# What is an “Unpaired Bland-Altman plot”?

I found this quote:

Unpaired Bland-Altman plots were used to check systematic or bias errors in the SPECT myocardial uptake coefficients with respect to the reference standard PET data.

in the following paper:

ALHASSEN, Fares, et al. Myocardial blood flow measurement with a conventional dual-head SPECT/CT with spatiotemporal iterative reconstructions-a clinical feasibility study. American journal of nuclear medicine and molecular imaging, 2014, 4.1: 53.

My knowledge of "Bland-Altman plot" is the following:

I have $n$ distinct objects and two instruments, A and B; the instruments measure a property $w$ of the objects.

$\mathbf{w}_A\in{\mathbb{R}}^n$, $\mathbf{w}_A=[w_{1A},w_{2A},\ldots,w_{nA}]$ and $w_{iA}$ is the measurement of the $i$-th object made with instrument A.

$\mathbf{w}_B\in{\mathbb{R}}^n$, $\mathbf{w}_B=[w_{1B},w_{2B},\ldots,w_{nB}]$ and $w_{iB}$ is the measurement of the $i$-th object made with instrument B.

The plot is made by the $n$ points $p_i(x_i,y_i)$ where

$\mathbf{x}\in{\mathbb{R}}^n$, $\mathbf{x}=\frac{\mathbf{w}_A+\mathbf{w}_B}{2}=[x_1,x_2,\ldots,x_n]$

$\mathbf{y}\in{\mathbb{R}}^n$, $\mathbf{y}=\mathbf{w}_A-\mathbf{w}_B=[y_1,y_2,\ldots,y_n]$

So, what is an "Unpaired Bland-Altman plot" and how it's made?

• @Penguin_Knight Thank you. If you convert your comment to an answer I will be glad to accept it. – Alessandro Jacopson Feb 26 '14 at 17:14
• Note that Bland-Altman is a widely accepted name within medical statistics (biostatistics), but not necessarily outside. The name is fitting in so far as Martin Bland and Douglas Altman wrote several very widely read expositions of method comparison, stressing this plot as one of the things to use. But plotting difference versus mean is a much older idea, being used by Tukey from the early 1960s if not earlier and by Neyman in the 1950s, and quite likely much earlier. – Nick Cox Feb 27 '14 at 16:29
• I sent this to Martin Bland, who said (as @NickCox already has) "I tried to comment [but failed], just to say that we never claimed priority for plotting difference versus mean and that adding the limits of agreement was our contribution." – Jeremy Miles Feb 27 '14 at 18:15
• That's entirely consistent with my comment, I think. – Nick Cox Feb 27 '14 at 18:24