Review

Computational Questions and Critical Analysis

• probabilities and confidence intervals and margin of error (see also ASUlearn questions and clickers) including
  • Probability and Chance in Birthday and Global Populations
  • David Blackwell and controversy of Friend or Foe
  • expected value
  • Benford's law
  • Clickers on probability
  • Fisher's experiment of a lady tasting tea
  • clicker review of confidence intervals
  • Gallup polls
  • price of a life
  • HIV testing
  • 2 independent tests
  • clicker review of readings on deciding public policy
  • detective lab
• mean and median including
  • real estate prices
  • comparing and ranking country data
  • salary data
  • mental rotation tests
  • Stumbling through data clickers
• box plots (see also ASUlearn and clicker questions) including
  • haircut costs
  • comparing and ranking country data
  • Nielsen boxplots
  • 1969 Vietnam draft
  • reaction time with cell phone usage
  • armspan and height
  • distance from home
  • Stumbling through data clickers
  • detective lab
• linear regression (see also lab, clickers, ASULearn questions, and class activities) including
  • what kind of predictor something is via the r² percentage (and put this chart on your reference sheet), what prediction the regression line gives for x-values or y-values, whether or not the prediction makes sense given the context of the problem, and the impact of adding or removing outliers on the slope of the line and the r² value.
  • midterm errors
  • multiple regressions and Bradford-Hill criteria, including the controversy of 1994
  • Correlation Lab
  • Clicker review of correlations
  • detective lab
  • confounding issues
  • critique media or other statistical data and representations (like Gallup polls or worst graph)---what kind of predictor something is via the r² percentage (and put this chart on your reference sheet) or visualizations like Gapminder, what prediction the regression line gives for x-values or y-values, whether or not the prediction makes sense given the context of the problem, and the impact of adding or removing outliers on the slope of the line and the r² value.
  • ethical standards, confounding variables, and bias

Other Directed Questions and Short Essay Questions

• 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
• misleading advertising and labeling

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.

• 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]].