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INF397C
Introduction to Research in Information
Studies
Fall, 2009
Week 12
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
1
From Blink, by Malcolm Gladwell
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• P. 32. The author is talking about negative
emotions that tend to predict subsequent
break-ups of marriages:
“. . . there is one emotion that [Dr. Gottman]
considers the most important of all: contempt.
If Gottman observes one or both partners in a
marriage showing contempt for one another,
he considers it the single most important sign
that the marriage is in trouble.”
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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p. 33
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“Gottman has found, in fact, that the
presence of contempt in a marriage can
even predict such things as how many
colds a husband or wife gets; in other
words, having someone you love
express contempt toward you is so
stressful that it begins to affect the
functioning of your immune system.”
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
3
More resources – Assorted things
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• http://www.stat.berkeley.edu/~stark/Java/Html/
NormHiLite.htm Use the slider bars! Man,
don’t you wish you had had access to this tool
for the last question on the midterm?!
• http://www.stat.berkeley.edu/~stark/Java/Html/
StandardNormal.htm Play with the standard
deviation slider bar!
• http://wwwstat.stanford.edu/~naras/jsm/NormalDensity/N
ormalDensity.html
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
4
More resources -- SE
•
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Dr. Phil Doty’s 26-minute online tutorial on standard error of the mean. Very
helpful:
http://cobra.gslis.utexas.edu:8080/ramgen/Content2/faculty/doty/research/dsmbb.r
m
–
–
–
Note, I had not talked of “expected value.” When you hear that “M is the expected value
of µ,” you can substitute “M is used to estimate µ.”
Note also we have not talked about “CV,” though last week I did say to expect that S is
kinda of the same general order of magnitude, but smaller than, M. Same idea.
Don’t forget Dr. Doty’s page of tutorials,
http://www.gslis.utexas.edu/~lis397pd/fa2002/tutorials.html
where you will find also an eight-minute introduction to inferential statistics, two tutorials on
confidence intervals, and one on Chi squared.
I think one thing you’ll find interesting in these tutorials is that here is a second professor,
using a different text book (Spatz), who studied at a different school, who’s never heard
me lecture (nor I him) . . . and we use much the same language to describe things. The
point is, this stuff (descriptive and inferential statistics) is universal.
•
Two pages of explanation of standard error of the mean:
http://davidmlane.com/hyperstat/A103735.html
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
5
More resources - Probability
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• A visual demonstration of probability and
outliers (or some such). Here’s a good one:
http://www.ms.uky.edu/~mai/java/stat/GaltonM
achine.html
• Here’s another:
http://www.stattucino.com/berrie/dsl/Galton.ht
ml
• http://www.mathgoodies.com/lessons/vol6/intr
o_probability.html
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
6
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• http://highered.mcgrawhill.com/sites/0072494468/student_view0
/statistics_primer.html
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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t tests
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• Go to the McGraw-Hill statistics primer and read the
subsections on Inferential Statistics. Not a lot of meat,
there, but it will help you to hear it stated in a slightly
different way.
• For some examples of the use of t tests . . .
– http://www.yogapoint.com/info/research.htm for an example of
some t tests.
– http://www.main.nc.us/bcsc/Chess_Research_Study_I.htm
Notice how they continually say “p>.05” rather than “p<.05”! Do
NOT, as they suggest at the end, “send a check for $39.95
payable to the American Chess School.”
Go find more examples, just for yourself.
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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Confidence Intervals
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• We calculate a confidence interval for a population parameter.
• The mean of a random sample from a population is a point
estimate of the population mean.
• But there’s variability! (SE tells us how much.)
• What is the range of scores between which we’re 95% confident
that the population mean falls?
• Think about it – the larger the interval we select, the larger the
likelihood it will “capture” the true (population) mean.
• CI = M +/- (t.05)(SE)
• See Box 12.2 on “margin of error.” NOTE: In the box they arrive
at a 95% confidence that the poll has a margin of error of 5%. It
is just coincidence that these two numbers add up to 100%.
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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CI about a mean -- example
•
•
•
•
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CI = M +/- (t.05)(SE)
Establish the level of α (two-tailed) for the CI. (.05)
M=15.0 s=5.0 N=25
Use Table A.2 to find the critical value associated with the df.
– t.05(24) = 2.064
• CI = 15.0 +/- 2.064(5.0/SQRT 25)
= 15.0 +/- 2.064
= 12.935 – 17.064
“The odds are 95 out of 100 that the population mean falls between
12.935 and 17.064.”
(NOTE: This is NOT the same as “95% of the scores fall within this
range!!!)
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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Another CI example
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• Hinton, p. 89.
• t test not sig.
• What if we did this via confidence
intervals?
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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Type I and Type II Errors
World
Our
decision
Reject the
null
hypothesis
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Null
Null
hypothesis is hypothesis is
false
true
Correct
decision
Type I error
(α)
Fail to reject Type II error Correct
the null
(β)
decision
hypothesis
(1-β)
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
12
Limitations of t tests
•
•
•
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Can compare only two samples at a
time
Only one IV at a time (with two levels)
But you say, “Why don’t I just run a
bunch of t tests”?
a) It’s a pain.
b) You multiply your chances of making a
Type I error.
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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ANOVA
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• Analysis of variance, or ANOVA, or F
tests, were designed to overcome these
shortcomings of the t test.
• An ANOVA with ONE IV with only two
levels is the same as a t test.
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
14
ANOVA (cont’d.)
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• Remember back to when we first busted out some
scary formulas, and we calculated the standard
deviation.
• We subtracted the mean from each score, to get a feel
for how spread out a distribution was – how DEVIANT
each score was from the mean. How VARIABLE the
distribution was.
• Then we realized if we added up all these deviation
scores, they necessarily added up to zero.
• So we had two choices: we coulda taken the absolute
value, or we coulda squared ‘em. And we squared
‘em.
Σ(X – M)2
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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ANOVA (cont’d.)
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• Σ(X – M)2
• This is called the Sum of the Squares
(SS). And when we add ‘em all up and
average them (well – divide by N-1), we
get S2 (the “variance”).
• We take the square root of that and we
have S (the “standard deviation”).
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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ANOVA (cont’d.)
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• Let’s work through the Hinton example
on p. 119.
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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M=
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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Total sum of squares = 328
(X-M)2
X
5 10 -5
25
11 10 1
1
14 10 4
16
6 10 -4
16
10 10 0
0
15 10 5
25
7 10 -3
9
9
1
17 10 7
49
5 10 0
25
11 10 1
1
13 10 3
9
3 10 -7
49
9
1
17 10 7
49
4 10 -6
36
10 10 0
0
14 10 4
16
X
M
X-M
160
M
X-M (X-M)2
10 -1
10 -1
X
M
4
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
XM
(X-M)2
164
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Within conditions sum of squares = 28
X-M
(X-M)2
X
5 5
0
0
11 10 1
1
14 15 -1
1
6 5
1
1
10 10 0
0
15 15 0
0
7 5
2
4
9
1
17 15 2
4
5 5
0
0
11 10 1
1
13 15 -2
4
3 5
-2
4
9
1
17 15 2
4
4 5
-1
1
10 10 0
0
14 15 -1
1
X
M
10
M
X-M (X-M)2
10 -1
10 -1
X
M
4
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
X-M (X-M)2
14
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Between conditions sum of
squares = 300
X
M
X-M
(X-M)2
times 6
5
10
5
25
150
10
10
0
0
0
15
10
5
25
150
50
300
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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So . . .
• Total sum of squares
• Within conditions SS
• Between conditions SS
(Magic!)
• How about df?
= 328
= 28
= 300
– Total = 17
– Within conditions df = 15
– Between conditions df = 2
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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From Hinton p. 127
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• Variance ratio (F) =
Between condition variance/Error variance
Or
Variance ratio (F) =
Systematic differences + Error variance
Error variance
• Think about it – why is the “within condition
variance” called “error variance”?
• Note, what happens where there are no systematic
differences?
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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Anova summary table, p. 128
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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So, from our example . . .
Source of df
variation
SS
MS
F
p
Between 2
conditions
300
150
80.21
< .01
Within
15
conditions
28
1.87
Total
328
17
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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Reading the F table
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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Check out . . .
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• ANOVA summary table on p. 128. This is for a
ONE FACTOR anova (i.e., one IV). (Maybe
MANY levels.)
• Sample ANOVA summary table on p. 132.
• The only thing you need to realize in Chapter
13 is that for repeated measures ANOVA, we
also tease out the between subjects variation
from the error variance. (See p. 154 and 158.)
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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Check out, also . . .
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• Note, in Chapter 15, that as factors (IVs)
increase, the comparisons (the number
of F ratios) multiply. See p. 172, 179.
• What happens when you have 3 levels of
an IV, and you get a significant F? (As
we did in our worked example.)
• Memorize the table on p. 182. (No, I’m
only kidding.)
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
28
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R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
29
Interaction effects
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• Here’s what I want you to understand about
interaction effects:
– They’re WHY we run studies with multiple IVs.
– A significant interaction effect means different levels
of one IV have different influences on the other IV.
– You can have significant main effects and
insignificant interactions, or vice versa (or both sig.,
or both not sig.) (See p. 164, 166.)
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
30
An Experiment
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• First, let’s divide into two groups – who
has an ODD SSN (last digit is odd).
• Group 1 – You’ll do List A first, then List
B. (Group 2 will keep their eyes closed
during List A.) (I’m just sure of it.) Then
we’ll all do List B. Then Group B will go
back and do List A.
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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List A
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I’ll present 10 words, one at a time.
Presented visually.
After the 10th I’ll say “go” and you’ll write down
as many as you can.
Don’t have to remember them in order.
Pencils down.
(Group 2 – please close your eyes.)
Ready?
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
32
i
balloon
doorknob
minivan
meatloaf
teacher
zebra
pillow
barn
sidewalk
coffin
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
33
List B
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•Now, 10 new words.
•Everyone (groups 1 and 2).
•Same task -- recall them.
•After the 10th one I’ll say “Go,” write
down as many of the 10 words as you
can.
•Again, don’t have to remember them in
order.
•Pencils down.
•Ready?
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
34
i
forget
interest
anger
imagine
fortitude
smart
peace
effort
hunt
focus
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
35
List A again
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Now, for Group 2. (Group 1 can keep their
eyes open – just don’t participate.)
I’ll present 10 words, one at a time.
Presented visually.
After the 10th I’ll say “go” and you’ll write down
as many as you can.
Don’t have to remember them in order.
Pencils down.
Ready?
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
36
i
balloon
doorknob
minivan
meatloaf
teacher
zebra
pillow
barn
sidewalk
coffin
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
37
List A
balloon
doorknob
minivan
meatloaf
teacher
zebra
pillow
barn
sidewalk
coffin
List B
i
forget
interest
anger
imagine
fortitude
smart
peace
effort
hunt
focus
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
38
Calculate your difference score
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• How many did you get right from List A?
• How many did you get right from List B?
• I’ll collect the data via a show of hands.
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
39
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• Was there a true difference?
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu
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