Quantitive Histogram Comparison

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SUMMARY

This discussion focuses on quantitatively comparing two histograms, where the first histogram includes relative errors for each bin while the second lacks statistical uncertainty. The user seeks advanced methods beyond basic probability calculations for assessing the relationship between the two distributions. A key recommendation is to utilize Pearson's Chi-square test for a robust statistical comparison, particularly given that the sample space width is consistent across bins and the value ranges span multiple orders of magnitude.

PREREQUISITES
  • Understanding of histogram data representation
  • Familiarity with statistical uncertainty and relative errors
  • Knowledge of Pearson's Chi-square test methodology
  • Basic concepts of probability distributions
NEXT STEPS
  • Research advanced statistical methods for histogram comparison
  • Learn about the implementation of Pearson's Chi-square test in Python using SciPy
  • Explore techniques for handling data with varying orders of magnitude
  • Investigate other statistical tests for comparing distributions, such as Kolmogorov-Smirnov test
USEFUL FOR

Data analysts, statisticians, and researchers involved in quantitative data analysis and histogram comparison will benefit from this discussion.

RobbieM.
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I have two histograms that I would like to compare quantitatively. The values of the first histogram have respective relative errors for each bin. The second histogram has no statistical uncertainty.

I could compute probabilities for each bin that the exact values would fall into a given uncertainty range about the corresponding value in the other distribution... but I'm wondering if there are more sophisticated alternatives that I could apply.

If it is relevant, the width of the sample space is the same for all the bins and values in the distributions span several orders of magnitude.
 
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Just in case that numerous people haven't already suggested this to you, try Pearsons Chi-square test.
 

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