MATH 251, Probability and Statistics I, Fall 2005, Oct. 3, Day 17 

Reading  for Friday:   Chapter 3:  Finish 3.2.  For Friday,  3.3.  Ahead, 3.4
Hand in Friday:
Sec. 3.2, p. 210ff.
3.15 tea and cataracts Use Table B to assign the rats.
3.35 nature of random digits
Fancier:
3.30 forest CO2
3.31 calcium
3.34 ultramarathon and C
3.32 reducing  For part b, there may be different correct ways to do the random assignment.  You want to avoid having all the lowest-excess-in-their-group people getting plan A, for instance.
+ + + + + + + + +
Sec. 3.3, p. 225ff.
3.36 students
3.41 SRS, use Table B
3.55 sampling frame
3.56 online poll
3.59 why biased?
 Read, discuss 
3.14, 3.16
  + + + + 

 3.37, 3.38

 Optional 

 
HW Questions?
Pick a digit, from 0,1,2,3,4,5,6,7,8,9.  Write it down.
First midterm: two parts: in-class exam this Wednesday, Oct. 5,  Day 18 (No LaReina Thurs-Sun)
   Exam will cover chapters 1, 2, and the first part of 9.  ("Exploratory" data analysis). No questions on how to create SPSS output; but reading SPSS output may be on it. Understanding and using formulas, definitions, properties + Derivations: For sure, either: Day 4 problem B (showing what a+bx does to mean and s.d.), or Day 10, problem B (showing that m = ybar minimizes sum of squared distances from a point m.)  Case n=3 is sufficient.
Using normal tables.

Plus data analysis project, in pairs.   * Handout: *  Preliminary report due 4pm Oct. 14, Day 20.  Final paper 9:30 am Oct.17, Day 22. Pairs:  See Day 15.
Some more data sources

Ch. 3:  Producing Data:  Aim:  create data sets that will allow us to make inferences to a larger world than just the data we have.
Design of experiments Sec 3.2       Day 15 ,

Principles of designing an experiment (p. 203) Control Randomize Repeat
  "Control what you can, Randomize the rest."

Day 16 Simple Random Sample (SRS) of size n:  n individuals chosen in such a way that every possible set of n individuals has an equal chance of being chosen.  (Sec. 3.3)
Fancier Experimental designs (not "completely randomized") Matched pairs: Block design: 

= = = = = = = = = = = = = =
Sampling Design Sec 3.3 (Observational study, usually)  "Sample survey"
>>Population: Entire group  that we want information about.
>>Sample: The part of the population we actually examine.
      Hope:  Sample will be representative of the population.

(SAMPLING) BIAS:  The design of a study is biased if it systematically favors certain outcomes.
    Check our "sample" of digits

Probability sample: sample chosen by an impersonal chance mechanism
Some refinements:
*Sampling frame: IPS p. 230 problem 3.55: the group from which the sample is actually chosen--as different from the "population"--the group you want information about. The sampling frame is often, unfortunately, smaller than the population.  The sample is (usually much) smaller than the sampling frame.
* "Chosen" sample may not turn out to be actual sample, if some individuals don't respond--"Nonresponse", p. 222.

Non-probability samples:

Simple Random Sample (SRS) of size n:  n individuals chosen in such a way that every possible set of n individuals has an equal chance of being chosen.

Sources of bias, even in probability samples:

Next:  some fancier sampling designs:  Systematic, Stratified, Multistage
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