Names for variables:

horizontal / vertical
x / y
independent / dependent
free / outcome
predictor / predicted
stimulus / response
cause / effect
controlled / uncontrolled
explanatory / explained
regressor / result

Put it on the horizontal axis:
*If we directly controlled or could directly control it (e.g. price, if we run the store)
*If we think it is the “cause”, and the other variable is the “result”
*If it is a date/time value, e.g. 2007 or 12:43pm (a “when”)

but “3 hours” or “78 years of age” (a “how long”) could be either x or y.
*If it is the first in a sequence of measurements (e.g. 5th grade test score vs. 8th grade test score)

If neither variable is a clear choice to go on the horizontal axis, it might help to try the graph both ways and see if one interpretation makes more sense than another (“try it both ways”)

If there is no clear preference for one variable vs. the other, then maybe “it doesn't matter” (# people at WMU, #people at CMU)

There is a difference between "try it both ways" and "it doesn't matter".
other common "synonyms" for association:
link, relationship, correlation, correspondence, trend

should regression be included in that list?

For each of the following studies, fill in “x=” or “y=” where appropriate. If neither way seems right, write either “try it both ways” or “doesn’t matter”. Also sketch what the graph might look like.

a. __ =Price charged, __=number of this book bought today on Amazon

b. __=weight, __=height of a sample of American 20-year-olds

c. __=Average murder sentence duration by state, __=murder rate, by state

d. __=Sales of Toyota, __=Sales of Chrysler minivans, by year

e. __=Year and __=U.S. national debt

f. __=A person’s height, __=salary

g. __=A person’s salary, __=years of education

h. __=Production costs, __=gross box office income, movie by movie

i. __=Student standardized test scores, __=avg teacher salary, school by school

j. __=Age of first cancer, __=packs/day smoked, by person

k. __=Cancer rate, __=distance to high-voltage power lines, by street/block

l. __=Student standardized math test scores, 5th grade and __= score in 8th grade

m. __=Average income, __=unemployment rate, by year

Lurking variable worksheet Name:______

Suppose you read an article that says that people who eat at least one carrot a day tend to spend less on health care than those that don’t. Does this mean you should eat more carrots to stay healthier? Give an argument based on what we’ve discussed in class.

Here’s a good argument: Perhaps a hidden variable is a person’s attitude toward health. People who try to take good care of themselves probably eat a lot of veggies. They probably also have better health than those who don’t care what they eat.

Notice what is good about this argument: it proposes a specific hidden (also known as lurking) variable (rather than saying “there is a lurking variable” with no further explanation), and it says how that variable affectsboth of the variables already mentioned. It doesn’t argue that the link doesn’t exist. Another good way to argue is to give a plausible reason why the causation might go the other way than was suggested. Now it’s your turn to practice. Write down good arguments about (usually against) these statements:

  1. There is a positive link between consumption of tobacco and non-use of seatbelts. So if you want to cut down on smoking, buckle up!
  1. There is a link between the # of years of math someone takes in high school and their future income. So, Michigan should require high school students to take at least Algebra 2.
  1. An actual article said something like: there is a link between credit card debt and health problems. So, to make yourself healthier, pay down your credit cards, since credit card debt causes stress which can cause health problems.
  1. There is a link between the presence of computers in K-12 schools and their standardized test scores. Therefore, we should spend more money on computers in schools.
  1. A study shows that couples that go to church more often have a lower divorce rate than other couples. So, to keep the divorce rate low, couples should go to church more often. (PS: is this a negative correlation?)
  1. Write down any other “link” claim you’ve heard recently, and write down an argument against it. I might pick the best ones to be on a future test—and then you’d have an advantage on that question, since you wrote it!

Consider this data set of average teacher salary vs. math test scores, district-by-district in Pennsylvania for one year:

For each statement, mark True or False. Write an explanation of why it is true or false.

  1. T/F: If you give a raise of $10,000 to each teacher in a particular district, that district’s avg. test score will go up 59 points.
  1. T/F: If you live in a district with a $50,000 average teacher salary and move to a district with a $60,000 average, your child’s test scores will go up, on average, by 59 points.
  1. T/F: If you live in a district with a $50,000 average and move to a district with a $60,000 average, the average student score in that district will be 59 points higher.
  1. T/F: If you live in a district with a $50,000 average and move to a district with a $60,000 average, then on average the scores in that district will be 59 points higher.
  1. T/F: Since there is a district with a salary of about $30,000 with test scores above 1400, and another district around $65,000 with test scores below 1200, we can see that there’s no correlation between salary and test scores.
  1. Now write some true statements and some false statements about this graph; x=% of kids in the district who get free or reduced lunch.

Name:______

The book “Born to Buy” by Juliet B. Schor (2004) talks about how companies are marketing toys and foods to children.

  1. On page 125 it says “In the 1970s, Marvin Goldberg studied differences between children who saw and did not see television advertising and found that sugared cereals were more likely to be present in the homes of the former.” Is this evidence that food marketing to children is effective? Explain.
  1. On page 128, paraphrased the way a reporter might paraphrase it: “A two-year study of eleven and twelve year olds, discovered that each additional soft drink consumed per day increased the likelihood of a child's becoming obese by 60 percent.” What do you think of this study, the way it is summarized here?
  1. Here is what it actually said on page 128: “A two-year study of eleven and twelve year olds, which controlled for exercise, other food intake, and media viewing, discovered that each additional soft drink consumed per day increased the likelihood of a child's becoming obese by 60 percent.” Now what do you think?
  1. Newsweek reported on July 12, 2010: “Five experiments by Northwestern’s Adam Galinsky showed that those who have lived abroad outperform others on creativity tasks.” Does this mean that living abroad increases creativity? Explain.
  1. Newsweek reported on July 12, 2010: “According to University of Texas professor Elizabeth Vandewater, for every hour a kid regularly watches television, his overall time in creative activities—from fantasy play to arts projects—drops as much as 11 percent.” Does this mean:

a) The R^2 value in this study is 0.11?b) The slope in this study is 0.11?c) The slope in this study is -0.11? d) The intercept in this study is 0.11? e) something else? What?