Normality and Assumption Tests
Mauchly Sphericity Test Statistical Calculator
Mauchly Sphericity Test Calculator test sphericity in repeated measures. Use Mauchly Sphericity Test Calculator to validate data matrix, alpha and report method, subjects, conditions, covariance_matrix, contrast_matrix, transformed_covariance with method-specific calculations, diagnostics, and interpretation. Use the tabbed test workspace below for data, variables, analysis, visualizations, results, interpretation and reporting.
Quick method summary
The Mauchly Sphericity Test Statistical Calculator calculates the named method using calculator-specific formulas and reports auditable results, warnings, and interpretation. It uses the calculator-specific formula and reports the intermediate values, final result, warnings, and interpretation.
Normality and Assumption Tests
Mauchly Sphericity Test Calculator
Test sphericity in repeated measures. Use Mauchly Sphericity Test Calculator to validate data matrix, alpha and report method, subjects, conditions, covariance_matrix, contrast_matrix, transformed_covariance with method-specific calculations, diagnostics, and interpretation.
Calculated result
Calculation method
Mauchly test transforms the repeated-measures covariance matrix with orthonormal contrasts, computes W from its determinant and trace, and uses the corrected chi-square approximation. Greenhouse-Geisser and Huynh-Feldt epsilon are also reported.
Formula
Mauchly test transforms the repeated-measures covariance matrix with orthonormal contrasts, computes W from its determinant and trace, and uses the corrected chi-square approximation. Greenhouse-Geisser and Huynh-Feldt epsilon are also reported.
Assumptions and limits
The selected sample, groups, residuals, or repeated-measure matrix must be the quantity whose assumption is being assessed. Results can be sensitive to sample size, rounding, ties, missingness, and extreme observations. Use the numerical test together with diagnostic plots and the robustness requirements of the planned analysis.
Formula review
Formula and independent control cases reviewed 2026-08-02; variable assumptions remain visible inputs.
Mauchly Sphericity Test Calculator method, assumptions and reporting guideComplete selected-test explanation, assumptions, formula and reporting details
Data Import and Variable Requirements
For the Mauchly Sphericity Test Statistical Calculator, upload or paste data, review the cleaning report, then select the outcome, group, subject, condition, or matrix roles required by Mauchly Sphericity Test Calculator. For Mauchly Sphericity Test Calculator, map Data matrix, Alpha from the cleaned browser-local table; every mapped variable remains editable before calculation, and the active dataset remains available while you work with this selected test and when you return to the Test Finder.
Uploaded files are processed locally in the browser. The cleaning report appears before variable selection, and the selected cleaned columns are mapped to this exact calculator rather than a generic fallback.
Mauchly Sphericity Test Calculator Workspace Features
- Dedicated Mauchly Sphericity Test Calculator variable mapping, calculation contract, result explanation, and diagnostics
- Manual inputs plus browser-local XLSX, CSV, or TSV analysis for this exact statistical method
- Auditable cleaning report before method-valid variable dropdowns are created
- Calculator-specific formulas, intermediate quantities, assumptions, warnings, and interpretation
- Responsive method-specific charts generated from the selected cleaned data
- Copy, result CSV, cleaned-data CSV, chart PNG, and result-only print controls
- Protected canonical URL, focused FAQs, and a dedicated selected-test workspace
About the Mauchly Sphericity Test Calculator
Test sphericity in repeated measures. Use Mauchly Sphericity Test Calculator to validate data matrix, alpha and report method, subjects, conditions, covariance_matrix, contrast_matrix, transformed_covariance with method-specific calculations, diagnostics, and interpretation. Assumption tests evaluate a named aspect of distribution shape, variance equality, or repeated-measures covariance structure.
When to Use the Mauchly Sphericity Test Calculator
Use the Mauchly Sphericity Test Statistical Calculator when your research question, variable types, and sampling or experimental design require mauchly sphericity test. Do not select it only because the data produce a convenient p-value or familiar output.
How the Mauchly Sphericity Test Calculator Works
Mauchly test transforms the repeated-measures covariance matrix with orthonormal contrasts, computes W from its determinant and trace, and uses the corrected chi-square approximation. Greenhouse-Geisser and Huynh-Feldt epsilon are also reported.
The calculation runs in the browser. Submitted values are validated for required numeric ranges, data shape, units and method-specific restrictions before results are shown.
Assumptions and Checks
- The selected sample, groups, residuals, or repeated-measure matrix must be the quantity whose assumption is being assessed.
- Results can be sensitive to sample size, rounding, ties, missingness, and extreme observations.
- Use the numerical test together with diagnostic plots and the robustness requirements of the planned analysis.
Required Inputs
- Data matrix (required)
- Alpha (required)
Results Reported
The result workspace shows the final answer and intermediate quantities needed to audit the calculation. Depending on the method, reported values include:
- Method
method - Subjects
subjects - Conditions
conditions - Covariance Matrix
covariance_matrix - Contrast Matrix
contrast_matrix - Transformed Covariance
transformed_covariance - Determinant
determinant - Trace
trace - Correction Factor
correction_factor - W Statistic
w_statistic - Chi Square Statistic
chi_square_statistic - Df
df - P Value
p_value - Greenhouse Geisser Epsilon
greenhouse_geisser_epsilon - Huynh Feldt Epsilon
huynh_feldt_epsilon - Lower Bound Epsilon
lower_bound_epsilon - Alpha
alpha - Decision
decision
Mauchly Sphericity Test Calculator Worked Example
Use the example data button to load a known sample, then calculate and review the statistic, p-value or estimate, and interpretation.
| Input | Example value |
|---|---|
| Data matrix | 8,9,11
7,10,12
9,11,13
6,8,10
10,12,15
8,10,12 |
| Alpha | 0.05 |
Verified Worked Result
The packaged automated fixture produces the following checked values from the example inputs. Display rounding can differ from the full-precision browser result.
| Result | Verified value |
|---|---|
| Subjects | 6 |
| Conditions | 3 |
| Covariance Matrix 0 0 | 2 |
| Covariance Matrix 0 1 | 1.8 |
| Covariance Matrix 0 2 | 2.2 |
| Contrast Matrix 0 0 | 0.70710678118655 |
| Contrast Matrix 0 1 | -0.70710678118655 |
| Contrast Matrix 0 2 | 0 |
| Transformed Covariance 0 0 | 0.2 |
| Transformed Covariance 0 1 | 0.11547005383792 |
| Determinant | 0.022222222222222 |
| Trace | 0.37777777777778 |
How to Use This Workspace
- Confirm that the method matches the quantity, hypothesis, model or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date or option format.
- Use Example Data to inspect a valid input layout, or enter your own values and run the calculation.
- Review the result table, formula, substitutions, warnings and interpretation rather than relying only on the headline number.
- Copy, download or print the result when you need a reusable analysis record.
Understanding and Reporting the Result
Review Method, Subjects, Conditions, Covariance Matrix, Contrast Matrix, Transformed Covariance, Determinant, Trace, Correction Factor, and W Statistic. Use the displayed assumptions, warnings, and interpretation before reporting the result. In the Mauchly Sphericity Test Calculator result workspace, interpret method, subjects, conditions, covariance_matrix, contrast_matrix, transformed_covariance together with the method assumptions, warning messages, confidence information, effect magnitude, and diagnostic plots shown for the selected variables.
Use plots and subject-matter judgment with p-values because assumption tests can have low power in small samples and excessive sensitivity in large samples.
Keep the entered values, units, selected options and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size and decision. For an estimate or conversion, report the formula convention and final unit.
How to Report the Result
When reporting results from the Mauchly Sphericity Test Statistical Calculator, identify the design and software, state the valid sample size and exclusions, then report Method, Subjects, Conditions, Covariance Matrix, Contrast Matrix, Transformed Covariance, Determinant, Trace. Include the selected alpha level, tail, coding, and assumption decisions when they apply. A reproducible Mauchly Sphericity Test Calculator report should identify the mapped variables, valid observations, exclusions or missing-data handling, selected options, principal outputs, uncertainty, diagnostics, and the practical conclusion supported by the analysis.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the Mauchly Sphericity Test Calculator calculate?
Test sphericity in repeated measures. Use Mauchly Sphericity Test Calculator to validate data matrix, alpha and report method, subjects, conditions, covariance_matrix, contrast_matrix, transformed_covariance with method-specific calculations, diagnostics, and interpretation.
Which formula does the Mauchly Sphericity Test Calculator use?
Mauchly test transforms the repeated-measures covariance matrix with orthonormal contrasts, computes W from its determinant and trace, and uses the corrected chi-square approximation. Greenhouse-Geisser and Huynh-Feldt epsilon are also reported.
When should I use the Mauchly Sphericity Test Statistical Calculator?
Use the Mauchly Sphericity Test Statistical Calculator when your research question, variable types, and sampling or experimental design require mauchly sphericity test. Do not select it only because the data produce a convenient p-value or familiar output.
What inputs does the Mauchly Sphericity Test Statistical Calculator require?
Upload or paste data, review the cleaning report, then select the outcome, group, subject, condition, or matrix roles required by Mauchly Sphericity Test Calculator.
What does the Mauchly Sphericity Test Statistical Calculator report?
Review Method, Subjects, Conditions, Covariance Matrix, Contrast Matrix, Transformed Covariance, Determinant, Trace, Correction Factor, and W Statistic. Use the displayed assumptions, warnings, and interpretation before reporting the result.
Can the Mauchly Sphericity Test Statistical Calculator analyze Excel or CSV data?
Yes. The file is cleaned locally in the browser, then method-valid variable dropdowns place the selected data into this exact calculator.