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The average error of an analysis state from the true state (distance TC) is known from statistical invesigationsinvestigations.  On this diagram therefore, the control analysis state is shown by the true state offset by the known average error between control and true states and, for each IFS model analysis, can lie anywhere on the blue curve centred on the true state (here the control analysis shown at C).  The average of the difference of the perturbed analyses from the control analysis is shown by the red circle centred on the control analysis, and the length of arc (ATB) is proportional, on average, to the number of perturbed analyses closer to the truth than the control analysis.   For the special conditions illustrated, only 35% of the perturbed analyses are, on average, closer to the truth than the control analysis.  As the average of the difference of the perturbed analyses from the control analysis varies (i.e. the radius of the red circle) so will the number of perturbed analyses (represented by the arc ATB) be, on average, closer to the truth than the control analysis.  The number will be zero where the red circle is tangent to the blue circle (i.e. where perturbed analyses are very similar to the control, or where the average of the difference of the perturbed analyses from the control analysis is twice (or more) the average error between control and true analyses.

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