Pedro Mardones wrote on 09/20/2011 12:46:54 PM:
> 
> Dear all;
> 
> A very basic question. I have the following data:
> 
> 
************************************************************************************
> 
> A <- 1/1000*c(347,328,129,122,18,57,105,188,57,257,53,108,336,163,
> 62,112,334,249,45,244,211,175,174,26,375,346,153,32,
> 89,32,358,202,123,131,88,36,30,67,96,135,219,122,
> 89,117,86,169,179,54,48,40,54,568,664,277,91,290,
> 116,80,107,401,225,517,90,133,36,50,174,103,192,150,
> 225,29,80,199,55,258,97,109,137,90,236,109,204,160,
> 95,54,50,78,98,141,508,144,434,100,37,22,304,175,
> 72,71,111,60,212,73,50,92,70,148,28,63,46,85,
> 111,67,234,65,92,59,118,202,21,17,95,86,296,45,
> 139,32,21,70,185,172,151,129,42,14,13,75,303,119,
> 128,106,224,241,112,395,78,89,247,122,212,61,165,30,
> 65,261,415,159,316,182,141,184,124,223,39,141,103,149,
> 104,71,259,86,85,214,96,246,306,11,129)
> 
> B <- 1/1000*c(351,313,130,119,17,50,105,181,58,255,51,98,335,162,
> 60,108,325,240,44,242,208,168,170,27,356,341,150,31,
> 85,29,363,185,124,131,85,35,27,63,92,147,217,117,
> 87,119,81,161,178,53,45,38,50,581,661,254,87,281,
> 110,76,100,401,220,507,94,123,36,47,154,99,184,146,
> 232,26,77,193,53,264,94,110,128,87,231,110,195,156,
> 95,51,50,75,93,134,519,139,435,96,37,21,293,169,
> 70,80,104,64,210,70,48,88,67,140,26,52,45,90,
> 106,63,219,62,91,56,113,187,18,14,95,86,284,39,
> 132,31,22,69,181,167,150,117,42,14,11,73,303,109,
> 129,106,227,249,111,409,71,88,256,120,200,60,159,27,
> 63,268,389,150,311,175,136,171,116,220,30,145,95,148,
> 102,70,251,88,83,199,94,245,305,9,129)
> 
> 
************************************************************************************
> 
> plot(A,B)
> abline(0,1)
> 
> At a glance, the data look very similar. Data A and B are two
> measurements of the same variable but using different devices (on a
> same set of subjects). Thus, I thought that a paired t-test could be
> appropriate to check if the diff between measurement devices = 0.
> 
> t.test(A-B)
> 
> 
************************************************************************************
> 
> One Sample t-test
> 
> data:  A - B
> t = 7.6276, df = 178, p-value = 1.387e-12
> alternative hypothesis: true mean is not equal to 0
> 95 percent confidence interval:
>  0.002451622 0.004162903
> sample estimates:
>   mean of x
> 0.003307263
> 
> 
************************************************************************************
> The mean diff is 0.0033 but the p-value indicates a strong evidence to
> reject H0.
> 
> I was expecting to find no differences so I'm wondering whether the
> t-test is the appropriate test to use. I'll appreciate any comments or
> suggestions.
> 
> BR,
> PM


The paired t-test could very well be an appropriate test to use, depending 
on the design of the study.

If you look at the distribution of difference between A and B it certainly 
looks like the mean of that distribution is not 0:

hist(A-B, nclass=50)
abline(v=0, lwd=2)

Perhaps what you need to think about is the difference between statistical 
significance and "practical" significance.  Is a difference of about 2% 
between measurement devices "important"?

Jean

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