Business Analytics Made Simple
Dr Arivazhagan Ondiappan, BE(Hons),PMP, PMI-RMP, MBB
Why Analytics : If you are a Book Store business owner and if you wanted to verify the proportions of customers that visit your store from each category (Adults, Teens, Children, Retired) and stock books accordingly so as to increase your sales, reduce your inventory, and enhance customer satisfaction, here is a simple Business Analytics technique that can help you solve this business problem. The good thing is that you don't need to be an ace Statistician.
The following simple case study from a similar business scenario will help you understand how such business problems could be solved with statistical techniques using past performance data.
The Business : Assume you are the Owner of "Software for Success", a software company that specializes in exam prep CDs that provide unlimited simulated mock exams for various competitive exams. If you wanted to check if the proportions of questions that appear in the simulated mock exams from your CD are same as the proportions of questions that are claimed or expected to appear, here is a simple way to do that.
The Premise : Assume that each simulated mock exam consists of 200 Multiple Choice Questions (MCQ) from 5 subject areas. Out of 200 questions, suppose the expected proportions of questions in any simulated mock exam from five subjects namely Maths, Physics, Chemistry, General Aptitude, and English are 13%, 24%, 30%, 25%, 8 % respectively, then using statistical methods like Chi-Square Goodness-of-Fit test in Minitab®, a statistical software, can be a good idea to validate the claim without the intimidating calculations of Statistics.
First, let us construct the Null Hypothesis (Ho) and Alternate Hypothesis (Ha) for the claim. Then, let us say we want to be 95% confident in declaring our results. This means we are willing to take a chance of 5% error in our judgment. If this is OK with you, then the significance level is 5% (Alpha,α = 0.05) and Confidence Level is 95%.
Ho : The proportions of questions observed are equal to the expected.
Ha : The proportions of questions observed are not equal to the expected.
The Results : A mock test containing 200 questions from the prep.CD was done to observe the number of questions that actually appeared as against the expected from the prep.CD and the results were analyzed using Minitab® to get the following outputs.
Inference : From the Chi-Square distribution plot for Goodness-of-Fit analysis shown above, since the P-value = 0.000 < 0.05,we reject the Null Hypothesis (Ho). That means, we accept the Alternate Hypothesis (Ha) that there is a significant difference in the proportions of questions that appeared in the mock exam from what was expected. We usually make these sort of statements with 95% confidence. (However, in this example we can make this statement even with 100% confidence since the P-Value = 0.000)
This conclusion is also supported by the fact that the calculated Chi-square test statistic value 51.9 (reference value in the chart) is much greater than the critical Chi-square value of 9.488 (for α = 0.05 & degrees of freedom, df = 4 ).
The business owner can increase the sample size (more number of mock tests) to see if the same trend exists in all simulated exams and, if so, can embark on revising the questions distribution pattern to align it to the expected pattern and issue a new version of the prep CD.
Other Applications : The Chi-Square Goodness-of-Fit test could be used to validate claims or hypotheses or assumptions in various business scenarios involving categorical variables / proportions like proportions of sales from various categories, nutrients in a potion, candies in a packet,composition of minerals in a metal, contaminants in potable water, calories in food products, distribution of people in a county, proportions of voters for a leader, proportions of defects, proportions of customers that visit a hotel / hospital / shopping mall etc.
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About the Author: The author, Ondiappan Arivazhagan "Ari", is an Honors graduate in Civil / Structural Engineering from University of Madras.He is a certified PMP, PMI-SP, PMI-RMP from PMI, USA. He is also a Master Black Belt in Lean Six Sigma and has done Business Analytics from IIM, Bangalore. He has 30 years of professional global project management experience in various countries around the World and has almost 14 years of teaching / training experience in Project management, Analytics, Risk Management and Lean Six Sigma .He is the Founder-CEO of International Institute of Project Management (IIPM), Chennai and can be reached at askari@iipmchennai.com
Pretty good explanation, I have used it same way many times. Somehow the statisticians or BBs seem confused on such simple applications and their use. When it comes to proportions, I have seem people get into DPU vs DPMO discussions or trying to prove based on DPU thier operating sigma levels or go the whole shebang to prove something- not sure the solution they found it their intelligence.:)
Ron, Thanks for sharing your experience. If there is any case study , you can publish, then we can comment or interact. I am sure you must be having lots of process improvement projects experience and some of them can be posted or shared for comments and interactions.
Interesting case study! I do similar analysis but with the focus on auditing production lines/ processes. The focus on my analysis is weak spots in these production lines for entering counterfeited half-products/ raw materials and components. I use here also the theory of Lean and Six Sigma. If there is any interest in my expertise? See my profile as well. Looking forward in your comments.
Hi Krithika, It is a typical problem business owners often face that BA can help solve. I'll give a brief outline of how this problem could be solved.The water supplier has to collect samples of his water ( say, n=15) and 15 samples of his competitors' water. Measure the TDS ( in ppm) of the suppliers' water. Since, you have to prove one sample is better than the other, the TDS of sampled waters could be analysed using 2-Sample t test to see if there is significant difference between the two sources of water. Since lower the TDS, the better the water quality is, verify if your supplier's water TDS is significantly lesser than his competitor's water TDS by conducting a 2-Sample t test and submit your findings to the residents' association secretary of the housing complex.