Quantitive Histogram Comparison

In summary, the speaker has two histograms that they wish to compare quantitatively. The values in the first histogram have relative errors for each bin, while the second histogram has no statistical uncertainty. The speaker is considering calculating probabilities for each bin to determine the likelihood of the exact values falling within a given uncertainty range in the other distribution. They are also wondering if there are more advanced methods they could use. They mention that the sample space width is consistent for all bins and the values in the distributions cover a wide range. Finally, they suggest trying the Pearsons Chi-square test as a potential alternative.
  • #1
RobbieM.
7
0
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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  • #2
Just in case that numerous people haven't already suggested this to you, try Pearsons Chi-square test.
 

What is quantitive histogram comparison?

Quantitive histogram comparison is a statistical method used to compare two or more histograms in order to determine if they represent the same underlying distribution.

What are the steps involved in quantitive histogram comparison?

The steps involved in quantitive histogram comparison typically include:

  1. Collecting data and creating histograms for each dataset
  2. Identifying the type of distribution for each histogram (e.g. normal, skewed, etc.)
  3. Calculating summary statistics for each histogram, such as mean and standard deviation
  4. Using statistical tests, such as the Kolmogorov-Smirnov test, to compare the histograms and determine if they have the same underlying distribution
  5. Interpreting the results and drawing conclusions based on the statistical analysis

What are the limitations of quantitive histogram comparison?

Quantitive histogram comparison can be limited by the quality and quantity of data collected, as well as the assumptions made about the underlying distribution. Additionally, this method may not be suitable for comparing histograms with different bin sizes or for highly skewed distributions.

What are some applications of quantitive histogram comparison?

Quantitive histogram comparison can be used in various fields, such as finance, economics, and biology, to compare distributions of data. It can also be used in quality control to ensure consistency in manufacturing processes.

How does quantitive histogram comparison differ from qualitative histogram comparison?

Quantitive histogram comparison involves using statistical tests and numerical measures to compare histograms, while qualitative histogram comparison focuses on visual inspection and subjective interpretation of the shape and patterns of the histograms. Quantitive comparison provides a more objective and rigorous analysis, while qualitative comparison may be more suitable for exploratory data analysis.

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