# Math W50: How do they know my opinion?
# January, 2000
Monday, January 3
Note: No Class
Tuesday, January 4
Note: No Class
Wednesday, January 5
Note: No Class
Thursday, January 6
Topic: Introduction
Topic: 7 Critical Components @ overheads/seven-critical.shtml
Topic: Measurement
Act: Survey 1 @ data/survey01.shtml
Act: Survey 2 @ data/survey02.txt
Read: Utts 1-3
Vocab:
Vocab: statistics, 7 critical components, %%
individual (unit), variable, value of variable, %%
categorical variable, measurement variable, %%
discrete, continuous, validity, reliabilty, bias, variability
#Note: Class begins 2pm in NH 295
course intro, student intros, why you are in the course
Def of stats
get student ideas (on board)
more than one use of word statistics
descriptive (summary measures)
inferential
Video - FAPP #6 beginning to about 4:00
in diner
some defs (primarily of inferential statistics)
Utts: a collection of procedures and principles for
gaining information in order to make decisions
when faced with uncertainty
Amabile: a way of taming uncertainty, of turning raw data
into arguments that can resolve profound questions
Moore: the science of gaining information from numerical data
Garfunkel: the science of drawing conclusions from data with
the aid of the mathematics of probability
dictionary: the mathematics of the collection, organization,
and interpretation of numerical data, especially the
analysis of a population's characteristics by inference
from sampling
etymology: latin: statisticus - of state affairs
political right down to etymology
key elements
data
uncertainty
information/decision-making ability
science or math?
Video - Against All Odds #1: beginning thru about 13:30, 26:00 to end
[whole thing if time -- but probably not]
Three phases of a statistical study (and outline of course)
1) collect data (statistical design)
2) organize data (data analysis)
3) draw conclusions from data (statistical inference)
Survey 1: Have students add to existing list
collect data from students, have them gather 2 more each
Quiz 0: info about students
-----------
Break
-----------
Fill out survey 1 and survey 2
7 critical components that determine soundness of statistical studies
1) source of funding (why was it done?)
2) researcher contact
3) individuals studied and how selected
4) measurements made (quesitons asked)
5) setting
6) extraneous differences (other explanations for effect)
7) magnitude of claimed effect
example: drug to cure excessive barking in dogs (page 22)
example: US Voters Focus on Selves, Poll says (from Moore S:C&C)
example: most women unhappy in their choice of husbands (page 24)
didn't do this one
How data are organized:
units/individuals/subjects
variables
values of variables
immagine a grid layout
Some terminology
categorical vs. measurement variables
continuous vs. discrete
validity (proxies)
reliability
bias -- systematically off in same direction
variability
pictures of variability/bias possibilities (target)
Some things are not easily or obviously measured:
happiness (happiness newpaper article)
Apply terminology to Survey 1
Summary -- Measuring is a difficult task
example: finding cheapest grocery store
Survey 2: Wording issues
did questions 1 and 2 in class
data: 1) 6-0; 0-6 in expected direction
2) 2-4; 2-4 in expected direction
Wording Pitfalls
Bias (Intentional or unintentional)
Elian Gonzalez
Do you agree that he should be returned to his father in
Cuba? [with US Immigration and Naturalization Service]
Do you agree that he should be allowed to remain with
his relatives in Florida? [agree with boy's attorneys]
Confidentiality and Anonymity (people may lie)
positive AIDS test?
financial and sexual issues
a methods to ask sensitive questions (some answers random)
Desire to Please
"How much do you smoke?" vs. cigarette sales
didn't discuss this particular pair,
put on quiz for tomorrow
Unneccessary complexity, misunderstandings
1992 American Jewish Committee [NY Times July 8, 1994]
Does it seem possible or does it seem impossible to you
that the Nazi extermination of the Jews never happened?
(22% possible)
Does it seem possible to you that the Nazi extermination
of the Jews never happened, or do you feel certain that it
happened? (1% possible)
-------------- only got this far --------------------
"do you own stock?" cartoon
Asking the uninformed
will see an example in a video
1975 Public Affairs Act [didn't exist] (page 35)
in 1978 1/3 expressed opinion
in 1995 nearly 1/2 expressed opinion
with leading political bias, 53% expressed opinion
and tended to go with political leanings
Ordering of questions, additional information
peer pressure example (34)
Open/closed questions
museum example
Levi jeans example (page)
Defining your terms
adolescent sex: increasing or decreasing? (page 37)
unemployment
changes have been made to survey questsions
- define week as sunday to saturday so people don't
underreport weekend work
- redesign questions so definitions of 'work', 'looking
for work', 'on layoff' are uniform
- emphasize difference between 'on layoff' and 'fired'
- also split long questions into series of short
questions
"The Truth but not the Whole Truth"
Friday, January 7
Topic: Sampling
Topic: Observation and Experimentation
Act: Random Samples of %%
Circles @ http://www.calvin.edu/~rpruim/cgi-bin/random-digits.cgi
Act: What comes to mind @ data/words.txt
Read: Utts 4
Read: Utts 5
Due: HW #1 @ hw01.shtml
Vocab:
Vocab: observational study, experiment, %%
unit, population, sample, sampling frame, sample survey, %%
census, margin of error, "1 Over Root n Rule", %%
simple random sampling, stratified random sampling, %%
cluster sampling, systematic sampling, %%
random digit dialing, %%
multi-stage sampling, convenience sample, response rate, %%
treatment, explanatory variable, %%
response variable (outcome variable), control, %%
interaction, %%
confounding, placebo, placebo effect, Hawthorne effect, %%
experimenter effect, double-blind, single-blind %%
Basic categories of studies
sample survey -- ask a bunch of people a question
experiment -- looking for relationships, cause/effect
key: treatment
observational study -- looking for relationship, but no treatment
meta-analysis
case study (popular in media -- clip from ABC news?)
First 3 all have something in common: you don't measure every unit
To conduct a study properly
1) get a representative sample
2) get a large enough sample
3) decide between observational study and experiment
Sampling
terminology: unit, population, sample, sampling frame,
sample survey, census,
margin of error
sampling vs. census: samples are often possible, faster, accurate
SRS: sampling circles using random digits
Video -- Against All Odds #14: skip 35:20-41:10
[14 without bead sampling, 21 minutes with]
Sampling Methods -- make sure they understand
SRS
stratified random sampling
cluster sampling
systematics sampling
random-digit dialing
multistage sampling
Sampling difficulties
wrong sampling frame
not reaching selected individuals
low response rate
volunteer sample
haphazard or convenience sample
Literary Digest poll (1936)
Alf Landon predicted to get 3-2 victory
volunteer response to sample from poor frame
George Gallup
Quiz 1
-------------------------------------
Break: do the three words experiment
-------------------------------------
Experiment terminology and set-up
treatment, explanatory variable, response variable, control
can't get cause/effect from observational study alone
individual divided into groups
each group gets different treatment
measurements taken and comparison made between groups
looking for cause/effect: treatment -> response
Video -- FAPP segment on Physicians Health Study
Problems with experiments
Placebo effect
Gastric freezing to relieve ulcer pain
(34% in gf group, 38% in placebo group)
Lack of control, confounding variables -- randomize
1940 propaganda experiment [Germany occupied France]
Interaction -- measure and report possible variables
can turn possible confounding variables into possible
interaction variables by mesureing
nicotine patch and smokers at home
Hawthorne effect -- not always possible to avoid this problem
new curricula
Experimentor Bias -- blindness
Ecological validity/generalizability
what is the population, was setting a factor?
over weekend:
how many words come to mind from 4 others
==
Monday, January 10
Topic: Statistical Summaries
Topic: Distributions
Read: Utts 7
Read: Utts 8
Act: How Many Raisins?
Due: HW #2 @ hw01.shtml
Vocab:
mean, median, mode, outlier, range, stemplot, histogram, %%
shape, symmetric, bell-shaped, unimodal, bimodal, skewed, %%
five-number summary, quartile, boxplot, interquartile range, %%
variance, standard deviation, frequency curve, normal curve, %%
proportion, percentile, standardized score, z-score, %%
standard normal distribution, "68-95-99.7 Rule"
Ethics of experiments
informed consent
use of doctors in physicians health study
kids in art experiment
human subjects & review boards
Stanley Milgram (Yale): shock and memory
done 1960's, probably not doable today
Penny's data collection in grad school
risk: cost/benefit analysis
reasonable hope, reasonable doubt criteria for clinical trials
(did friday)
Some specific examples and issues
Nazi data
give them article (2 versions) and then discuss
twins studies -- ideal matched pairs?
PHS used only middle-aged men, what about women? minorities
1 in 5 men has heart attack before age 65
1 in 17 women has heart attack before age 65
(did friday)
AIDS and slow process of clinical trials
measuring easier but less reliable things
pressure to release drugs before effectiveness demonstrated
(mentioned friday, mention again)
domestic violence: warn and release or arrest
can a randomized experiment be done? [no informed consent]
Tuesday, January 11
Topic: Pictures of Data
Topic: Relationships between Categorical Variables
Topic: Chi-Squared
Read: Utts 9
Act: Golf Balls in the Yard
Due: HW #3 @ hw02.shtml
Vocab: pie chart, bar chart, pictogram, line graph, scatter plot
Common problems with plots, graphs, and pictures
1) missing labels
2) scale doesn't start at 0
3) changes in labeling along an axis
4) misleading units
5) poor information
Picture Checklist
overall impression
1) is message clear?
2) is purpose clear?
10) is there any clutter?
source
3) is source given?
4) is source reliable?
labeling
5) is labeling clear?
6) do axes start at 0?
7) is scale constant?
8) are there any breaks along axis? are they easy to spot?
9) was inflation adjustment made?
Banner chart and follow-up letters
Utts, Figure 9.9 (page 149) and fixed version
Read: Utts 12
Vocab: contingency table, cell, row, column, conditional percentage, %%
rate, test statistic, chi-sqaured statistic, p-value, %%
statistical significance, proportion, odds, relative risk, %%
odds ratio, Simpson's paradox %%
Golf ball distribution and test statistics
Chi-squared statistic (on golf ball data again)
what should we expect if there is no association?
how can we adjust our measurement to account for sample size?
Relative Risk
Misrepresenting risk
1) no baseline risk given
2) no time period given
3) unclear population (may not apply to you)
Simpson's Parodox
hospital example (Utts chapter 12, pages 213-215)
give combined results first, then separate
discrimination example (Utts, chapter 12, pages 215-217)
get graduate school acceptence data from Moore
Wednesday, January 12
Topic: Probability and Randomness
Read: Utts 15
Vocab: probability, relative frequency, personal probability, coherent,
Vocab: mutually exclusive events, independents events,
Vocab: cummulative probability, expected value, four probability rules
Due: HW #4 @ hw02.shtml
axiomatic method
Read: Utts 16
Thursday, January 13
Topic: More Probability
Topic: Sampling Distributions
Read: Utts 17
Read: Utts 18
Due: HW #5
Friday, January 14
Topic: Inference for Proportions
Read: Utts 19
Read: Utts 20
Due: HW #6
==
Monday, January 17
Topic: Inference for Proportions
Topic: Chi-Squared Again
Read: Utts 21
Read: Utts 22
Due: HW #7
Tuesday, January 18
Topic: More about Inference
Topic: Significance and Importance
Read: Utts 23
Due: HW #8
Wednesday, January 19
Topic: Risk Assessment
Read: Utts 12.3-12.4
Due: HW #9
Greatest Risks (problem 11.4 on page 191 of Utts)
have students rank risks of 10 to 30 different items
discuss how to measure relative risk
Act: Video: Are We Scaring Ourselves to Death?
Thursday, January 20
Topic: Test
Friday, January 21
Topic: TBA
==
Monday, January 24
Topic: Inference for Measurement Variables
Due: HW #10
Tuesday, January 25
Topic: Wrap-Up
Due: HW #11
Wednesday, January 26
Topic: Test
Thursday, January 27
Note: no class
Friday, January 28
Note: no class
== end of calendar
Read: Utts 13, 14
Vocab: CPI, price index numbers, leading economic indicator,
Vocab: coincident economic indicator, lagging economic indicator,
Vocab: time series, long-term trend, seasonal adjustment