Dear all,

We are trying to validate a new measurement method by comparing it to a reference method, but we don't manage to find out how to do it...

Here are the data we have :

***
Sample# ; Ref_1 ; Ref_2 ; Ref_3 ; Ref_4 ; Ref_5 ; Ref_6 ; Ref_7 ; Ref_8 ; Ref_9 ; Ref_10 ; New_1 ; New_2 ; New_3 ; New_4 ; New_5 ; New_6 ; New_7 ; New_8 ; New_9 ; New_10
1 ; 58 ; 56 ; 60 ; 64 ; 76 ; 78 ; 73 ; 73 ; 83 ; 76 ; 61 ; 70 ; 61 ; 61 ; 54 ; 48 ; 60 ; 56 ; 82 ; 63
2 ; 46 ; 51 ; 48 ; 57 ; 61 ; 74 ; 54 ; 63 ; 60 ; 71 ; 77 ; 69 ; 53 ; 56 ; 58 ; 61 ; 64 ; 63 ; 57 ; 71
3 ; 60 ; 79 ; 68 ; 69 ; 70 ; 67 ; 68 ; 71 ; 66 ; 72 ; 76 ; 68 ; 53 ; 82 ; 40 ; 58 ; 51 ; 66 ; 87 ; 68
4 ; 67 ; 59 ; 52 ; 63 ; 61 ; 60 ; 57 ; 54 ; 61 ; 62 ; 71 ; 45 ; 66 ; 56 ; 55 ; 66 ; 56 ; 63 ; 56 ; 76
5 ; 100 ; 112 ; 89 ; 96 ; 111 ; 78 ; 91 ; 93 ; 96 ; 93 ; 92 ; 81 ; 82 ; 102 ; 89 ; 82 ; 69 ; 68 ; 73 ; 98
6 ; 88 ; 77 ; 93 ; 81 ; 77 ; 70 ; 83 ; 67 ; 84 ; 94 ; 81 ; 80 ; 54 ; 101 ; 77 ; 91 ; 104 ; 66 ; 80 ; 92
7 ; 31 ; 48 ; 44 ; 33 ; 49 ; 47 ; 38 ; 33 ; 29 ; 39 ; 21 ; 40 ; 30 ; 27 ; 25 ; 29 ; 25 ; 21 ; 26 ; 37
8 ; 33 ; 40 ; 20 ; 31 ; 30 ; 28 ; 20 ; 25 ; 29 ; 34 ; 30 ; 32 ; 18 ; 32 ; 22 ; 28 ; 27 ; 35 ; 17 ; 28
9 ; 34 ; 31 ; 32 ; 37 ; 38 ; 26 ; 22 ; 40 ; 43 ; 23 ; 26 ; 37 ; 39 ; 33 ; 35 ; 41 ; 26 ; 27 ; 24 ; 36
10 ; 45 ; 47 ; 53 ; 49 ; 47 ; 62 ; 44 ; 55 ; 52 ; 50 ; 59 ; 32 ; 40 ; 43 ; 46 ; 56 ; 34 ; 38 ; 44 ; 56
***

First line are headers.
The 10 following lines refer to 10 independent samples.
On each line, the first column is the sample number, the next 10 columns are reps of measurements performed with the "reference method", and the 10 last columns are reps of measurements performed with the "new method" we would like to validate.

Each of the 20 reps measurements are performed on distinct subsets of the sample, so they're not supposed to be identical (in particular, Ref_i and New_i are performed on different subsets)

Let's come to our question : we would like to statistically validate the fact that the new measurement method is "as good as" the older one. At the end, what interests us is the average of the 10 measurements we perform. Ouf course, there always are some differences between the averages obtained by the reference and the new method, but we are convinced this difference is actually "contained" within the "subseting" fluctuation.

We've been told using a Bonferroni correction would be a good way to address our problem, but despite reading quite a lot of documentation, we were unable to find out how to implement it. 

All the examples we've seen apply Bonferroni correction to pairwise tests between 2 vectors, can it actually be applied to a set of paired vectors as in our data? 
Or should we just compare the averages of the reference and the new measurement methods for each sample?
Finally, will this test actually answer our question, or would be another data treatment more appropriated?

Thanks in advance for your help, it will be very appreciated since we're running out of resources to solve our issue...

Best regards,
Stephanie
 		 	   		  
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