Hello,
I performed a variance components analysis in Minitab. I have 3 factors (Mixer, 2 levels; Batch, nested in mixer, 5 batches/mixer; box, nested in batch, 5 boxes/batch) and a covariate. The ANOVA and the table of variance components looks as follows:
Analysis of Variance for Can PSI, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F P
Net Wt (gm) 1 1347.660 646.910 646.910 1043.76 0.000
Mixer 1 44.177 45.305 45.305 2.09 0.187 x
Batch(Mixer) 8 173.732 172.638 21.580 11.85 0.000 x
Box(Mixer Batch) 40 74.852 74.852 1.871 3.02 0.000
Error 545 337.784 337.784 0.620
Total 595 1978.205

x Not an exact F-test.


S = 0.787266 R-Sq = 82.92% R-Sq(adj) = 81.36%


Term Coef SE Coef T P
Constant -45.216 1.921 -23.54 0.000
Net Wt (gm) 0.172733 0.005347 32.31 0.000

Expected Mean Squares, using Adjusted SS

Source Expected Mean Square for Each Term
1 Net Wt (gm) (5) + Q[1]
2 Mixer (5) + 11.4043 (4) + 57.0215 (3) + 285.1077 (2)
3 Batch(Mixer) (5) + 11.3292 (4) + 56.6458 (3)
4 Box(Mixer Batch) (5) + 11.8032 (4)
5 Error (5)


Error Terms for Tests, using Adjusted SS

Source Error DF Error MS Synthesis of Error MS
1 Net Wt (gm) 545.00 0.620 (5)
2 Mixer 8.00 21.719 1.0066 (3) - 0.0066 (5)
3 Batch(Mixer) 41.12 1.821 0.9598 (4) + 0.0402 (5)
4 Box(Mixer Batch) 545.00 0.620 (5)


Variance Components, using Adjusted SS

Estimated
Source Value
Mixer 0.08273
Batch(Mixer) 0.34881
Box(Mixer Batch) 0.10603
Error 0.61979

Can anyone tell me how to interpret this last Variance components table? For each factor, what is the % of total variance (taking into account the covariate)?
Thank you very much!
Despina

From Minitab Help:
Variance components

Use to evaluate sources of variation. In Minitab, components of variance are used in ANOVA and Gage R&R.
ANOVA

Variance components assess the amount of variation in the response due to random factors. Random factors have levels that are selected at random; whereas fixed factors have levels that are controlled by the experimenter. For example, you conduct a study on the effect of two levels of pressure on output measured by randomly chosen operators. Pressure is fixed (2 levels); and operator is random. The variance components output lists the estimated variance for the operator and error term.

See NIST Statistical Handbook (http://www.itl.nist.gov/div898/handbook/prc/section4/prc44.htm)for information on interpretation.