I am working on a product fabrication process, and I want to demonstrate the consistency of my product. To do this, I am trying to measure the variation in the extent to which a biological material is able to deform different regions of my product. I.e. I want to show that all regions of my product deform with similar consistency, by using the Brown-Forsythe (BF) test to compare variances between groups. However, because of biological factors, the strength of the biological material varies significantly from test to test.

For example, let's say Material 1 deforms Area 1 three times, by 60 mm, 70 mm, and 80 mm. Material 2 deforms Area 2 three times, by 6 mm, 7 mm, and 8 mm.

Sample data

Assuming I know that the 10x difference in magnitude is due to differences between Material 1 and Material 2, how should I standardize these values to compare them with the BF test? The variances of these groups is 1 and 100 respectively, but to my mind these sample groups have identical variances once the effect of the different Materials is discounted. My current approach is to divide each value by the average of the set. E.g. 6/avg(6,7,8) = 0.857, 60/avg(60,70,80) = 0.857. I'm concerned that this method biases my data towards a non-significant BF test.

So: Is my method biased/is there a better way? Is my belief that the two sample columns should have identical variations after discounting the Material effect unfounded? Should I move away from the BF test approach as a whole? Also in my actual data, I have many groups of measurements but the groups each consist of 3 measurements. Is this too few for what I want?

-I'm using Levene's test as a tag for this question, as the BF test is a modified Levene's test.

  • 1
    $\begingroup$ What you did is called scaling, you could try standardizing as well, that is further diving by each group standard deviation. Then each group will have mean 0 and standard deviation equal to 1. $\endgroup$ – user2974951 Feb 11 at 8:40

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