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Hypothesis Testing Calculators

Choose the right statistical test for your data. Our interactive selector helps you find the appropriate test based on your research question and data characteristics, or browse the comprehensive table of tests with their assumptions and formulas.

Test Name	Check	Test Statistic	Assumptions
ANCOVA Parametric	Mean	$F = \frac{MS_{adj}}{MSE_{adj}}$	Normality Independence Equal Variance Linearity of Covariate Homogeneity of Regression
Dunnett's Test Parametric	Mean	$d = \frac{\bar{x}_i - \bar{x}_c}{\sqrt{2MSE/n}}$	Normality Independence Equal Variance
Friedman Test Non-parametric	Mean	$\chi^2(df) = \frac{12}{bk(k+1)}\sum R_j^2 - 3b(k+1)$	Dependent Groups Ordinal Data
Kruskal-Wallis Test Non-parametric	Mean	$H = \frac{12}{N(N+1)}\sum_{i=1}^k \frac{R_i^2}{n_i} - 3(N+1)$	Independence Ordinal Data
One Sample Z-Test Parametric	Mean	$z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}}$	Normality Independence Known σ
One Sample t-Test Parametric	Mean	$t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$	Normality Independence Known σ
One Way ANOVA Parametric	Mean	$F = \frac{MSG}{MSE}$	Normality Independence Equal Variance
Paired t-Test Parametric	Mean	$t = \frac{\bar{d}}{s_d/\sqrt{n}}$	Normality Paired Data
Permutation Test Non-parametric	Mean	$p = \frac{\sum_{i=1}^{N} I(T^*_i \geq T_{obs})}{N}$	Independence Normality Equal Variance
Repeated Measures ANOVA Parametric	Mean	$F = \frac{MSG}{MSE}$	Normality Dependent Groups Sphericity
Three-way ANOVA Parametric	Mean	$F = \frac{MSG}{MSE}$	Normality Independence Equal Variance
Tukey's HSD Test Parametric	Mean	$q = \frac{\bar{x}_i - \bar{x}_j}{\sqrt{MSE/n}}$	Normality Independence Equal Variance
Two Sample Z-Test Parametric	Mean	$Z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$	Normality Independence Known σ
Two Sample t-Test (Pooled variance) Parametric	Mean	$t = \frac{\bar{x}_1 - \bar{x}_2}{s_p\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$	Normality Independence Known σ Equal Variance
Two Sample t-Test (Welch's) Parametric	Mean	$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$	Normality Independence Known σ Equal Variance
Two Way ANOVA Parametric	Mean	$F = \frac{MSG}{MSE}$	Normality Independence Equal Variance
Chi-Square Goodness of Fit Test Parametric	Proportion	$\chi^2 = \sum \frac{(O - E)^2}{E}$	Normality Independence
Chi-Square Test of Independence Parametric	Proportion	$\chi^2 = \sum \frac{(O - E)^2}{E}$	Normality Independence
Fisher's Exact Test Non-parametric	Proportion	$p = \frac{(a+b)!(c+d)!(a+c)!(b+d)!}{n!a!b!c!d!}$	Independence Fixed Row/Column Totals
One Sample Proportion Test Parametric	Proportion	$z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$	Independence Binomial Data
Two Sample Proportion Test Parametric	Proportion	$Z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}}$	Independence Binomial Data
Dunn's Test Non-parametric	Rank	$z_{ij} = \frac{\bar{R}_i - \bar{R}_j}{\sqrt{\frac{N(N+1)}{12}(\frac{1}{n_i} + \frac{1}{n_j})}}$	Independence Ordinal Data
Mann-Whitney U Test Non-parametric	Rank	$Z = \frac{U - \mu_U}{\sigma_U}$	Independence Ordinal Data
Wilcoxon Signed Rank Test Non-parametric	Rank	$Z = \frac{W - \mu_W}{\sigma_W}$	Paired Data Ordinal Data

Descriptive Statistics Calculators

Choose from our comprehensive collection of descriptive statistics calculators for both quantitative and qualitative data analysis.

Central Tendency

Calculator	Formula	Description
Mean	$\bar{x} = \frac{\sum_{i=1}^n x_i}{n}$	Calculate arithmetic average of numerical data
Median	$\text{Middle value when ordered}$	Find the middle value in ordered data
Mode	$\text{Most frequent value}$	Identify most common value(s) in dataset
Geometric Mean	$\sqrt[n]{x_1 \times x_2 \times ... \times x_n}$	Calculate mean for multiplicative relationships
Harmonic Mean	$\frac{n}{\sum_{i=1}^n \frac{1}{x_i}}$	Calculate mean for rates and speeds

Variability

Calculator	Formula	Description
Standard Deviation	$s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$	Measure average deviation from mean
Mean Absolute Deviation	$\text{MAD} = \frac{\sum \|x_i - \bar{x}\|}{n}$	Measure average deviation from mean
Variance	$s^2 = \frac{\sum(x_i - \bar{x})^2}{n-1}$	Measure spread of data points
Range	$\text{max}(x) - \text{min}(x)$	Calculate difference between largest and smallest values
IQR	$Q_3 - Q_1$	Calculate spread of middle 50% of data
Coefficient of Variation	$CV = \frac{s}{\bar{x}} \times 100\%$	Compare variability between datasets

Position

Calculator	Formula	Description
Percentiles	$P_k = \text{value at }k\text{th percentile}$	Find value at specified percentile
Z-Score	$z = \frac{x - \bar{x}}{s}$	Calculate standardized scores

Shape

Calculator	Formula	Description
Skewness	$\frac{\sum(x_i - \bar{x})^3}{(n-1)s^3}$	Measure asymmetry of distribution
Kurtosis	$\frac{\sum(x_i - \bar{x})^4}{(n-1)s^4}$	Measure tailedness of distribution

Probability Distribution Calculators

Access our suite of probability distribution calculators for both discrete and continuous random variables. Calculate probabilities, find critical values, and visualize distributions.

Common Discrete

Distribution	Probability Function	Description
Binomial	$P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$	Model number of successes in fixed trials
Poisson	$P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}$	Model rare events in fixed interval
Geometric	$P(X=k) = p(1-p)^{k-1}$	Model trials until first success
Negative Binomial	$P(X=k) = \binom{k-1}{r-1}p^r(1-p)^{k-r}$	Model trials until r successes
Hypergeometric	$P(X=k) = \frac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}$	Model sampling without replacement

Chart Makers

Choose the right visualization based on your data type and analysis goals. Our tools help you create clear, effective visual representations of your data.

Categorical Data

Chart Type	Description	Best Used For	Example
Bar Chart	Display frequencies or counts for categories	Comparing categories, showing distributions	Product sales by category
Pie Chart	Show part-to-whole relationships	Displaying proportions, percentages	Market share by company

Numerical Data

Chart Type	Description	Best Used For	Example
Histogram	Display distribution of continuous data	Examining data distribution shape	Age distribution of customers
Box Plot	Show data distribution and outliers	Identifying outliers, comparing distributions	Test scores distribution
Violin Plot	Combine box plot with kernel density	Detailed view of data distribution	Income distribution by department

Confidence Interval Calculators

Choose from our comprehensive collection of confidence interval calculators for estimating population parameters and analyzing differences between groups.

Population Parameters

Interval Type	Description	Best Used For	Example
Mean	Estimate population mean	Continuous data, normal distribution	Average customer spending ± margin of error
Proportion	Estimate population proportion	Binary outcomes, categorical data	Customer satisfaction rate ± margin of error
Standard Deviation	Estimate population variability	Process variation, quality control	Manufacturing tolerance limits

Regression Analysis Calculators

Choose from our collection of regression analysis tools for modeling relationships between variables and making predictions from your data.

Linear Regression

Model Name	Description	Example
Simple Linear Regression	Model relationship between two continuous variables	Height vs weight relationship
Multiple Linear Regression	Model with multiple predictors	House price prediction using area, location, age

Non-Linear Regression

Model Name	Description	Example
Quadratic Regression	Model curved relationships with quadratic terms	Projectile motion, optimal pricing models
Exponential Regression	Model exponential growth or decay patterns	Population growth, radioactive decay, compound interest

Classification Models

Model Name	Description	Example
Logistic Regression	Model binary outcomes	Customer churn prediction

Statistical Resources

Access our collection of statistical tables, interactive simulations, and reference materials to support your statistical analysis.

Distribution Tables

Resource	Description
Z-Table	Standard normal distribution critical values for Z-tests and standardized scores
T-Table	Student's t-distribution critical values, ideal for small sample tests with unknown population σ
Chi-Square Table	Chi-square distribution critical values used in goodness of fit and independence tests
F-Table	F-distribution critical values for ANOVA and variance comparisons
Wilcoxon Signed-Rank Table	Critical values for Wilcoxon signed-rank test and paired sample comparisons

Analyze Your Data with Confidence

Fast, accurate statistical analysis trusted by students and researchers