Are devices exposed to the same exposure measuring the same? WHICH TEST?

[mariia8b]

Hello! 

SAS newbie here, so I hope someone can help me!

A little context: 

I did an experiment where I attached nine acceloremeters to a blood turner.
The acceloremeters detects movement and collects data every 60 second as 'Counts per minute' (CPM). The blood turner turned for 10 minutes. That means I have 10 measurements for each accelerometer (9 x 10 measurements in total). The rotation was constant and all the nine accelerometers were attached at the same time. 

The aim of the experiment was to examine whether the accelerometers measures the same movement - maybe some kind of reliability test(?). Since the accelerometers were exposed to the same rotation my hypothesis is that there is no difference between the measurements. However, I am unsure about what is the right approach to this including which statistical test I should do? 

To make a long story short: I want to examine if the different accelerometers are measuring the same when the exposure, the rotation, is the same.

I hope someone can help. I'm really desperate 🙂 

Best regards
Maria

My data: 

Time	accelerometer_ID	CPM
00:01	1	23871,13
00:02	1	24357,09
00:03	1	23883,17
00:04	1	23843,27
00:05	1	23810,54
00:06	1	23824,35
00:07	1	23827,39
00:08	1	23819,94
00:09	1	23827,7
00:10	1	23834,48
00:01	2	23482,77
00:02	2	23323,05
00:03	2	23514,34
00:04	2	23507,99
00:05	2	23520,11
00:06	2	23495,93
00:07	2	23482,15
00:08	2	23501,74
00:09	2	23487,59
00:10	2	23309,01
00:01	3	24367,35
00:02	3	25030,93
00:03	3	23924,86
00:04	3	23824,59
00:05	3	23805,19
00:06	3	23789,9
00:07	3	23800,91
00:08	3	23782,73
00:09	3	23798,33
00:10	3	23833,54
00:01	4	23788,85
00:02	4	23621,23
00:03	4	23759,49
00:04	4	23810,91
00:05	4	23821,34
00:06	4	23800,15
00:07	4	23802,32
00:08	4	23820,26
00:09	4	23794,8
00:10	4	23808,73
00:01	5	23523,54
00:02	5	23563
00:03	5	23471,06
00:04	5	23504,21
00:05	5	23503,65
00:06	5	23521,73
00:07	5	23506,33
00:08	5	23491,45
00:09	5	23524,15
00:10	5	23523,19
00:01	6	23501,65
00:02	6	23612,43
00:03	6	23531,49
00:04	6	23567,37
00:05	6	23592,66
00:06	6	23587,56
00:07	6	23569,51
00:08	6	23577,08
00:09	6	23569,36
00:10	6	23565,01
00:01	7	23668,53
00:02	7	24571,37
00:03	7	23833,24
00:04	7	23755,22
00:05	7	23765,99
00:06	7	23740,07
00:07	7	23724,57
00:08	7	23760,98
00:09	7	23727,77
00:10	7	23740,25
00:01	8	23789,84
00:02	8	24796,97
00:03	8	23912,49
00:04	8	23818,4
00:05	8	23820,1
00:06	8	23822,9
00:07	8	23804,95
00:08	8	23807,48
00:09	8	23830,52
00:10	8	23806,69
00:01	9	24538,05
00:02	9	26018,59
00:03	9	24001,34
00:04	9	23740,09
00:05	9	23735,53
00:06	9	23679,07
00:07	9	23726,67
00:08	9	23695,23
00:09	9	23701,06
00:10	9	23543,47

[StatDave]

Since it's always good to start by plotting the data, the picture from the following makes them look pretty different  I assume that the CPM values are decimal values even though you say they are counts, suggesting integers. 

proc sgplot;
series y=cpm x=time/group=id;
run;

There appears to be several IDs that spike upwards at time=2 and several that don't. If you want to compare the centers of the values, it's probably best to use a nonparametric test that doesn't assume a distribution for the values, such as this.

proc npar1way wilcoxon;
class id;
var cpm;
run;

Results suggest the centers of the ID distributions are not the same which is also suggested in the plot even when ignoring time 2.

[SteveDenham]

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