Sebastian Hellmann

@sehellmann.bsky.social

143 Followers 214 Following

PostDoc working at TU Munich. Interested in on computational modelling, decision-making, and confidence. Cat owner, Ireland lover and brass music fan

A Figure with two panels, demonstrating the transformation of a normally distributed random variable resulting from transforming the values using the standard normal CDF to the interval 0 to 1. The figure shows the discrepancy between the mean of the transformed values and the result from simply transforming the mean of the normal distribution using the standard normal CDF.
The left side shows a normal distribution with low variance, such that the transformed values also show small variance and a symmetrical shape. The mean of the transformed values and the value resulting from transforming the mean directly coincide.
The right side shows a distribution with high variance. Due to the non-linearity of the normal CDF, the distribution of transformed values is non-symmetrical and highly skewed. The mean of the distribution is therefore pulled to the center of the range 0 to 1, compared to the result from directly transforming the mean of the normal distribution.

Line graphs comparing correct and biased computations for exponential and probit (Φ) transformations in statistical modeling. Colored lines show how the bias changes with different group means and standard deviations.