amchang.net/simon Home Page
Posting 1 : 2024/01/18 : Overlap
One of the questions was, given two groups of normally distributed data, what is the proportion of the total data that have overlapping values. The answer is as follows
- In two groups (true T and false F), if the two means are μF and μT, and they have the same Standsrd Deviation σ
- then the effect Size is the difference between the means divided by the common Standard Deviation, z = (μT-μF) / σ
- and the proportion of the total data that overlaps is the Gaussian probability of the half the Effect Size α = P(z/2)
- α can be obtained by the function norm.cdf(z), in the Python package of scipy.stats
- Detailed discussions are presented in Overlap/Overlap.html
I have appended this page on Jan 23rd., adding some observations and opinions
Posting 2 : 2024/01/22 : Gaussian Transform
We discussed that, given two groups of normally distributed values, how to estimate the probability of any given value (d) belonging to either group.
- I have now finished a page describing what I understand about this problem, and provided a short algorithm for its calculations.
- This allows a translation of the overlapping values from the two groups from that of a normal (Gaussian) to that of a probabilistic (Logistic) distributionion
- Detailed discussions are presented in GaussianTransform/GaussianTransform.html