Descriptive statistics
Quiz on Wed
- Bring your book (open book) and you will need the tables
- drawing or interpreting histograms
- how to compute mean and SD,
- use normal approximation to estimate percentages.
Normal distribution
Example from last week: take a die and roll it
1,000 times and take the average. If I repeat that 100 times, I will also get a normal
distribution. Can we histogram it and estimate the standard deviation?
see dieAverage.py
Measurement Error
- Where does error come from?
- How large is it likely to be?
- Is it biased?
When we measure things, e.g. weights, there is always some error. Mostly the chance errors cancel
out. Systematic errors that don't cancel are labelled as bias. Examples of bias are: NFIP study
on Salk vaccine. using a yard stick that is missing the beginning.
Example: NB 10 is the National Bureau of Standards 10 gram weight. It has been calibrated with
Kilogram #20. The results are shown in Table 1, p. 99. It weighs approximately 405 micrograms
less than 10.000000 grams. Note that the histogram of measurements on p. 102 does not fit a noraml
distribution. What do we do about that?
Problem 15, p 108 on pretrial conferences. Hypothesis is that conferences speed up trial.
- treatment: mandatory conference
- control: no conference
- requested conference
Is there a bias
Plotting graphs
- Draw the points: (0,0), (0.5, 0.5), (1,2), (-2.5, -2.5). Which one doesn't lie on the line?
- Draw the points: (-1, -1), (-0.5, -0.5), (0.5,0), (1,-1), Which one doesn't lie on the line?
- Draw the straight line whose equation is y = 0.5 * x + 1.5
- The slope of a line is rise/run or (change in y)/(change in x). Draw a line with slope 2 through the
origin.