MANOVA Calculator

How to use the manova calculator

1. Prepare the values for this calculation

   Run a one-way MANOVA for two numeric response variables using Wilks’ lambda and Bartlett’s large-sample chi-square approximation. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.

2. Enter and check each input

   • group,response 1,response 2 — one observation per line: keep one record per line and preserve the column order shown in the example. Replace the example data with your own complete dataset.

   The input table gives a complete example. Keep units and time periods consistent across related fields.

3. Calculate and resolve any input error

   Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.

4. Interpret the answer

   Check MANOVA p-value first. With the unchanged example inputs, it is 0.001381126826. Compare the additional metrics with the primary result; each has its own label and unit.

5. Compare and keep a useful result

   The result diagram shows the inputs, method and output. A numeric chart is shown only when the calculation supports a meaningful numeric relationship.

   Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.

MANOVA Calculator formula

Λ=|W|/|W+B|. Bartlett approximation: χ²=−[N−1−(p+g)/2]lnΛ with p=2 responses and df=p(g−1).

Inputs and units

Worked example

Using the example inputs above, the manova p-value is 0.001381126826.

MANOVA p-value

0.001381126826

Wilks’ lambda

0.071794871795

Bartlett χ²

13.169711144742

df

2

Groups

2

Observations

8

Results and assumptions

One-way, two-response MANOVA using Bartlett’s large-sample chi-square approximation. It assumes independent multivariate-normal observations and a common within-group covariance matrix.

Fix an input or unexpected result

If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.

If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.

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