ICP: Applying F Test Results

Dear A.H.,

The significance of apparent differences in two estimates of a standard deviation is of interest in situations such as yours, i.e. where there are possible changes in precision when analyzing control chart data. Do the two methods used differ in their precisions? Is one analyst, instrument, or laboratory producing more precise results than another?

I'm assuming that you have a standard deviation for your data with a given number of degrees of freedom (N-1). If you're looking to determine if your precision is significantly different (in this case larger) than a data set from another laboratory, company, operator, etc., then the F test will help in making that determination. The statistical significance of apparent differences can be judged on the basis of an F test, conducted as follows:

Let s1 = standard deviation (larger and—I am assuming—your value) based upon N measurements

Let s2 = standard deviation that you're comparing your results to (from another operator, laboratory, test method, etc.) with D measurements

The F tables will ask for degrees of freedom, which will be N-1 for s1 and D-1 for s2. Calculate F = (s1)2/(s2)2 (the numerator is always the larger standard deviation in this equation). Look up the critical of F (Fc) from the F table (you can find these on the web). To use the table, go to the column with the correct number of degrees of freedom for s1 and then go down that column to where it intersects the row for the correct number of degrees of freedom for s2. If the value of Fc is greater than your calculated value of F, then s1 and s2 are not significantly different, i.e. they can be considered the same. If Fc < F, then s1 and s2 are different. This suggests that your precision is significantly larger/different.

I know this seem rather involved, but it's fairly straight forward. Take a look at the following F test instructions for clarification. Please feel free to call me if you need help performing the calculations.

Serving you in chemistry,
Paul R. Gaines, Ph.D.
CEO of Inorganic Ventures & Fellow Chemist

DISCLAIMER: Advice offered by the chemists at Inorganic Ventures is intended for the individual posing the question. Feel free to contact us to verify whether these suggestions apply to your unique circumstances.