Portfolio Project #3: Inference
In this project, you will implement three types of hypothesis tests: A Chi-square test of goodness of fit, a one sample hypothesis test, and a two-sample hypothesis test.
Deliverable 1: Benford’s Law (Excel and Video Submission)
When interviewing for quantitative positions, you'll often meet with professionals who are just a few years ahead of you in their careers and may believe they have a much stronger grasp of math than you do. If you can share something intriguing about mathematics that they’re unfamiliar with, you’ll demonstrate both your knowledge and quantitative expertise.
In this deliverable, you will learn about “Benford’s Law”, a seeming paradox / unexpected fact about the distribution of leading numbers in datasets which draw from distributions that span multiple orders of magnitude. You will show that Benford’s Law holds in all sorts of surprising datasets.
Fortunately, few people know about this interesting law, so it’s a perfect way to surprise an interviewer with how smart you are!
Deliverable 1: Is a Brightspace submission and has 3 Parts.
• Learn about Benford: Nothing needs to be submitted.
• Chi-square tests: (60 points available) Submit an Excel file with your Chi-Square tests.
• Video of you discussing Benford: (20 points available) Submit a short video of you
explaining Benford’s Law, why it is so surprising, and how it can be used to detect fraudulent business records.
Part 1: Learn about Benford’s Law (Just learning, not a submission).
Learn about Benford’s Law. Here are places where you can learn about it. You’ll know you’ve learned about it when you can say what it is, when it can be applied, and why it’s interesting / useful.
1. Readings:
a. https://en.wikipedia.org/wiki/Benford%27s_law
b. https://www.isaca.org/resources/isaca-journal/past-issues/2011/understanding-and-applying-benfords-law
c. https://www.scientificamerican.com/article/what-is-benfords-law-why-this-unexpected-pattern-of-numbers-is-everywhere/
2. On YouTube, you can watch some of the following:
a. (Great video) Numberphile: https://www.youtube.com/watch?v=XXjlR2OK1kM
b. (About politics) Stand-up Maths:
https://www.youtube.com/watch?v=etx0k1nLn78
c. (Short and sweet) Minding The Data:
https://www.youtube.com/watch?v=42fGFDNs-0A
3. If you have Netflix, watch Season 1 Episode 4 “Digits” of the show “Connected: The Hidden Science of Everything”. This is a little pop-sciencey, but it’s entertaining.
4. If you don’t understand Benford’s Law after these resources, it is a good time to practice hunting for information you don’t know. Google Benford’s law and see if people have discussed what you don’t understand.
Part 2: Chi-square tests: Conducting Chi-square Goodness of Fit tests on data from Benford website (Part 2 is an Excel submission)
Go to https://testingbenfordslaw.com/ and select 3 of the available datasets that interest you.
Then, run hypothesis tests on each to see if they follow Benford’s Law.
If you need help testing Benford’s Law in Excel, read this article which describes it:
https://www.isaca.org/resources/isaca-journal/past-issues/2010/using-spreadsheets-and-benfords-law-to-test-accounting-data
1. (10 points each) Go to https://testingbenfordslaw.com/ and select 3 of the available datasets that interest you. For each dataset:
a. (1 point) Record the number of records.
b. (1 point) Record the frequency of each leading digit.
c. (3 points) Find the expected count and the actual count of each leading digit.
d. (5 points) Using a Chi-square goodness of fit test, test whether the observed distribution matched the expected distribution of Benford’s Law at the 5% significance level.
2. (10 points) For each of your three datasets, discuss whether Benford’s Law held up and discuss what surprised you about these findings. Use 4-5 sentences to discuss.
**You will end up with 3 separate chi-square tests, one for each of your datasets.
Part 3: Video of you discussing Benford,s Law: Practice describing Benford,s Law to potential recruiters (Part 3 is a video submission you will upload to Brightspace)
Record a 60 second video of yourself explaining Benford's Law. You can record using your computer or phone – both file formats will be available for upload to Brightspace.
1. (20 points) Record a video of yourself succinctly explaining Benford's Law. You should cover three topics:
a. What is Benford’s Law
b. What makes it interesting (using one of your datasets as an example)
c. Describe how it can be used to detect fraud in business settings.
2. The video should be a minimum of 60 seconds long.
Deliverable 2: One- and Two-Sample Hypothesis Tests & Business Plan
Here, you will conduct hypothesis tests on real-world data and use hypothesis testing to justify a business strategy of your own creation.
This assignment will have you thinking ahead. You will select indicators on the World Bank data repository on your own and use them in combination to justify a business proposal.
Data is available here: https://data.worldbank.org/indicator
Deliverable 2 is a Gradescope pdf submission. Create a slide deck9 save it as a pdf9 submit the pdf
• Submit one slide deck (you can create the slide deck in any program, but it should be saved as a .pdf when submitted on GradeScope).
o One-sample HT: (20 points available) The first 2 slides of the slide deck.
o Two-sample HT: (20 points available) Slides 3 and 4 of your slide deck.
o Business Plan: (20 points available) Slides 5 and 6 of your slide deck. (If your
business proposal for slide 6 needs to be longer, you may extend your slide deck.)
One-sample HT: Conducting One-Sample Hypothesis tests on real-world data.
1. Go tohttps://data.worldbank.org/indicator
2. Select an indicator that interests you and download its associated data as an Excel file.
a. Warning: not all data is as available as other data. Make sure you select a dataset which has enough data to run your analyses!
3. Calculate an average of your indicator of interest, either across a single year for many countries, across multiple years for a single country, or across a single year for a single region. Ensure that you have at least 30 points of data in this average.
a. For your indicator of interest, what is an important threshold value under or over which important things happen? (For example, we are concerned if infant mortality is above X). How did you find this threshold?
b. Conduct a one sample hypothesis test to see if the world is above or below that threshold. Select a significance level you find appropriate.
Slides 1 & 2:
1. (10 points) Answer the following questions on Slide 1:
a. Summarize what data you choose.
b. Summarize any cleaning you needed to do to make it suitable for hypothesis testing.
c. Explain why this indicator is interesting / important.
2. (10 points) Answer the following questions on Slide 2:
a. What were your null and alternative hypotheses?
b. Why did you choose the threshold that you did? What makes it an important threshold?
c. What was your significance level?
d. What were the results of your hypothesis test, including your p value and conclusion?
Two-sample HT: Conducting Two-Sample Hypothesis tests on real-world data.
1. Select another indicator of interest (Different from your one-sample indicator)
2. Select two regions within the world, as grouped by the world bank metadata.
3. Conduct a two-sample hypothesis test of the difference in means for this indicator of interest. Choose your own significance level. What are your results?
Slides 3 & 4:
1. (10 points) Answer the following questions on Slide 3:
a. Summarize what data you choose.
b. Summarize any cleaning you needed to do to make it suitable for hypothesis testing.
c. Explain why this indicator is interesting / important.
2. (10 points) Answer the following questions on Slide 4:
a. What were your null and alternative hypotheses?
b. What was your significance level?
c. What were the results of your hypothesis test, including your p value and conclusion?
Business Plan: Using Hypothesis tests as a foundation for solid business planning.
Consider a real international corporation or government entity whose business is impacted by the indicators you chose in your one- and two-sample hypotheses. Create a business plan which incorporates the results of your hypothesis tests (i.e., your one- and two-sample HTs).
Slides 5 & 6:
1. (5 points) On slide 5, answer the following questions:
a. How is the organization related to your indicator?
b. How do the results of your hypothesis tests impact your business’ operations?
2. (15 points) On slide 6 (and beyond), create a proposal for your business which accounts for your hypothesis test. You may use multiple slides for this purpose.
a. How would your plan differ if your hypothesis test concluded the other way?
b. Of course, a simple hypothesis test isn’t enough to make a decision of international proportions. What other data would you collect and what tests would you run to help ensure that your proposal was worthwhile?