Do you really want to test that the accelerometers are the "same", or is it sufficient to test for "at least one accelerometer is clearly different from the others". The reason is that the first is an equivalence test where two one-sided tests (TOST), or some generalization of that, would be used (ANOM ?), and you have to state what the boundaries on the equivalence interval are. For the second, an ANOVA would suffice (although you may want to fit a generalized linear model, depending on the residuals and a histogram plot). The issue with the equivalence test approach is that there are 36 pairwise comparisons, all of which would have to pass the equivalence criteria in order to say that the instruments were the "same". If one of the accelerometers is accepted as a standard, the number of comparisons drops to 8, and that may be tractable.   SteveDenham ... View more