Ratio? I don't need no stinking F ratio!

In completing the analysis of the antibody aggregate and its dependence upon the load and load conductivity, I mentioned the ANOVA results:

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	1	0.00001758	0.000018	22.0356
Error	8	0.00000638	7.979e-7	Prob > F
C. Total	9	0.00002397		0.0016*

There's a lot of data in this table and worth leveraging in your discussions.  Recall that the modeling results found
Aggregate % = Load*Load Conductivity

In the table, the DF stands for degrees of freedom. The model has 1 DF because only the load*load conductivity is the active term.  That leaves 8 DF to estimate the pure error.  We estimate the error for the model and the pure error by dividing the Sum of Squares term by associated DF.  The F ratio is the ratio of the Mean Square Model to the Mean Square Error (22.0356, in this case).  The F ratio gives a quantitative measure of how well the model fits the data better than say chance.  What makes a good F ratio?  The key is to use a table of F ratios with the associated degrees of freedom.  In this case, for a system with 1 DF in the model and 8 DF in the error term an F ratio (at the 95% CI level) would need to be greater than 5.32 to be considered significant.  Our result, at 22 is 4x higher.  As a result, we can conclude the model is significantly better than chance at explaining the output variation.  I've read, and I'll have to get the source from work, that a good rule of thumb is to have an F ratio that is 3-10x greater than required by the 95% CI.  This gives the process engineer a high degree of confidence that the model is meaningful.

Once the model is demonstrated to be significant, the Mean Square Error term can be used to estimate the standard deviation resulting from the experiment itself.  This is obtained by the square root of the Mean Square Error, or 0.0009 in this case.  The value is about 2 orders of magnitude below the precision of the SEC method (about 0.01%).  The implication is that the pure error resulting from sample prep, day to day variation, etc is way below the assay precision which lends further support to predictions made from the model.