gardnerAltmanPlot (X, Y) draws the observations of the samples X and Y at the horizontal positions 1 and 2, and the difference between their means, with its confidence interval, at position 3, measured against a second vertical axis on the right. That axis is placed so that its zero is level with the centre of Y and the effect size level with the centre of X, so the effect reads off the data it comes from. X and Y are vectors of type double or single, and a missing value (NaN) is left out.

Two unpaired samples are drawn as swarms, the points of each spread sideways where they crowd, with a black line from the centre of each sample to the effect size: solid for X, dashed for Y. The centre is the median for 'mediandiff' and the mean otherwise. Paired samples are drawn as a line from each observation of X to its partner in Y, the pairs that increase, decrease and stay equal each in a colour of their own. For 'cliff' and 'kstest', whose values do not share the scale of the data, the right axis spans the values the effect can take, [-1.1, 1.1] and [-0.1, 1.1], and two unpaired samples get a reference line at zero instead of the lines from their centres.

gardnerAltmanPlot (ax, …) draws into the axes ax rather than the current axes.

gardnerAltmanPlot (…, Name, Value) takes the options 'Effect', 'Paired', 'VarianceType', 'Alpha', 'ConfidenceIntervalType', 'NumBootstraps', 'BootstrapOptions' and 'Resampling' of meanEffectSize, which computes the effect size and its interval; 'Effect' names a single effect. 'Mean' does not apply, there always being two samples.

H = gardnerAltmanPlot (…) returns the graphics objects drawn, in a row vector. For two unpaired samples they are the two swarms, the error bar, and the lines from the centres of X and Y, or the reference line. For paired samples they are the lines of the pairs that increase, decrease and stay equal, each where there is any, and the error bar. Where 'ConfidenceIntervalType' is 'none' the error bar is a line holding a single marker.

MATLAB draws the effect size on a second vertical axis of the same axes; Octave has no such axis, so here it is a second axes laid over the first, which follows the first’s position and vertical limits. The error bar is Octave’s errorbar object, whose bounds are its 'ldata' and 'udata' properties.

Reference: M. J. Gardner and D. G. Altman (1986). Confidence intervals rather than P values: estimation rather than hypothesis testing. British Medical Journal, 292(6522), 746-750.

See also: meanEffectSize, swarmchart, errorbar

Source Code: gardnerAltmanPlot