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I would like to compare different measurements in regard to agreement. Quite often this is done using a Bland-Altman plot (also called Tukey mean difference plot) in medical literature.

What I would like to do is compare more than 2 devices (namely, 4 devices). 3 of the devices are commercially available and one has been newly developed. I am eager to find out how well the newly developed device performs compared to the other ones. None of the commercially available devices can be considered a "gold standard". What would be the best way to do so?

I am currently considering the following two options (but I am open to any other solutions):

  1. Calculating a new variable "commercially_available" that is the mean of all commercially available devices and then plot the mean of the "commercially_available" and the new device vs. the difference between the "commercially_available" and the new device. (So basically, combining the measurements obtained be the commercially available devices into one measurement using the MEAN function)

  2. Creating three different plots, each comparing one commercially available device with the newly developed device.

kjetil b halvorsen
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Ihkavs
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    What is your data (is it continuous or discrete)? What do you mean by *agreement*? The second question is very important, since if you mean by agreement that $x = y$ it is very different then if you mean $|x - y| \leq \varepsilon$ and those two definitions could lead to totally different results (agreement of 0% vs 100% in some cases). – Tim Jul 20 '15 at 07:43
  • All data is continuous in this case. Ideally, agreement would be x=y, but since all devices incur an error of measurement, I would be interested in |x-y| – Ihkavs Jul 20 '15 at 07:58
  • In continuous case $P(X = x) = 0$, so defining agreement as $x=y$ makes no sens. – Tim Jul 20 '15 at 08:04
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    I am trying to clarify it: It's about measuring the concentration of a substance in blood using different devices. Any concentration is possible, therefore data is continous. Now, if I draw a blood sample and measure the concentration using 4 different devices, I (ideally) obtain 4 measurement values that are exactly the same. Now, this is very unlikely to happen (as none of the devices is "totally accurate" and each device includes a certain error). I am interested to know how accurately the newly developed device measures the concentration. – Ihkavs Jul 20 '15 at 08:26

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