Again if no measurement error exists in any of the three testing procedures, Equations xx, xx and xxx and hence \(e_{rs}\), \(e_{os}\)and \(e_{qs}\) would be 0. Equations 3, 5 and 6 (the equations containing \(e_{rot}\)) 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 \(e_{rs}\), \(e_{os}\) and and and \(e_{qs}\) 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 assumption 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 variance (assuming the samples are arbitrarily aligned). The distribution would be the expected difference between the cuts and it would become possible to estimate 95% confidence bounds on the value of another hypothetical cut on the same sample.
Unfortunately none of these tests have zero measurement error, however, because 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. test. test. Note that this is not necessarily 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 distribution formed by the same test run on the same sample in the same orientation an infinite number of times, i.e. the precision of the testing procedure. times, i.e. the precision of the testing procedure. times, i.e. the precision of the testing procedure, the true value. The QS2 test encompasses two types of error, \(e_{rot}\), discussed above, and \(e_{qs}\), the error associated with the quartering test with respect to the RS and OS tests. Fortunately because this test is used twice on each sample, the two errors are separable.