"2 Variances" test for Paired Data in Minitab - How to proceed

[Berg.Jlle]

In Reply to Parent Post by Miner

Take a look at the attached analysis. Ask any specific questions that you may have, and I will respond.

The biggest concern that I would haveover this data is that you would expect the data to fall on either side of a 45 degree line. The Orthogal regression equation should be close to B = A. In this case the slope of the line is close to 1.3 instead of 0. There is also an overall bias greater than -2 for the means. Now, the 2-sample t and the test for equal variances both indicate that this is not significant, and that is true FOR THE RANGE OF VALUES STUDIED. If you exceed this range, there is every indication that it will become significant.

Hi Miner.

I checked the file attached and I have some questions:

1) Using the regression orthogonal, we have the equation B = - 2.854 + 1.280*A. In order to consider that the two instruments (A and B) measure the same thing, the slope must be 1 and the constant 0, instead of 1.280 and -2.854, respectively.
Since these conditions are not met, can I conclude that the instruments A and B do not measure the variability equally. Right ?

2) Using the test for "2 Variances", this shows that there is no significant difference between the devices A and B, contrary to what was stated with regression orthogonal test in item #1.
Can I conclude that the test "2 Variances" does not show the reality and that the variability of instruments A and B are really different ?

3) To make the orthogonal regression analysis you used the "Error Variance Ratio" (B/A) equals to 1.
How did you come to that conclusion/valor ?

[Miner]

Questions 1 & 2) If you take the results of the orthogonal regression, the Bland Altman Plot, the paired t-Test and the test for equal variances together, I would draw the following conclusion. The slope between tests A and B is not equal to 1 and there is a bias between the two tests. Within the range of data that you evaluated, this difference is not statistically significant and the two test method could be treated as equivalent. HOWEVER, there is a strong indication that if you were to exceed this range of data, that difference would become statistically significant. As I see it you have three options:

1. If you intend to stay within the range of data, use the two tests as equivalent.
2. Expand the range of testing, solidify the orthogonal regression equation, and use it to correct the results of the new test.
3. Reject the new test and try another.

Question 3) That is based on the best information that you have available at the time and was supported by the test for equal variances. If you follow option 2 above, you will have better data, and should revise the Error Variance Ratio to fit your new data.