Distribution of Non-Gaussian Data: Analysis & Presentation

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Discussion Overview

The discussion revolves around the analysis and presentation of non-Gaussian data, specifically focusing on a dataset related to fish catch. Participants explore statistical characteristics such as skewness, standard deviation, and potential distributions applicable to the data, while also considering how to effectively present the findings.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents statistical metrics of the fish catch dataset, noting a high skewness and asking for applicable correlations and presentation methods for non-normally distributed data.
  • Another participant suggests the Poisson distribution, indicating it cannot have a standard deviation that is double the mean, and proposes the possibility of a gamma distribution instead.
  • A different participant questions the nature of the data, implying variability in catch amounts among individuals and seeking clarification on the average and standard deviation related to the total catch.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate statistical distribution for the data, with no consensus reached on the best approach to analyze or present the non-Gaussian data.

Contextual Notes

There are unresolved assumptions regarding the nature of the data distribution and the implications of the statistical measures presented. The discussion reflects uncertainty about the appropriate statistical models to apply.

Who May Find This Useful

This discussion may be of interest to statisticians, data analysts, and researchers dealing with non-Gaussian data distributions, particularly in ecological or biological contexts.

JohnFishy
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Any help would be much appreciated.

The problem lies in the non-Gaussian distribution of the sample. If we take the entire data set of total fish catch, the skewness statistic equals 7.463 with a std. error of skewness of 0.39. Accordingly, the Z dist. (7.463/0.39)=19.14. Overall, the mean=8.75, std deviation=15.27, and std. error of mean=.245, median=4.5, range=299.97. Percentiles at 25%=2, 50%=4.5, and 75%=9.7. here is a histogram of the entire data set: http://imgur.com/4nHCyRl. I would like to split the data into season so what kind of correlations can be applicable in this scenario with such a non-normally distributed data set? Likewise, how would one present this data? the std deviation is almost twice as large as the mean. Would you use std error of mean instead?
 
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Hi John,

Are you familiar with the Poisson (:smile:) distribution ? If not, then you should read up on it.
 
BvU said:
Hi John,

Are you familiar with the Poisson (:smile:) distribution ? If not, then you should read up on it.

A Poisson distribution can not have a standard deviation that is double that of the mean.

It might be a gamma for example though.
 
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Yeah, well some guys catch nothing and others hook 250. So the question is: what are we looking at, dear JohnFishy ?
From looking at the other thread I suspect we are looking at 4765 kg of bird caught by 400 people ?
So 12 kilogram of bird on average, and we are trying to find a standard deviation to accompany this 12 kg ?
 

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