I want to get back to our discussion of Mathematics and Statistics:
We've begun talking about mathematics (or, more precisely,
statistics). We've discussed surveys, and we talked in particular about bias.
I want to add a few things into the mix today.
- Surveys:
- Bias: two kinds that we need to avoid:
- sampling bias
- confirmation bias
- We generally survey to capture the essense of some
quantity: we collect data to create a "proxy" or
"surrogate", something measurable (but which isn't
exactly what we want).
- Variables
- Categorical (e.g. male, female)
- Ordinal (e.g. Likert scales -- from 1 to 5)
- Continuous (e.g. income)
- Metrics
- A metric is a measure of something (maybe
it's better to think of it as the "measuring stick").
- The metric is usually a proxy for something else:
e.g. schools try to reach certain scores on metrics, to
show that they're doing a good job.
- Changing units in which data are expressed shouldn't
change metrics.
- Measures of central tendency: to illustrate, let's collect heights
of you all.
- 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: something which fails to fit a pattern;
- Normalization:
- We can combine both central tendency and
deviation/variation to normalize a variable.
- This allows us to "weight things equally".
- 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.