This dialog is activated by selecting the **Bland-Altman Plot...** command from the Plot -> Statistical Graphs menu. It can be used in order to create and customize a Bland-Altman plot of the selected data columns in the active table window.

A Bland-Altman plot is used to compare two measurements of the same variable. That is, it is a method
comparison technique. In the initial design of this analysis, that has been used for many years, each of the two
measurement methods is used once on each subject. You need to provide two input data columns,
one for each measurement method, via the *Method 1* and *Method 2* list
boxes. The *Subject* box should be set to *None* in this design.
A big drawback of this simple design is that no repeatability parameter can be computed.

Considering *n* paired observations for method 1 (M_{1k}) and method
2 (M_{2k}), with *k = 1, 2,...,n*, the simplest form of a Bland-Altman
plot is obtained by plotting the differences d_{k} = M_{1k} -
M_{2k} on the Y axis versus the pair means (M_{1k} +
M_{2k})/2 on the X axis.

A horizontal line representing the *bias* is
drawn at the mean difference: d_{mean} = ∑d_{k}/n.

Two other horizontal lines, known as the *limits of agreement* (*LoA
*) are added to the plot at:

LoA_{up,low} = d_{mean} ± 1.96 S_{d}

where S_{d} is the standard deviation:

S_{d} = [1/(n-1)∑(d_{k} - d_{mean
})^{2}]^{1/2}

Sometimes the 1.96 multiplier for the standard deviation is replaced with 2 or with another value.
The default value in the *Multiplier (SD)* box is therefore set to 1.96 and can be freely
modified.

The α% confidence interval for the mean difference (the bias) is calculated as
d_{mean} ± t_{(1 + α)/2,n-1}V^{1/2}
, with the variance: V = S_{d}^{2}/n and
t_{(1 + α)/2,n-1} being the Student's t distribution with *n - 1*
degrees of freedom. The default value for α is set to 95 in the *Confidence Level (%)*
box.

The α% confidence interval for the limits of agreement is calculated as:

LoA_{up,low} ± t_{(1 + α)/2,n-1}V_{LoA}^{1/2}

with the variance:

V_{LoA} = [1/n + 0.5*1.96^{2}/(n-1)]S_{d}^{2}

There are four display modes available for the X axis of a Bland-Altman plot:

- Mean
The abscissas are calculated as the arithmetic mean of the paired values. This is the default mode.

- Method1
The abscissas are the values measured using the first method.

- Method2
The abscissas are the values measured using the second method.

- GeometricMean
The abscissas are calculated as the geometric mean of the paired values.

There are three display modes available for the Y axis of a Bland-Altman plot:

- DifferencePercent
The ordinates are calculated as the difference of the paired values, divided by their arithmetic mean and multiplied by 100.

- Difference
The ordinates are calculated as the difference of the paired values. This is the default mode.

- Ratio
The ordinates are calculated as the ratios of the paired values.

Multiple observations by each method on each subject are needed in order to compare the repeatability of the two methods. For this more complex design of the Bland-Altman analysis three columns of input data are required: one with the measurements of the first method, one with the measurements of the second method and one with the subject values.

In this design only one display mode is available for the Y axis of a Bland-Altman plot:
the default *Difference* mode. Also, the result curve displays the data points corresponding
to each subject with a different color.

Two methods are available for calculating the *Confidence interval for the limits of agreement (LoA)
* in the case of replicated measurements: *Delta* method and *MOVER*
(Method of Variance Estimates Recovery). The calculation steps for each of these two methods are explained in detail by
GY Zou in his paper
Confidence interval estimation for the Bland-Altman limits of agreement with multiple observations per individual,
Statistical Methods in Medical Research, 2013 Dec;22(6):630-42.

The use of the option *True Value is Constant* is very clearly explained by Bland and
Altman in their paper from 2007 Agreement between methods of
measurement with multiple observations per individual, Journal of Biopharmaceutical Statistics, 17: 571-582:
"There are two different situations to consider for replicated data.
We can think of the observations for the same subject as a series of measurements of a quantity
that does not vary over the period of observation... Or we can think of them as
pairs of measurements by two methods of a changing quantity, where it is the
instantaneous measurement for the subject which we want to capture....The distinction is
important, as it determines whether we need to consider pairing of observations by the two methods.
Indeed, for the first (constant) case we do not require equal replication of each method for each individual,
whereas this is a requirement for the second (non-constant) case."

If the option *True Value is Constant* is checked, the data columns for
*Method 1* and *Method 2* may have a different number of input cells,
since pairing is not required. The calculations for the limits of agreement and the corresponding confidence
intervals will take into account the different number of observations for each method, nevertheless,
only paired observations will be displayed by the output result curve.

By checking the option *Plot Subjects as Bubbles*, it is possible to group
the measurements for each subject and represent them as one bubble with the center located at the following
coordinates: mean of group (X) and mean difference (Y). The sizes of the bubbles are proportional to the number
of replicates. This option does not affect in any way the calculations of the various reported values,
only the drawing of the result data curve.

This tab helps controlling the drawing of the various horizontal lines: the equality line
(*Zero* difference), the bias (*Mean* difference) and the limits of agreement.
The drawing of the confidence intervals, their color filling and opacity can also be customized via this tab.

The *Table* button, when pressed, activates the results table.
The user may type the name of the result table in the edit box.
Please beware that if the name corresponds to an existing table, the contents of that table will
be altered.

The last two columns in the result table, *Statistics* and
*Values*, display the names and, respectively, the values calculated for the bias
(*Mean*), the limits of agreement (*Mean ± Multiplier*SD*)
and their corresponding confidence intervals. Other two calculated values are the
*Mean of Pairwise Means* or MPM, which is the mean of all paired values
and the *Bland-Altman Ratio*, which is calculated as: (LoA_{up} -
LoA_{low})/MPM. In the case of repeated observations, these columns also display the
information about the *True Value is Constant* setting (1 if checked, 0 if not)
and about the method used to calculate the confidence intervals for the limits of agreement
(*Delta* or *Mover*).