Normally distributed data errors

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SUMMARY

The discussion clarifies the distinction between normally distributed data errors and normally distributed data. It emphasizes that while data errors can be normally distributed, this does not imply that the underlying data itself is normally distributed. The conversation highlights the importance of context in defining "data errors," particularly in relation to measurements and predictive equations, such as using height predictions based on weight. The clarification provided resolves the original query regarding the interpretation of data errors and their distribution.

PREREQUISITES
  • Understanding of statistical concepts, particularly normal distribution
  • Familiarity with measurement errors and their implications
  • Knowledge of predictive modeling, specifically regression analysis
  • Basic grasp of statistical confidence intervals
NEXT STEPS
  • Research the properties of normal distribution in statistics
  • Study the concept of measurement errors in data analysis
  • Learn about regression analysis and its applications in predictive modeling
  • Explore confidence intervals and their significance in statistical inference
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Statisticians, data analysts, researchers, and students seeking to understand the nuances of data errors and their relationship to data distributions.

James.L
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Homework Statement


Hello

If my data errors are normally distributed, is this the same as the data being normally distributed? I mean, by "normally distributed data errors" is meant that with 68% confidence the data lies within the true value?
 
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You aren't expressing your question clearly. It isn't clear whether you have a set of measurements (such the heights of various persons) or a set of vectors of measurements (such as the height and weight of various persons). So it isn't clear what a "data error" would be.

For example, if we use the rather strange terminology that the average height h_bar of the population is the "true" height, then for a person's height h, we could call h - h_bar an "error". However, I don't think most people regard deviating from the average as an error.

If we have an equation H(.) that attempts to predict a persons height from their weight then for a given person with weight w and height h, we could call the quantity (h - H(w)) an "error" since it is an error in in how the equation predicts the weight.
 
Last edited:


I think I get it. My original question got answered by your post, even though my question is poorly formulated.

Thanks!
 

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