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Exercises 2.9 Exercises

1.

Objective: Understand the sources and consequences of error in a single measurement.

Method: Develop a method to measure the height of your instructor (teacher, professor, etc) and make the measurement. Use that measurement to make another measurement. Then use the second measurement in an equation.

Instructions

  1. Split up into teams of two or more.

  2. One team gets a tape measure. Another team gets a yardstick. Still another team gets a 1-ft ruler.

  3. Agree on how you will measure your instructor's height.

  4. Make the measurement according to the selected approach.

  5. Now measure the length, width, and/or height of the classroom using the instructor's height.

  6. Calculate the volume of the classroom using the length, width, and height.

  7. Compare the methods selected, the tools available, the individual measurements, and the result from the equation for the different groups.

  8. Have each group identify the possible sources of error in the exercise and how they propagate.

  9. Discuss the groups' results with respect to the five Cs explained in the text: coincidence, correlation, causation, convergence, and consensus. Which ones apply?

  10. Extrapolate the findings to general sources of misinformation, misleading information, studies and research taken in isolation, etc.

2.

Objective: Understand the assumptions which go into a "forecast" or a simulation, in this case an on-line financial calculator, and its purpose.

Method: Study the instructions, narrative, and results for an on-line calculator that forecasts/estimates how you much you will need to save to achieve certain retirement savings goals.

Instructions:

  1. Thoroughly review the material at this link: https://www.nerdwallet.com/investing/retirement-calculator. Note: there's no need to download the app, just work with this page and see how the numbers change and, importantly, the colors adjust on the graphics

  2. Identify as many of the assumptions used to "build" this calculator - some may be obvious, some may not. Hint: A "default" value is also an assumption. There are also hidden assumptions.

  3. After reading thoroughly, go through the forms on the left and "play" with the numbers - record the "scenarios" you try by listing and grouping the values you use - age, pre-tax income, current savings, monthly savings rate, etc. You can think of the differences in the "values" you select in the same way as "errors" in the previous example.

  4. See if you can identify the assumption(s) or defaults which have the greatest impact on the results

  5. Contemplate why this calculator is available free of charge. What is the purpose of the company making this calculator available? Hint: Where does the "Get started" button take you?

  6. Did you remember to hit the link at the very top in very small print, "advertiser disclosure"? And did you click on the "list of partners" at the end of the text box?

  7. Discuss and defend whether you would classify this "calculator" as good information, misleading information, or misinformation? Or, is it independent/objective 'content' or advertising? Is it "useful" content regardless of how you classify it?

3.

Objective: Assess the validity of claims made in a public policy advertisement.

Method: Apply "reverse quantitative analysis" (RQA), or working backwards from the numerical result to assess the error, biases, assumptions, uncertainties, exaggerations, dramatization, etc.., to this headline: "Social Isolation Is As Deadly As Smoking Up to 15 Cigarettes a Day," in a public policy/campaign ad by Meals on Wheels (www.mealsonwheelsamerica.org) to encourage viewers/readers to donate money.

Instructions

  1. First, from a "math for the people" point of view, what are the most important words in the headline?

  2. Research this 'claim" by doing as much searching on the internet as possible and write up your findings.

  3. Ask yourself how do they define "social isolation?" How do they measure it?

  4. Explain to yourself how they have arrived at this association between social isolation and smoking.

  5. Apply the 5 Cs to this situation.

  6. Would you characterize this statement as good information, misleading information, misinformation, or a flat out lie? Or a worthwhile dramatization, useful exaggeration, or hype?

4.

Objective: Learn to identify a flawed graph.

Method: Find a flawed graph, indicate how the creator of the graph wants people to interpret it, and then discuss how it would be interpreted if the y-axis or x-axis were constructed differently.

Instructions:

  1. In a previous class, ask students to bring in graphs they find online. Partisan news organizations are a good place to look.

  2. Ask each student to show the class their graph.

  3. For each, first ask the students as a whole the likely interpretation intended and then how it could be fixed to cause people to interpret it more accurately.