Calculator
Example Data Table
| Design item | Example value | Meaning |
|---|---|---|
| Factor A levels | 3 | Three teaching methods |
| Factor B levels | 4 | Four study times |
| Replications per cell | 5 | Five observations in each treatment cell |
| Omnibus tests | 3 | A, B, and A × B |
| Pairwise A tests | 3 | 3(3 - 1) / 2 |
| Pairwise B tests | 6 | 4(4 - 1) / 2 |
Formula Used
Cells: ab
Total observations: abn
Omnibus tests: A main effect + B main effect + A × B interaction
Pairwise A tests: a(a - 1) / 2
Pairwise B tests: b(b - 1) / 2
All cell pairwise tests: (ab)(ab - 1) / 2
Simple A effects: b
Simple B effects: a
Simple pairwise A inside B: b × a(a - 1) / 2
Simple pairwise B inside A: a × b(b - 1) / 2
Bonferroni alpha: alpha / total tests
Sidak alpha: 1 - (1 - alpha)1 / total tests
How to Use This Calculator
- Enter the number of levels for factor A.
- Enter the number of levels for factor B.
- Enter the replications per cell.
- Set the family alpha value.
- Select omnibus, pairwise, simple effect, and contrast options.
- Press Calculate to view results above the form.
- Use CSV or PDF download buttons for reporting.
Two Way ANOVA Test Planning
Why Test Count Matters
Two way ANOVA often creates more than one statistical test. The usual model checks factor A, factor B, and their interaction. Those three omnibus tests answer broad questions. Many studies also need follow up comparisons. This calculator counts those extra tests before the analysis starts.
Test counting matters because each test adds another chance of a false positive. A clean count helps you plan Bonferroni, Sidak, or Holm adjustments. It also helps you write methods sections. Your reader can see how many questions were tested.
Design Inputs
The calculator accepts the number of levels in two factors. It also accepts replications per cell. Replications do not change the number of tests. They do change the degrees of freedom. This is useful when checking whether the design has enough data.
You can include or remove omnibus tests. You can count pairwise tests across factor A levels. You can count pairwise tests across factor B levels. You can also count all cell mean comparisons. These are larger families. They grow quickly as levels increase.
Simple Effects and Contrasts
Simple effects are also included. A simple A effect tests factor A inside each level of B. A simple B effect tests factor B inside each level of A. Simple pairwise comparisons go deeper. They compare levels within each slice of the other factor.
Planned contrasts are entered as a separate number. This keeps the tool flexible. You may have custom theory based comparisons. You may also have orthogonal contrasts. Enter only the contrasts you truly plan to test.
Interpreting the Output
The output gives a total test count. It also gives family alpha values. Bonferroni divides alpha by the number of tests. Sidak gives a slightly different threshold. Holm starts with the same smallest threshold, then steps upward.
Use the result as a planning guide. It does not run the ANOVA itself. It counts the tests that may follow from your design. Always choose tests before looking at outcomes. This reduces bias and improves reporting.
For balanced designs, the count is easy to inspect. For larger designs, manual counting becomes risky. This tool keeps every selected family visible. You can review rows, remove families, and export the same calculation for a worksheet or report. Review it before finalizing your analysis plan carefully.
FAQs
1. What does this calculator count?
It counts selected tests in a two way ANOVA plan. This includes omnibus tests, pairwise comparisons, simple effects, simple pairwise tests, and planned contrasts.
2. Does it run the ANOVA?
No. It does not analyze raw data. It counts tests from the design structure and selected comparison families.
3. What are omnibus tests?
Omnibus tests are broad ANOVA tests. In two way ANOVA, they usually test factor A, factor B, and the A × B interaction.
4. Why include replications per cell?
Replications help calculate degrees of freedom. They do not change the number of comparison tests, but they describe the design more fully.
5. What is a simple effect?
A simple effect tests one factor within one level of the other factor. It is often used after a meaningful interaction.
6. What are all cell mean pairs?
They compare every treatment cell mean with every other cell mean. This family can become large in bigger designs.
7. What is Bonferroni alpha?
Bonferroni alpha divides the chosen alpha by the total number of tests. It is a simple multiple testing adjustment.
8. Can I add custom contrasts?
Yes. Enter the number of planned contrast tests. The calculator adds them to the total test count.