Weighted average with uneven errors

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SUMMARY

The discussion focuses on the challenge of calculating a weighted average for two values with asymmetric errors, specifically x1 = 10 +2/-1 and x2 = 12 +3/-4. The original poster seeks guidance on normalizing these values to achieve symmetric errors for averaging. A contributor highlights that the asymmetry in confidence intervals (CIs) suggests that the underlying data may have been transformed due to non-normal distribution, complicating the combination of estimates. The contributor advises against attempting to combine the estimates without further information due to the skewness of the samples.

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  • Understanding of weighted averages and their application in statistics
  • Familiarity with confidence intervals (CIs) and standard error concepts
  • Knowledge of data transformation techniques in statistical analysis
  • Basic principles of data distribution, particularly normal vs. non-normal distributions
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  • Research methods for calculating weighted averages with asymmetric errors
  • Learn about confidence intervals and their implications in statistical analysis
  • Explore data transformation techniques for handling non-normally distributed data
  • Investigate statistical methods for combining estimates from skewed distributions
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Statisticians, data analysts, researchers dealing with measurement errors, and anyone involved in statistical data analysis requiring precise averaging techniques.

freeman2
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Cant seem to find information on this anywhere...

If I want to average two values with errors, say

x1 = 10 +/- 2
x2 = 12 +/- 4

I would do a regular weighted average that would reflect the fact that x1 is a more precise measurement.

But what if my errors are asymmetric? So if I had

x1 = 10 +2/-1
x2 = 12 +3/-4

How would I take the average of those values? My first thought was to somehow "normalize" x1 and x2 such that they have symmetric errors, but I am not sure whether that is valid or how I would do that. Anyone have any ideas? thanks...
 
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freeman2 said:
Cant seem to find information on this anywhere...

If I want to average two values with errors, say

x1 = 10 +/- 2
x2 = 12 +/- 4

I would do a regular weighted average that would reflect the fact that x1 is a more precise measurement.

But what if my errors are asymmetric? So if I had

x1 = 10 +2/-1
x2 = 12 +3/-4

How would I take the average of those values? My first thought was to somehow "normalize" x1 and x2 such that they have symmetric errors, but I am not sure whether that is valid or how I would do that. Anyone have any ideas? thanks...

What are these values? Assuming they are random sample means from the same population, it's usual to express the uncertainty of the estimate in terms of confidence intervals (CI)which in turn are based on the standard error of the sample mean.

If so, the asymmetry of these intervals suggest the original data was transformed for analysis because the data was not normally distributed. Moreover the CIs should not be this different. Because of this and the lack of other information, I can't recommend any "safe" way to combine the two estimates.

EDIT: To make matters worse, the asymmetry indicates the two samples are skewed in different directions!
 
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