Distribution of Non-Gaussian Data: Analysis & Presentation

In summary, the conversation discusses a non-Gaussian distribution of a sample and the use of the Poisson distribution. The skewness statistic and Z distribution are mentioned, along with the mean, standard deviation, and standard error of the mean. The idea of splitting the data into seasons and finding correlations is also brought up. The question of how to present the data, given its non-normally distributed nature, is raised. The use of the standard error of the mean instead of the standard deviation is suggested. It is also mentioned that the Poisson distribution cannot have a standard deviation that is double the mean. The topic of bird catching is briefly touched upon, with a suggested average of 12 kilograms and a need to find a standard deviation to
  • #1
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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  • #2
Hi John,

Are you familiar with the Poisson (:smile:) distribution ? If not, then you should read up on it.
 
  • #3
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.
 
Last edited:
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Likes BvU
  • #4
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 ?
 

What is the importance of analyzing and presenting non-Gaussian data?

Non-Gaussian data is data that does not follow a normal distribution, and therefore cannot be analyzed using traditional statistical methods. It is important to analyze and present this type of data because it can provide important insights and trends that may not be apparent when using traditional methods. It can also help identify potential outliers or anomalies in the data.

What are some common methods for analyzing non-Gaussian data?

Some common methods for analyzing non-Gaussian data include using non-parametric tests, such as the Wilcoxon rank-sum test or the Kruskal-Wallis test, or transforming the data to make it more normally distributed. Additionally, machine learning algorithms can be used to analyze and model non-Gaussian data.

How should non-Gaussian data be presented?

Non-Gaussian data should be presented in a way that accurately represents its distribution. This can be done through visualizations, such as histograms or box plots, or through descriptive statistics, such as median and interquartile range. It is important to also note the type of distribution the data follows, such as a skewed or bimodal distribution.

What are some challenges associated with analyzing non-Gaussian data?

One challenge is that non-Gaussian data may not follow a specific pattern or distribution, making it difficult to apply traditional statistical methods. Another challenge is that outliers can have a significant impact on the results, so it is important to identify and address them appropriately. Additionally, the interpretation of results may be more complex with non-Gaussian data.

How can non-Gaussian data be transformed to make it more normally distributed?

Non-Gaussian data can be transformed using mathematical functions, such as logarithmic or square root transformations. These transformations can help reduce skewness and make the data more normally distributed. It is important to note that the interpretation of results may be different after transformation, and the original data should still be reported.

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