### Test 3 Study Guide: Consumer Statistics and Probability

The purpose of this test experience is to help you understand the material and make connections. Research has shown that the effort you expend in studying for tests and clearly explaining your work solidifies your learning.

### At the Exam

• One 8.5*11 sheet with writing on both sides allowed. You can put anything you like on your sheet.
• One scientific calculator or graphing calculator mandatory (but no cell phone nor other calculators bundled in combination with additional technologies)
• Bring a straight edge/ruler like your school i.d.
• You may have out food, hydration, ear plugs, or similar if they will help you (however any ear plugs must be stand alone--no cell phone, internet or other technological connections)

On the test, your grade will be based on the quality and depth of your responses in the timed environment (the test must be turned in when time is called). Questions will mainly consist of computations and short answer or essay types. There is NO need to write in full sentences - bullet points, etc will be fine.

The test will be a mixture of computational questions as well as critical reasoning and reflection. You will be expected to answer questions similar to activities related to class, lab and homework, although they may be on new data or media representations.

### Review

• Here is a partial sample test so that you can see and have some practice with some diverse examples of the formatting and style of questions. The actual test will differ and will be about 5 pages long.
• The main web page and class highlights page contain links to homework readings and class activities and clickers, which also serve as a good review.
• The ASULearn Review Questions for Test 3 and glossary/wiki also serve as a good review.
• Be sure you read through the following overview of topics and that you could respond to questions about these topics on the exam. I want you to understand the material and I am happy to help in office hours or on the ASULearn forum!

### Computational Questions and Critical Analysis

We have been focusing on multilayered connections from probability and statistics problem solving, including:

### Other Directed Questions and Short Essay Questions

Know big picture ideas, but it is NOT necessary to know the calculation details, i.e. I won't ask you to do a calculation, but I do expect you to be able to discuss the highlights and point of our homework readings, activities and discussions on
• golden mean (1+sqrt(5))/2 and statistics of nature
• census and sampling issues, including chicken soup
• election issues [Landon and Roosevelt, Buchanan and Gore, and the 2016 election].
• stereotype vulnerability and success in mathematics
• Leonardo da Vinci's assertion about the relationship between Armspan and Height
• correlation versus causation, including underlying variables and Bradford Hill dimensions
• meta studies and consensus to obtain reasonable certainty
• The cigarette controversy
Creating various statistical representations of data: Aside from possibly asking you to calculate the mean and/or median of a data set, computing margin of error, confidence intervals or similar computations we had in class and hw, I will not give you problems where you must create your own boxplots or regression graphs but you do need to understand how to use, read off, plug into, or analyze representations, like reading from a boxplot and then computing Median-Q1, or plugging into a regression line that is on the graph or similar.

Analyzing and critiquing various statistical representations of data:

1. Make sure that you understand what kind of information you can get from statistical representations where you are not given the underlying data points
2. Make sure that you understand how to give various spins on data and statistical representations (as if you were in advertising and wanted to use the stats to say something positive or negative about the situation, like "Here's Good News... SAT scores are declining at a slower rate").
3. Make sure that you understand how to analyze the context of the real life problem that we are working on in order to critique statistical methodology of data collection, interpretations, conclusions and predictions
• problematic instructions like those before the Mental Rotation Test may affect the results,
• it doesn't make sense to predict someone's ability when they haven't slept for 2000 hours because a human can't stay awake that long
• It is problematic to use data to predict long in the future except in very specialized circumstances like the egg bungee where we had good reason to expect a linear trend to continue because the slope, the change in distance stretched per change in rubber bands, was approximately a constant since each rubber band stretched about the same amount...
• In order to trust a causality relationship like (does cell phone use cause brain cancer?) we would like to see lots of different types of studies by different people to try and isolate hidden, underlying variables that satisfy the Bradford Hill criteria. Understanding what the possible underlying variables are and conducting sufficiently controlled experiments with alternative hypotheses are the key to examining coincidence versus causation, like in our class discussion on birds flying south, or the GE experiment on turning up or down the lights and measuring productivity, or in the Bradford Hill criteria for examining smoking and cancer.
Big Picture Connections For this test you will be asked to look at examples from the statistics segment and discuss the similarities. Ideas from the rest of this study guide work well here. For example:
• Local to global connections: data on ourselves, nature, and around the world, in addition to local to global mathematical regions
• Impossibility of checking all the cases, but finding a solution by shifting our viewpoint (Jeff Weeks' research).
It is impossible to conduct a census of everyone for most data collection situations, so we have to carefully shift our view to sampling issues (elaborate on random samples and Gallup). Note that this can also connect to local to global connections as well as truth and consequences-what is truth? When are we convinced? What are the consequences of certain truths? What is the role of chance and probability?

• Viewing objects that are impossible to see by managing small pieces at a time (Jeff Weeks' research).
When we examined the Vietnam Draft info, we obtained a scatterplot that looked random to the naked eye, but it was hard to tell because there were so many points. The regression line had a negative slope, indicating that as the birthday occurred later in the year, the draft number was lower, but the r2 value was very small, indicating a very weak correlation. It was impossible to see any patterns via the complete picture, so instead we broke the data up into smaller pieces - by month, via 12 boxplots. Here it was easy to see the pattern. November and December birthdays had a 75% chance of being drafted because q3 was under the 196 draft number, while earlier birthdays only had a 50% chance, since the median was near the 196 draft number. It turned out that the later birthdays had been thrown in on top, and not mixed well enough, so indeed it was not a random sample. Note that this is also local to global connections.

• Impossibility of constructing a solution but finding a non-constructivist approach [You might explore the notion that there is no proof in statistics, but that we can still eventually be convinced that smoking causes cancer, via the Bradford Hill criteria for example, which also relates to truth and consequences-what is truth? When are we convinced? What are the consequences of certain truths? What is the role of chance and probability?].
• Think about ethical connections such as twisting or misrepresenting statistics and the price of life
• people and their successes: David Blackwell, Florence Nightingale, George Gallup, Nate Silver, Leonardo da Vinci, Ronald Fisher, Austin Bradford Hill, psychics/stock whiz...
• critiquing pros and cons of representations
• how we connected statistics to each of the first 2 segments [geometry of the earth and universe [sum of squares Pythagorean theorem compared to least squares regression for instance], and personal finance and beyond [lottery probabilities]].

I want you to succeed!