# 4.1.- The double angle plot and ellipses

In the BigSIA, astigmatism (positive cylinder) is considered with-the-rule from 60º to 120º and against-the-rule between 30º and 150º in the double angle plot. Remaining meridians are considered oblique. Therefore, if the mean (square black point) is located at the left side of the plot you are inducing WTR astigmatism, on the other hand, at the right side you are inducing against the rule astigmatism and in top and bottom locations of the plot, oblique astigmatism.

Two ellipses are included in the plot:

**Red ellipse:**95% confidence ellipse of the centroid. If the center of the coordinates from the graph is within this ellipse, the magnitude of the mean astigmatism may be due to chance, so it should not be considered.**Blue ellipse:**95% limits of agreement of the centroid. Estimates the variability in the sample in such a way that 95% of the sample is inside the blue ellipse. It is an indicator of the bias of your astigmatism results, the smaller the size of the ellipse, the lower is the variability