Interpreting Normal Distribution Logic for Data Analysis

[Mark J.]

Hi.
I need some arguments to move forward the hypothesis that my data are normally distributed.
Except fact that I build histogram and it is similar of shape as normal distribution how can I find some other math arguments (I mean interpreting the logic of normal distribution) to argue about this hypothesis before beginning hypothesis testing with different criteria and tests?

Regards

 

[Stephen Tashi]

One common explanation for a phenomena producing a normal distribution is that it the sum (meaning literally an arithmetic sum) of many independent random random variables.

A hazier philosophical version of this is reasoning is that a phenomena that results from the combined effect of many small and independent random causes will have a normal distribution. (This argument is too vague to be tested mathematically, but you haven't made it clear what kind of "justification" for a normal distribution you want.)

 

[Mark J.]

I have a process of bus arrivals.
While taking inter-arrival times between 2 following buses as random variables I build histogram and it has shape of normal distribution but meanwhile it is similar to log-normal ,etc.
Now I am in search of some math arguments (theory)to check in order to follow the hypothesis of normal distribution.
If you can advice me on that pls

 

[SW VandeCarr]

I have a process of bus arrivals.
While taking inter-arrival times between 2 following buses as random variables I build histogram and it has shape of normal distribution but meanwhile it is similar to log-normal ,etc.
Now I am in search of some math arguments (theory)to check in order to follow the hypothesis of normal distribution.
If you can advice me on that pls

There are a number of tests of normality. You can directly evaluate the third and fourth moments (skewness and kurtosis) which both should be close to 0. In addition there are specific tests which you can look up: Kullbach-Leiber distance, Kolmogorov-Smirnoff (adaption), Agostino's K squared test, Anderson-Darling, Shapiro-Wilks and tests in SPSS and other statistical software.

http://webspace.ship.edu/pgmarr/Geo441/Examples/Normality Tests.pdf

 

[blue_raver22]

,

I understand the importance of ensuring that our data is normally distributed before conducting any hypothesis testing. A normal distribution is a bell-shaped curve that represents the distribution of a continuous variable. It is characterized by its mean, median, and mode being equal, and the majority of the data falling within one standard deviation of the mean.

One way to further support your hypothesis that your data is normally distributed is by calculating the skewness and kurtosis of your data. Skewness measures the symmetry of the data distribution, while kurtosis measures the peakedness of the distribution. In a normal distribution, the skewness should be close to 0 and the kurtosis should be close to 3.

Another important aspect to consider is the Central Limit Theorem. This theorem states that as the sample size increases, the distribution of sample means will approach a normal distribution, regardless of the shape of the population distribution. Therefore, if your sample size is large enough, it is likely that your data will follow a normal distribution.

Additionally, you can use statistical tests such as the Kolmogorov-Smirnov test or the Shapiro-Wilk test to formally assess the normality of your data. These tests compare your data to a theoretical normal distribution and provide a p-value to indicate the likelihood of your data being normally distributed.

In conclusion, there are several mathematical arguments and tests that can be used to support your hypothesis that your data is normally distributed. It is important to thoroughly examine your data and use a combination of approaches to ensure the validity of your results. Good luck with your analysis!