Name that tune.
Song title? Performer(s)?
R.G. Bias | rbias@ischool.utexas.edu |
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Scientific Method and
Statistics
(continued)
“Finding New Information”
3/28/2010
R.G. Bias | rbias@ischool.utexas.edu |
2
Objectives
 Continue experimental design and statistics.
-
Randolph – remember to take roll.
- Who thinks there are two people in this
classroom with the same birthday? (Month and
day – not year.)
http://www.nytimes.com/2009/08/06/technology/06
stats.html
R.G. Bias | rbias@ischool.utexas.edu |
To summarize
Mode
Range
-Easy to calculate.
-May be misleading.
Median
SIQR
Mean
(µ)
SD
(σ)
-Capture the center.
-Not influenced by
extreme scores.
-Take every score into
account.
-Allow later
manipulations.
R.G. Bias | rbias@ischool.utexas.edu |
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 Let me work an example all the way
through.
R.G. Bias | rbias@ischool.utexas.edu |
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Summary
 An experiment is “personkind’s way of asking nature a question.”
 I manipulate some variables (IVs), control other variables, count on
random assignment to wash out the effects of all the rest of the
variables, and look for an effect on the DVs.
 Independent Groups = Between-subjects design
 Repeated Measures = Within-subjects design
 Natural Groups Design = Pseudoexperiment = NO inference of
causality
 I start with a null hypothesis and an alternate hypothesis.
 If I find a difference (in my DV), I infer it was caused by the IV (the
treatment) and I reject my H0 and accept my HA.
 If I find no difference I do NOT accept the H0, rather I say that we do
not have any evidence to reject it at this time. (NOTE how hard it is
to prove the absence of something!)
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R.G. Bias | rbias@ischool.utexas.edu |
Role of Data Analysis in Exps.
 Primary goal of data analysis is to
determine if our observations support a
claim about behavior. Is that difference
really different?
 We want to draw conclusions about
populations, not just the sample.
 Two different ways – statistics and
replication.
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R.G. Bias | rbias@ischool.utexas.edu |
Scales
 The data we collect can be represented on
one of FOUR types of scales:
– Nominal
– Ordinal
– Interval
– Ratio
 “Scale” in the sense that an individual
score is placed at some point along a
continuum.
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R.G. Bias | rbias@ischool.utexas.edu |
Nominal Scale
 Describe something by giving it a name. (Name
– Nominal. Get it?)
 Mutually exclusive categories.
 For example:
– Gender: 1 = Female, 2 = Male
– Marital status: 1 = single, 2 = married,
3 = divorced, 4 = widowed
– Make of car: 1 = Ford, 2 = Chevy . . .
– Thinks sex is a good thing: 1 = Yes, 2 = No
 The numbers are just names.
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R.G. Bias | rbias@ischool.utexas.edu |
Ordinal Scale
 An ordered set of objects.
 But no implication about
the relative SIZE of the
steps.
 Example:
– The 50 states in order
of population:
•
•
•
•
– People “Sue” has ever
wanted to have sex
with, by height:
•
•
•
•
1 = Vern
2 = Joe
3 = Mick
4 = Tim
1 = California
2 = Texas
3 = New York
. . . 50 = Wyoming
R.G. Bias | rbias@ischool.utexas.edu | 10
Interval Scale
 Ordered, like an ordinal scale.
 Plus there are equal intervals between each pair
of scores.
 With Interval data, we can calculate means
(averages).
 However, the zero point is arbitrary.
 Examples:
– Temperature in Fahrenheit or Centigrade (of the room
where someone had sex)
– IQ scores
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R.G. Bias | rbias@ischool.utexas.edu |
Ratio Scale
 Interval scale, plus an absolute zero.
 Sample:
– Distance, weight, height, time (but not years –
e.g., the year 2002 isn’t “twice” 1001).
– Number of times “Mary” thought about sex.
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R.G. Bias | rbias@ischool.utexas.edu |
Scales (cont’d.)
It’s possible to measure the same attribute on
different scales. Say, for instance, your midterm
test. I could:
 Give you a “1” if you don’t finish, and a “2” if you
finish.
 “1” for highest grade in class, “2” for second
highest grade, . . . .
 “1” for first quarter of the class, “2” for second
quarter of the class,” . . .
 Raw test score (100, 99, . . . .).
– (NOTE: A score of 100 doesn’t mean the person
“knows” twice as much as a person who scores 50,
he/she just gets twice the score.)
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R.G. Bias | rbias@ischool.utexas.edu |
Scales (cont’d.)
Nominal
Ordinal
Interval
Ratio
Name
=
=
=
Mutuallyexclusive
=
=
=
Ordered
=
=
Equal interval
=
+ abs. 0
Days of wk.,
Temp.
Inches, Dollars
Gender,
Yes/No
Class rank,
Survey ans.
R.G. Bias | rbias@ischool.utexas.edu |
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Critical Skepticism
 Remember the Rabbit Pie example from
earlier?
 The “critical consumer” of statistics asked
“what do you mean by ’50/50’”?
 Let’s look at some other situations and
claims.
– From How to Lie with Statistics.
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R.G. Bias | rbias@ischool.utexas.edu |
Company is hurting.
 We’d like to ask you to take a 50% cut in
pay.
 But if you do, we’ll give you a 75% raise
next month. OK?
 Problem: Base rate.
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R.G. Bias | rbias@ischool.utexas.edu |
Sale!
 “Save 100%”
 I doubt it.
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R.G. Bias | rbias@ischool.utexas.edu |
Probabilities
 “It’s safer to drive in the fog than in the
sunshine.” (Kinda like “Most accidents occur
within 25 miles of home.” Doesn’t mean it gets
safer once you get to San Marcos.)
 Navy literature around WWI:
– “The death rate in the Navy during the SpanishAmerican war was 9/1000. For civilians in NYC
during the same period it was 16/1000. So . . . Join
the Navy. It’s safer.”
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R.G. Bias | rbias@ischool.utexas.edu |
Are all results reported?
 “In an independent study [ooh, magic
words], people who used Doakes
toothpaste had 23% fewer cavities.”
 How many studies showed MORE cavities
for Doakes users?
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R.G. Bias | rbias@ischool.utexas.edu |
Sampling problems
 “Average salary of 1999 UT grads –
“$41,000.”
 How did they find this? I’ll bet it was
average salary of THOSE WHO
RESPONDED to a survey.
 Who’s inclined to respond?
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R.G. Bias | rbias@ischool.utexas.edu |
Correlation ≠ Causation
 Around the turn of the 20th century, there
were relatively MANY deaths of
tuberculosis in Arizona.
 What’s up with that?
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R.G. Bias | rbias@ischool.utexas.edu |
Remember . . .




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I do NOT want you to become cynical.
Not all “media bias” is intentional.
Just be sensible, critical, skeptical.
As you “consume” statistics, ask some
questions . . .
R.G. Bias | rbias@ischool.utexas.edu |
Ask yourself. . .
 Who says so? (A Zest commercial is unlikely to tell
you that Irish Spring is best.)
 How does he/she know? (That Zest is “the best
soap for you.”)
 What’s missing? (One year, 33% of female grad
students at Johns Hopkins married faculty.)
 Did somebody change the subject? (“Camrys are
bigger than Accords.” “Accords are bigger than
Camrys.”)
 Does it make sense? (“Study in NYC: Working
woman with family needed $40.13/week for adequate
support.”)
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R.G. Bias | rbias@ischool.utexas.edu |
Claims
 “Better chance of being struck by
lightening than being bitten by a shark.”
 Tom Brokaw – Tranquilizers.
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R.G. Bias | rbias@ischool.utexas.edu |
The Normal Distribution
(From Jaisingh [2000])
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R.G. Bias | rbias@ischool.utexas.edu |
Notice
 Many things influence how easy or hard it
is to discover a difference.
– How big the real difference is.
– How much variability there is in the population
distribution(s).
– How much error variance there is.
– Let’s talk about variance.
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R.G. Bias | rbias@ischool.utexas.edu |
Sources of variance
 Systematic vs. Error
– Real differences
– Error variance
 What would happen to the DV if our measurement
apparatus was a little inconsistent?
 There are OTHER sources of error variance, and the
whole point of experimental design is to try to minimize
‘em.
Get this: The more error variance, the harder for real
differences to “shine through.”
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R.G. Bias | rbias@ischool.utexas.edu |
Z distribution
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R.G. Bias | rbias@ischool.utexas.edu |
Probability
 VERY little of life is certain.
 It is PROBABILISTIC. (That is, something
might happen, or it might not.)
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R.G. Bias | rbias@ischool.utexas.edu |
Prob. (cont’d.)
 Life’s a gamble!
 Just about every decision is based on probable
outcomes.
 None of you is a “statistical wizard.” Yet every
one of you does a pretty good job of navigating
an uncertain world.
– None of you touched a hot stove (on purpose.)
– All of you made it to class.
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R.G. Bias | rbias@ischool.utexas.edu |
Probabilities
 Always between one and zero.
 Something with a probability of “one” will
happen. (e.g., Death, Taxes).
 Something with a probability of “zero” will not
happen. (e.g., My becoming a Major League
Baseball player).
 Something that’s unlikely has a small, but still
positive, probability. (e.g., probability of
someone else having the same birthday as you
is 1/365 = .0027, or .27%.)
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R.G. Bias | rbias@ischool.utexas.edu |
Just because . . .
 . . . There are two possible outcomes,
doesn’t mean there’s a “50/50 chance” of
each happening.
 When driving to school today, I could have
arrived alive, or been killed in a fiery car
crash. (Two possible outcomes, as I’ve
defined them.) Not equally likely.
 But the odds of a flipped coin being
“heads,” . . . .
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R.G. Bias | rbias@ischool.utexas.edu |
Let’s talk about socks
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R.G. Bias | rbias@ischool.utexas.edu |
Prob (cont’d.)
 Probability of something happening is
–
–
–
–
# of “successes” / # of all events
P(one flip of a coin landing heads) = ½ = .5
P(one die landing as a “2”) = 1/6 = .167
P(some score in a distribution of scores is greater
than the median) = ½ = .5
– P(some score in a normal distribution of scores is
greater than the mean but has a z score of 1 or less is
...?
– P(drawing a diamond from a complete deck of cards)
=?
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R.G. Bias | rbias@ischool.utexas.edu |
Yet more prob.
 http://www.midcoast.com.au/~turfacts/maths.htm
l
– The product or multiplication rule. "If two chances
are mutually exclusive the chances of getting
both together, or one immediately after the other,
is the product of their respective probabilities.“
– the addition rule. "If two or more chances are mutually
exclusive, the probability of making ONE OR OTHER
of them is the sum of their separate probabilities."
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R.G. Bias | rbias@ischool.utexas.edu |
What’s the probability . . .






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That the next card is a king?
That the next card is a heart?
That the next card is a spade?
That the next card is a club and a king?
That the next card is a spade OR a heart?
That the next two cards are kings?
R.G. Bias | rbias@ischool.utexas.edu |
Think this through.
 What are the odds (“what are the
chances”) (“what is the probability”) of
getting two “heads” in a row?
 Three heads in a row?
 Three flips the same (heads or tails) in a
row?
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R.G. Bias | rbias@ischool.utexas.edu |
So then . . .
 WHY were the odds in favor of having two
people in our class with the same
birthday?
 Think about the problem!
 What if there were 367 people in the class.
– P(2 people with same b’day) = 1.00
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R.G. Bias | rbias@ischool.utexas.edu |
Happy B’day to Us
 But we had 50.
 Probability that the first person has a
birthday: 1.00.
 Prob of the second person having the
same b’day: 1/365
 Prob of the third person having the same
b’day as Person 1 and Person 2 is 1/365 +
1/365 – the chances of all three of them
having the same birthday.
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R.G. Bias | rbias@ischool.utexas.edu |
Sooooo . . .
 http://en.wikipedia.org/wiki/Birthday_parad
ox
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R.G. Bias | rbias@ischool.utexas.edu |
References
 Hinton, P. R. Statistics explained.
 Shaughnessy, Zechmeister, and
Zechmeister. Experimental methods in
psychology.
R.G. Bias | rbias@ischool.utexas.edu | 42
 http://highered.mcgrawhill.com/sites/0072494468/student_view0/
statistics_primer.html
 Click on Statistics Primer.
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