Q 549. The statistical analysis tools we commonly use often assume data conforms to a Normal Distribution. Nevertheless, it is widely acknowledged that data might not adhere to a Normal Distribution. In these situations, it becomes essential to determine the distribution of the data before proceeding with any analysis. What methods can we use to identify the distribution of the data? Please explain one method with the help of an example.

 

Note for website visitors -

• This platform hosts two questions per week, one on Tuesday and the other on Friday. 
• All previous questions can be found here: https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/. 
• To participate in the current question, please visit the forum homepage at https://www.benchmarksixsigma.com/forum/.
• The question will be open until the following Tuesday or Friday evening at 5 PM Indian Standard Time, depending on the launch day. 
• Responses will not be visible until they are reviewed, and only non-plagiarised answers with less than 5-10% plagiarism will be approved. 
• If you are unsure about plagiarism, please check your answer using a plagiarism checker tool such as https://smallseotools.com/plagiarism-checker/ before submitting. 
• All correct answers shall be published, and the top-rated answer will be displayed first. The author will receive an honourable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term.

There are multiple method to check data distribution

1.       Histogram

Histogram shows data visualization of a variable using bars. It present frequency per value of dataset. If bell shape curve is there we can say data follows normal distribution.

 

In above figure first histogram looks normally distributed and second one looks uniformly distributed.

 

2.       Box plot

Box Plot is technique can be used to identify data type from samples. The Box Plot plots five variable: min, max, median, 1st & 3rd Quantiles. if at both sides of rectangle width is almost equal we can say data is normally distributed

In the figure first plot has outliers and belongs to non –normal data with outliers and second (bottom) graph can be considered normally distributed.

 

3.       QQ plot

QQ plots need more understanding, QQ means Quantile vs quantile, and here we are plotting theoretical vs actual quantiles for variables, this graph is better than box plot to visualize deviation from normal distribution. Uniform distribution has many observation in both extreme however normal plot follow a straight line.

 

4.       Kolmogorov Smirnov test

Kolmogorov Smirnov test calculate the difference between the empirical distribution and the theoretical distribution and defines the test statistic based on those differences. This test can evaluate all type of distribution.

 

5.       Lilliefors test

This test is based on the above test. Here it is accepted that the mean and variance of the population distribution are estimated rather than pre-specified by the user. if p value is > 0.05 we assume normal distribution else non normal.

 

6.       Shapiro Wilk test

This test is the wonderful test and highly used when testing for a normal distribution. It has been developed specifically for the normal distribution and it cannot be used for testing against other distributions. if p value is > 0.05 we assume normal distribution else non normal

7.       Anderson darling Method: This test also use widely along with Shapiro Wilk test and similarly used for detecting normal distribution. if p value is > 0.05 we assume normal distribution else non normal

 

Kirpa Shanker Tiwari has posted the best answer to the question. While these tests and graphs will help us identify the underlying distribution, there are other methods like goodness of fit tests that can also be used. Most of the statistical packages also have in built functionality for distribution identification.