Again if no measurement error exists in any of the the three testing procedures, Equations 1, 2 and 4 and hence ers, eos and eqs would be 0. Equations 3, 5 and 6 (the equations containing erot) would only also be zero if all of the stems contain a completely homogeneous strain field - in reality this is not the case, and therefore, if eros, eos and eqs are zero, any differences between QS2 and other tests would be the result of the change in strain by cutting the sample at a different angle. If this asumption were to hold, the difference between the results from the first cut and the results from the second would provide a distribution with a mean of zero and a non-zero varance (assuming the samples are abataraly aligned). The distribution would be the expected difference between the cuts and it would become posable to estimate 95% confidence bounds on the value of another hypothetical cut on the same sample.
Unfortunately none of these tests have zero measurment error, however, beacuse there are three tests which should all produce the same result (as they are measuring the same thing) we can estimate the error associated with each test. Note that this is not nessaserally the error from the "true" value, but error in the sense of what confidence we can hold that the result of one sample from one test can estimate the hypothetical mean of the distrobution formed by the same test run on the same sample in the same orentation an infinite number of times. The QS2 test encompasses two types of error, erot, discussed above, and eqs, the error associated with the quartering test with respect to the RS and OS tests. Fortunately because this test is used twise on each sample, the two errors are separable, eqs is a measurement error identified by the differences contained equations 2 and 4, while eqs and erot are both present in equations 3, 5 and 6 making the two errors separable.