The "doublePlot" function draws, in a double angle plot, the data from an astigmatism sample. Two plots are possible, the old one which represents the mean and standard deviation by means of a square and an ellipse, respectively. The new one contains the mean and the covariance ellipses with 95% confidence ellipse of the centroid (in red) and 95% confidence ellipse of the dataset (in blue)
Astigmatism analysis is based on vector arithmetic. The current standard method in Ophthalmology practice is the Alpins method1 whereas in Optometry practice is more common to use the Thibos method.2 In practice, both methods result in similar outcomes. The figure shows an example of the new representation with the standard deviation along the axis of displacement of the centroid and perpendicular to it (covariance ellipse).3 The old representation that you can find in some papers4 refers to the standard deviation in the axis 0º-180º and the axis 45º-135º (obsolete). In this new figure you have two ellipses:
The difference between the two ellipses is analogous to the concept of 95% Confidence Interval and 95% Agreement Limits (Bland-Altman). If you want to know more about the difference between both you can access to our Statistics Online Course.
The Refractive Analysis is an Open Source Toolbox for Matlab developed by Rodríguez-Vallejo M for the Analysis of Vision Science Results. It is freely available for the students of our online course but you need the Matlab software to use it. Matlab software is not provided with the course.
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