Thanks for all the replies and comments. I've followed Marc's suggestion of using the Bland-Altman's approach which I found pretty clarifying for comparing data collected on the same subjects.
BR, PM On Wed, Sep 21, 2011 at 1:39 PM, Marc Schwartz <marc_schwa...@me.com> wrote: > Jeremy, > > Correlation alone is irrelevant when comparing two separate sets of > measurements on the same specimen. Correlation does not mean good agreement, > but good agreement tends to infer high correlation. > > T1 <- rnorm(50, mean = 100) > >> mean(T1) > [1] 99.80257 > > T2 <- T1 * 1.5 > >> mean(T2) > [1] 149.7039 > > The two measures are off by a systematic 50%, but: > >> cor(T1, T2) > [1] 1 > > > The key here, as I noted in my reply yesterday and as Greg noted in his this > morning regarding Bland-Altman, is whether or not the two measures agree > within an acceptable margin of error and whether or not there is systematic > bias in the measures, either overall or perhaps one measure tends to be low > at one end of the range, while high at the other. > > HTH, > > Marc Schwartz > > > On Sep 21, 2011, at 11:20 AM, Jeremy Miles wrote: > >>> cor(A, B) >> [1] 0.9986861 >> >> The data are very, very highly correlated. The higher the correlation, >> the greater the power of the t-test to detect the same difference >> between the means. >> >> Jeremy >> >> On 20 September 2011 10:46, Pedro Mardones <mardone...@gmail.com> wrote: >>> 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 >>> >>> ______________________________________________ >>> R-help@r-project.org mailing list >>> https://stat.ethz.ch/mailman/listinfo/r-help >>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >>> and provide commented, minimal, self-contained, reproducible code. >>> >> >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
