate statistics

The best online calculator to calculate statistics.