Ted Harding wrote on 09/20/2011 05:26:58 PM:
>
> Further to the plot suggested below, the plot
>
> plot(log(A),log(B/A),pch="+",col="blue")
>
> reveals an interesting structure to the data. Distinct curved
> sequences are clearly visible. While their curved form is a
> consequence of the fact that, for large A, A/B is close to 1
> and so they tend to approach 1 "asymptotically" (hence the
> curving over towards flatness), what is really interesting
> is the appearance of distinct curves, as if there were at least
> 7 (or at least 8) distinct subsets to the data, each subset
> following a different curve. Perhaps these are related to
> observed variables?
>
> Ted.
The distinct curves that you observed are a side effect of the data being
rounded to the nearest thousandth. They disappear if noise is added to
the data.
a <- A + runif(length(A), -0.0005, 0.0005)
b <- B + runif(length(B), -0.0005, 0.0005)
plot(a, b/a, log="xy")
Jean
> On 20-Sep-11 18:15:50, Ted Harding wrote:
> > As can be seen by plotting as follows:
> >
> > plot(A,B,pch="+",col="blue") ## The raw data
> >
> > plot(A,B-A,pch="+",col="blue") ## The differences versus A
> > lines(c(0,0.7),c(0,0))
> >
> > Ted.
> >
> > On 20-Sep-11 17:54:15, Timothy Bates wrote:
> >> Yes, in over 3/4s of the data points A is > B? which suggests the A
> >> measure is reading higher than the B measuring system.
> >>
> >> length(A[A>B])/length(A)
> >>
> >>
> >> On 20 Sep 2011, at 6:46 PM, Pedro Mardones 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.
> >
> > --------------------------------------------------------------------
> > E-Mail: (Ted Harding) <ted.hard...@wlandres.net>
> > Fax-to-email: +44 (0)870 094 0861
> > Date: 20-Sep-11 Time: 19:15:47
>
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <ted.hard...@wlandres.net>
> Fax-to-email: +44 (0)870 094 0861
> Date: 20-Sep-11 Time: 23:26:53
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