10.8: One-Way ANOVA Calculations Chart
- Page ID
- 50151
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Phase 1: Calculations For Each Group |
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Find the five statistics that focus on calculations for each group, one by one.* |
Sample Sizes |
Means |
Sum of Squares Within |
Standard Deviations |
Sum of Squares Between |
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Group 1 |
\(n_1\) = |
\(\bar{X_1}\)= |
\(SS_{w1}\)= |
\(s_1\) = |
\(SS_{b1}\) = |
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Group 2 |
\(n_2\) = |
\(\bar{X_2}\)= |
\(SS_{w2}\)= |
\(s_2\) = |
\(SS_{b2}\) = |
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Group 3 |
\(n_3\) = |
\(\bar{X_3}\)= |
\(SS_{w3}\)= |
\(s_3\) = |
\(SS_{b3}\) = |
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Phase 2: Summary Calculations |
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Find the five statistics that use data across groups. |
Summary Components |
\(N\) = |
\(\bar{X}_{\text {grand }}\) = |
\(SS_{w}\) = |
\(k\) = |
\(SS_{b}\) = |
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Find both forms of degrees of freedom. |
Degrees of Freedom |
\(d f_w\) = |
\(d f_b\) = |
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Phase 3: ANOVA (omnibus) Calculations |
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Plug the parts into the ANOVA formula and find \(F\). |
Between |
\(SS_{b}\) = |
\(d f_b\) = |
\(MSS_{b}\) = |
\(F\) = |
Critical Value = |
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Within |
\(SS_{w}\) = |
\(d f_w\) = |
\(MSS_{w}\) = |
Is the result significant? |
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Phase 4: Post-ANOVA Calculations |
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If ANOVA is significant, complete follow-up calculations. |
Follow-Up |
Formula |
How to use and interpret it: |
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Effect Size |
\(\eta^2=\dfrac{S S_b}{S S_T}\) |
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Post-Hoc (Tukey) |
\(HSD=q \sqrt{\dfrac{M S_w}{n}}\) |
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*Note: The first section shows room for three groups, however, rows can be added to accommodate the data when using ANOVA to compare more than three groups.