Graphical interpretation of confidence curves in rankit plots


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Abstract

A well-known transformation from the bell-shaped Gaussian (normal) curve to a straight line in the rankit plot is investigated, and a tool for evaluation of the distribution of reference groups is presented. It is based on the confidence intervals for percentiles of the calculated Gaussian distribution and the percentage of cumulative points exceeding these limits.The process is to rank the reference values and plot the cumulative frequency points in a rankit plot with a logarithmic (ln=loge) transformed abscissa. If the distribution is close to ln-Gaussian the cumulative frequency points will fit to the straight line describing the calculated ln-Gaussian distribution. The quality of the fit is evaluated by adding confidence intervals (CI) to each point on the line and calculating the percentage of points outside the hyperbola-like CI-curves. The assumption was that the 95% confidence curves for percentiles would show 5% of points outside these limits. However, computer simulations disclosed that approximate 10% of the series would have 5% or more points outside the limits.This is a conservative validation, which is more demanding than the Kolmogorov-Smirnov test. The graphical presentation, however, makes it easy to disclose deviations from ln-Gaussianity, and to make other interpretations of the distributions, e.g., comparison to non-Gaussian distributions in the same plot, where the cumulative frequency percentage can be read from the ordinate. A long list of examples of ln-Gaussian distributions of subgroups of reference values from healthy individuals is presented. In addition, distributions of values from well-defined diseased individuals may show up as ln-Gaussian.It is evident from the examples that the rankit transformation and simple graphical evaluation for non-Gaussianity is a useful tool for the description of sub-groups.

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