## The deviation of the differences. A Bland-Altman plot is

The limits of agreement are calculated with the following formulas:
If the differences of the data are normal distributed, 95\% of the data will be between the upper and lower limit of agreement. If it is unsafely which distribution the differences follow, a histogram can be made. If the tail is long or the distribution is skew, the assumption of a normal distribution does not hold, and other techniques must be used to estimate the limits of agreement. These techniques will be explained later in this thesis.
A starting point to analysis agreement is to look at the paired difference of the two measurements. The mean difference is called the bias. About the mean difference there will be some variation and this variation can be found as the standard deviation of the differences. The limits of agreement can be calculated using the bias and standard deviation of the differences.
A Bland-Altman plot is a plot which shows the mean-values for the paired measurements on the \$x\$-axis and the difference-values from the paired measurements on the \$y\$-axis.
Instead a Bland-Altman plot is a useful tool to assess the agreement. Bland-Altman is a common plot in clinical analysis which is used to check if a new measurement method can replace the old measurement method (cite{Altman} Altman and Bland 1986). Bland-Altman plot can also be used to check that values (for example the SUV value) in repeated measurement agrees.\
A classical common method for seeing the relation between two variables, is to plot the data where one measurement method is on the \$x\$-axis and the other measurement method is on the \$y\$-axis. The line of equality is draw, which all points would lie on the line, if the two measurement methods give exactly the same reading every time. From the plot it is possible to calculate the correlation coefficient which can give an idea about the relation for the two measurement methods. A big mistake would be to use the correlation coefficient as a parameter to analyses the agreement. The correlation coefficient does not give a picture of the agreement. The correlation coefficient only tells about the strength of the relation between two variables and nothing about the agreement between them. The agreement will be fine if the data points lie along the line of equality, whereas the correlation coefficient will be fine in spite of which straight line the points follow. Therefore, data can produce a high correlation even if the agreement is poor. \
In clinical measurements it is common to compare a new method with an established one. When two measurement methods are compared, there will always be some lack of agreement between the methods. The question is how big this lack of agreement will be. If it is unlikely that the two measurement methods give readings that differ more than some clinical threshold value, it implies that the new method can be established and replace the old method. The concerned threshold value is a clinical decision and not a statistical decision. To figure out the agreement statistical methods must be used. \

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