Normally distributed data errors

AI Thread Summary
Data errors being normally distributed does not imply that the data itself is normally distributed. The discussion clarifies that "data errors" can refer to deviations from a true value, but the context of measurements is crucial for understanding this concept. For instance, if height is measured against an average, the difference can be termed an error, but it may not be viewed as such in all contexts. The conversation highlights the importance of clearly defining what constitutes "data errors" in relation to the measurements being analyzed. Overall, the distinction between normally distributed data and normally distributed errors is essential for accurate interpretation.
James.L
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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.
 
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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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