MATH 251, P&S I, Fall 2007, Oct. 7, Day 19 .After class.

Old HW comments:  Please label graphs! (by hand if necessary...)
"Granularity"--p. 81, graph p. 92.  Rounding or being at the limits of precision of a measuring instrument means "continuous" data can pile up on the same numbers--get lines or "steps".
Transformations:  2.118 a)  x words/minute to y seconds/word:   1/x is minutes/word, 1min=60 sec., so
   y seconds/word = (1/x )(minutes/word) (60 sec/min) = (60/x) (sec/word)  monotonic decreasing.
d) y = (t-5)², not monotonic.

A. Tornado damage is not much helped by log transformation--shifts skewness the other way.  But Guinea Pig survival turns into a passable Normal curve.  The theoretical distribution model which turns normal when you take logs of all the x-values is the "lognormal" distribution (Math 300).
2.124 (fish) length and width have a linear relationship.  Fish's shape doesn't change as it grows (many coldblooded creature)--everything stays proportional.  Humans; proportions change; small children have disproportionately large heads...
2.123 (fish)  "Consider a spherical cow."  Volume = K(length)³  where K is constant of proportionality. Sphere, cube, rectangular solid with same proportions in different sizes.
And Volume on cube of length gives a nice straight line!
2.136 (heart rate on weight)  Harder, and I didn't give you the answer!  Is there now, p. 12.

Project * Handout: *  Preliminary reports due today. Please write on it if you want it back by 1 today (outside my door) or if Wed. is good enough! (i.e. if you know you won't be doing anything on it over break)  I won't be on Email after 1, till Tues. night.
Final paper 9:30 am Oct.12, Day 21. 
Presentations? Probably W or F the following week--10 min. max.  Show and tell.
   What your data set "is" and 1 or 2 results:  The most interesting, or the most curious or surprising thing, or the most clever or sophisticated or different thing you did to the data to look for meaning. 
Homework questions?  Day 18
    p.231, #3.59"how many children in your family?"  What's the bias?
  Ask:  How are missing data handled?  Police response time:  calls that were never answered were entered as "0" time.
Literary Digest poll, narrative
- - - - - - - - - - - -
Probability samples, not SRS:  details   Day 18
    Stratified Random, Multistage, Systematic Random

Start here after Break:

3.4, Toward Statistical Inference.   Details Day 18 
Outline:
Chance  behavior (a random phenomenon): Unpredictable in the short run,  predictable regular pattern in the long run.
  Sec. 3.4 :     Sample Chosen from a  Population
          (varies)             (fixed, but usually unknown)
Calculate
Numerical summary: Statistic (Latin) Parameter(Greek letter)
    Examples:           Sample mean xbar    Population mean mu (µ)  etc.
"Sampling variability"
The Statistic "estimates" the Parameter.  We hope it is close to the parameter.
  If we choose simple random samples, we can understand the pattern of values the statistic can take.

Sampling distribution of a statistic:  If we could repeat the sampling process, distribution of values for that statistic calculated from "all possible" samples (of the given size.)  Assumes probability sampling or randomized experiment design.
Shape, center, spread. (nice, often  normal)

--SRS produces unbiased estimators for most common statistics.
--Larger (random) sample produces less variability (spread)
          Size of sample matters, not proportion of population (as long as population is at least 10 times sample size).