Day 7, Mat115H

• Announcements:
  • Reminder: Wednesday we'll meet at Sis's on Monmouth (837 Monmouth Street, to be precise):
    • Try to get there early, to engage in informal conversations
    • We'll have a formal discussion from 9:00 to 9:30. Those who need to get back to NKU for a 10:00 may leave then, and the rest of us might hang out until about 9:50, and take the bus back.
    • I'm sure that if you need (or want) to bring your own breakfast, that will be okay. Just be discreet about it!
    • Questions or comments?

  • Your second assignment is returned: tables and impressions. Let me comment on a few things, and let's think about what we might like to ask Monica Remmy on Wednesday:
    • I'd assumed that each person would make their own report (two groups combined their efforts). I'll try to be more explicit in the future, but, as a general rule, please write up your own work.

      Regarding this Friday's presentation, you are free to write a combined report.

    • One common observation was that 505 did not appear to be the worst off. Suggestions were that 506 and 501 might be in even worse shape. What confounds this apparent effect? For example, if there are more retirees in an area, then one might expect a lower median income than for an area with more people in the labor force, even though everyone is perfectly comfortable. How do we handle this effect?

      Is there an argument for considering West Side Newport, rather than 505?

    • Some of you noticed that tract 532 used to be composed of 502 and 503. How does this mess up our analysis? What might we do?

    • Some of you did not include 501. If not, why not?

    • Is there an argument for considering West Side Newport, rather than 505? Marisa says "Maybe we should shift our focus slightly to what Mr. Neikirk is concerned with" -- namely the West Side.

    • Betsy used the word "correlation" -- this is a very important word. "One can assume that there would be a correlation between high school graduation rate and income level...."

      In what other ways do we need to keep correlation in mind?

    • Tables are better than lists. Allie highlighted the row of 505, which is great (to provide a quick point of reference). Even better: order one column. It allows us to more quickly identify correlations!

  • Reminder that you'll present on NKU interventions on Friday.

• Today we continue our discussion of Mathematics and Statistics:

  A few more general comments before we begin an exercise for today.

  • Measures of central tendency: let's look again at our height information, and compute an average height. One of our observations from last time is that the mean is sensitive to outliers, whereas the median is not.
    • arithmetic mean (which we will just call the mean)
    • median

  • Variation: things vary from the center.
    • deviation from the mean/median (sign generally matters!)
      • below average
      • above average

      Do you want to be "below average"? No -- not generally. That's an example of a bias introduced through our use of language, and a preference for a certain directionality in our use of averages.

      Do you want to be below average on "poverty"?

    • "standard deviation"
    • variance
    • outlier: a datum which fails to fit a pattern. Generally considered a "mistake" of some sort (not just an extreme case).

  • Normalization:
    • We can combine both central tendency and deviation/variation to normalize a variable.
    • This allows us to "weight things equally", or at least to assign weights properly.

  • Graphical representation
    • graphs and maps give us a better feeling sometimes for how things relate than mere numbers. We'll be playing with a computer tool for representing census data next time (I hope -- I'm trying to arrange for the computer lab for next time).
    • Graphs can be deceiving. We need to be cautious with them. They can also be very powerful.
    • In any event, graphical representation will be a very important complement to our work with numbers from the census bureau.

  • Distributions:
    • Normal distribution (the "bell-shaped curve")
    • Other distributions

• Now I'd like to conduct an exercise, using data on heights from NKU students that I obtained from a statistics class a few years back. Here's your challenge: how do we determine that male and female populations have different mean heights?
  • We know that men tend to be taller than women. So let's suppose we have a suspicion -- e.g. that one census tract is higher than another on some measure. How do we decide statistically that it is so?
  • What tools can we use? Some tools we've already discussed; others we've not yet considered (perhaps you know of some that we might use).
    • numerical
    • graphical

Some Links:

• A cool tool to allow you to visualize the neighborhood on several census variables by census tract.
  Here's what may be a commercial version of the same thing? It's got a little more resolution. I'm checking with our library to see if we can have the professional access.
• Tract 505 ACS 2006-2010 census Profiles
• Map showing Census Tract 505
• Google Earth map of the tracts of Kentucky (505 is number 27302)
• What's the Matter With Eastern Kentucky?