Interpret the key results for Fully Nested ANOVA

Complete the following steps to interpret a fully nested ANOVA. Key output includes the p-value and the variance components.

Step 1: Determine whether the association between the response and the term is statistically significant

To determine whether the association between the response and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis. The null hypothesis is that there is no association between the term and the response. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that an association exists when there is no actual association.
P-value ≤ α: The association is statistically significant
If the p-value is less than or equal to the significance level, you can conclude that there is a statistically significant association between the response variable and the term.
P-value > α: The association is not statistically significant
If the p-value is greater than the significance level, you cannot conclude that there is a statistically significant association between the response variable and the term. You may want to refit the model without the term.
If there are multiple predictors without a statistically significant association with the response, you can reduce the model by removing terms one at a time. For more information on removing terms from the model, go to Model reduction.

All factors in a fully nested ANOVA model are random. Consequently, a factor that is statistically significant indicates that it contributes to the amount of variation in the response.

Analysis of Variance for Temp Source DF SS MS F P Plant 3 731.5156 243.8385 5.854 0.011 Operator 12 499.8125 41.6510 1.303 0.248 Shift 48 1534.9167 31.9774 2.578 0.000 Batch 128 1588.0000 12.4062 Total 191 4354.2448
Key Results: P-Value

In these results, the ANOVA table indicates that plant and shift are statistically significant at the 0.05 level. The operator effect is not statistically significant at the 0.05 level. The effects in the model use all of the degrees of freedom, so no degrees of freedom remain to test the statistical significance of the different batches.

Step 2: Examine the variance components

Examine the variance components to determine how much of the variation in the study can be attributed to each random term. Higher values indicate that the term contributes more variability to the response.

Variance Components % of Source Var Comp. Total StDev Plant 4.212 17.59 2.052 Operator 0.806 3.37 0.898 Shift 6.524 27.24 2.554 Batch 12.406 51.80 3.522 Total 23.948 4.894
Key Results: Variance components

In these results, the variance component estimates indicate that the variability attributable to batches, shifts, and plants was 52%, 27%, and 18%, respectively, of the total variability.

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