Statistical Analysis Tools

Perform comprehensive statistical analyses directly in your browser with no installation required. StatFusion’s analysis tools combine powerful statistical methods with intuitive interfaces and educational content to help you understand your data.

Statistical Testing Categories

StatFusion offers a wide range of statistical tests organized by category. Each tool includes interactive analysis capabilities, assumption checking, visualization options, and detailed result interpretation.

Our collection of statistical tools is continuously expanding. Subscribe to our updates to be notified when new tools become available.

Descriptive Statistics

Essential tools for summarizing and understanding the basic properties of your data.

Basic Summaries

Understand the central tendencies and distributions in your data:

Summary Statistics - Compute means, medians, standard deviations and more
Frequency Analysis - Create frequency tables and distributions
Percentile Calculator - Calculate percentiles and quartiles

Relationship Measures

Analyze relationships between variables:

Correlation Analysis - Measure and test variable relationships
Covariance Calculator - Compute covariance between variables
Contingency Tables - Analyze relationships between categorical variables

Inferential Statistics

Statistical tests to make inferences about populations based on sample data.

Mean Comparisons

Compare means between groups or against reference values:

Independent Samples t-Test - Compare means between two independent groups
Paired Samples t-Test - Compare paired measurements
One-Sample t-Test - Compare a sample mean to a known value
One-Way ANOVA - Compare means across multiple groups
Repeated Measures ANOVA - Analyze repeated measurements
Factorial ANOVA - Test effects of multiple factors and interactions

Non-Parametric Tests

Distribution-free alternatives when parametric assumptions aren’t met:

Mann-Whitney U Test - Non-parametric alternative to independent t-test
Wilcoxon Signed-Rank Test - Non-parametric alternative to paired t-test
Kruskal-Wallis Test - Non-parametric alternative to one-way ANOVA
Friedman Test - Non-parametric alternative to repeated measures ANOVA

Categorical Data Analysis

Tests for analyzing categorical and count data:

Chi-Square Test - Test independence between categorical variables
Fisher’s Exact Test - Alternative to Chi-Square for small samples
McNemar’s Test - Compare paired proportions
Proportion Test - Compare proportions between groups

Correlation & Association Tests

Tests for measuring relationships between variables:

Pearson Correlation - Test linear relationship between variables
Spearman Correlation - Test monotonic relationship between variables
Point-Biserial Correlation - Correlation between binary and continuous variables

Distribution & Variance Tests

Tests for analyzing data distributions and variances:

Normality Tests - Test if data follows a normal distribution
Levene’s Test - Test homogeneity of variances
F-Test - Compare variances between two groups
Bartlett’s Test - Test homogeneity of variances across multiple groups

Post-Hoc & Multiple Comparison Tests

Controlled tests after finding significant overall effects:

Tukey’s HSD - Compare all possible pairs of means
Bonferroni Correction - Control family-wise error rate
Scheffé’s Method - Test all possible contrasts
Dunnett’s Test - Compare each group to a control

Regression Analysis

Methods for modeling relationships between variables and making predictions.

Linear Regression

Model linear relationships between variables:

Simple Linear Regression - Model relationship between two variables
Multiple Linear Regression - Model using multiple predictors
Polynomial Regression - Model non-linear relationships
ANCOVA - Combine ANOVA with regression

Generalized Linear Models

Models for various types of dependent variables:

Logistic Regression - Model binary outcomes
Poisson Regression - Model count data
Ordinal Regression - Model ordered categorical outcomes

Advanced Statistical Methods

Sophisticated techniques for complex data analysis problems.

Multivariate Analysis

Techniques for analyzing multiple variables simultaneously:

Principal Component Analysis - Reduce dimensionality while preserving variance
Factor Analysis - Identify underlying factors in data
Discriminant Analysis - Classify observations into groups

Cluster Analysis

Methods for finding natural groupings in data:

K-Means Clustering - Partition data into k clusters
Hierarchical Clustering - Build a hierarchy of clusters

Time Series Analysis

Methods for analyzing time-ordered data:

Time Series Decomposition - Separate trend, seasonality, and residuals
Autocorrelation Analysis - Measure serial correlation
Forecasting Models - Predict future values based on historical data

Survival Analysis

Methods for analyzing time-to-event data:

Kaplan-Meier Estimator - Estimate survival function
Cox Proportional Hazards - Model influence of covariates on survival

Study Design & Power Analysis

Tools to plan studies and ensure adequate statistical power.

Sample Size Calculation

Determine required sample sizes for robust studies:

t-Test Sample Size - Calculate sample size for t-tests
ANOVA Sample Size - Calculate sample size for ANOVA
Proportion Sample Size - Calculate sample size for proportion tests

Effect Size Calculators

Quantify the magnitude of effects in your data:

Cohen’s d Calculator - Effect size for t-tests
Eta-squared Calculator - Effect size for ANOVA
Odds Ratio Calculator - Effect size for categorical data

How to Choose the Right Statistical Test

Selecting the appropriate statistical test is crucial for valid analysis. Here’s a guide to help you choose:

Based on Research Question

Comparing two independent groups: Independent Samples t-Test
Comparing paired measurements: Paired Samples t-Test
Comparing a sample to a known value: One-Sample t-Test
Comparing multiple groups: One-Way ANOVA
Examining relationship between variables: Correlation/Regression
Analyzing categorical data: Chi-Square Test

Based on Data Type

Two continuous variables: Correlation, Regression
One categorical, one continuous variable: t-Test, ANOVA
Two categorical variables: Chi-Square Test, Fisher’s Exact Test
Ordered categorical data: Spearman Correlation, Ordinal Regression
Count data: Poisson Regression, Chi-Square Test
Time-to-event data: Survival Analysis

Tip

Not sure which test to use?

Our interactive Statistical Test Selector can help you choose the right statistical test based on your research question and data characteristics.

Statistical Analysis Workflow

For most analyses in StatFusion, we recommend following this general workflow:

Data Preparation
- Check for missing values and outliers
- Verify data types and structure
- Consider necessary transformations
Exploratory Analysis
- Calculate descriptive statistics
- Create visualizations to understand distributions
- Examine relationships between variables
Assumption Checking
- Verify the assumptions of your planned statistical test
- Consider alternative tests if assumptions are violated
Hypothesis Testing
- Run the appropriate statistical test
- Interpret the p-value and effect size
- Consider practical significance alongside statistical significance
Post-Hoc Analysis
- Conduct follow-up tests as needed
- Explore unexpected findings
Report Results
- Present findings with appropriate visualizations
- Include test statistics, p-values, and effect sizes
- Provide confidence intervals when applicable

Each tool in StatFusion guides you through this workflow with specific instructions for that analysis.

Common Statistical Questions

What’s the difference between parametric and non-parametric tests?

Parametric tests (like t-tests and ANOVA) assume that your data follows a specific distribution (usually normal) and work with parameters like means and standard deviations. Non-parametric tests (like Mann-Whitney U and Kruskal-Wallis) don’t make assumptions about the underlying distribution and often work with ranks rather than raw values. Non-parametric tests are generally less powerful but more robust to violations of assumptions.

How do I know if my data is normally distributed?

You can assess normality using: 1. Visual methods: Histograms, Q-Q plots 2. Statistical tests: Shapiro-Wilk test, Kolmogorov-Smirnov test

Remember that with large sample sizes, minor deviations from normality usually don’t affect parametric tests due to the Central Limit Theorem.

What p-value threshold should I use?

The conventional threshold is p < 0.05, meaning there’s less than a 5% chance of observing your results if the null hypothesis is true. However, this is somewhat arbitrary. In some fields, more stringent thresholds (p < 0.01 or p < 0.001) are used, especially for multiple comparisons. Consider your research context, sample size, and potential implications when interpreting p-values.

Why is effect size important?

P-values tell you whether an effect exists but not how large or meaningful it is. Effect sizes quantify the magnitude of the effect, helping you assess practical significance. With very large samples, even tiny, practically meaningless differences can be statistically significant. Effect sizes provide context for interpreting your results.

When should I use a one-tailed vs. two-tailed test?

Two-tailed tests (more common) detect effects in either direction. Use when you’re interested in whether there’s a difference, regardless of direction.
One-tailed tests only detect effects in one specific direction. Use only when you have a strong theoretical reason to expect an effect in only one direction and would consider any effect in the opposite direction as equivalent to no effect.

Note that one-tailed tests should be specified before seeing the data to avoid misuse.

Statistical Analysis Resources

For more information on statistical methods and best practices, we recommend these resources:

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Citation

BibTeX citation:

@online{kassambara2025,
  author = {Kassambara, Alboukadel},
  title = {Statistical {Analysis} {Tools} \textbar{} {StatFusion}},
  date = {2025-04-10},
  url = {https://www.datanovia.com/apps/statfusion/analysis/index.html},
  langid = {en}
}

For attribution, please cite this work as:

Kassambara, Alboukadel. 2025. “Statistical Analysis Tools | StatFusion.” April 10, 2025. https://www.datanovia.com/apps/statfusion/analysis/index.html.