PowerPoint PresentationR. G. Bias | School of Information | UTA
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INF397C
Fall, 2009
Week 12
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
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From Blink, by Malcolm Gladwell
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 |
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p. 33
“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 |
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More resources – Assorted things
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://www-stat.stanford.edu/~naras/jsm/NormalDensity/NormalDensity.html
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
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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.rm
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 |
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More resources - Probability
A visual demonstration of probability and outliers (or some such).
Here’s a good one:
http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html
Here’s another:
http://www.stattucino.com/berrie/dsl/Galton.html
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
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t tests
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.
Go find more examples, just for yourself.
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
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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 |
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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
= 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 |
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What if we did this via confidence intervals?
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
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World Our decision
Type II error (β)
Correct decision (1-β)
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
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Only one IV at a time (with two levels)
But you say, “Why don’t I just run a bunch of t tests”?
It’s a pain.
You multiply your chances of making a Type I error.
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
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ANOVA
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 |
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ANOVA (cont’d.)
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
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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 |
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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
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M =
10.unknown
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
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X
M
X-M
(X-M)2
X
M
X-M
(X-M)2
X
M
X-M
(X-M)2
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
10
-1
1
17
10
7
49
5
10
0
25
11
10
1
1
13
10
3
9
3
10
-7
49
9
10
-1
1
17
10
7
49
4
10
-6
36
10
10
0
0
14
10
4
16
160
4
164
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
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X
M
X-M
(X-M)2
X
M
X-M
(X-M)2
X
M
X-M
(X-M)2
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
10
-1
1
17
15
2
4
5
5
0
0
11
10
1
1
13
15
-2
4
3
5
-2
4
9
10
-1
1
17
15
2
4
4
5
-1
1
10
10
0
0
14
15
-1
1
10
4
14
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
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X
M
X-M
(X-M)2
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
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So . . .
Within conditions SS = 28
Between conditions SS = 300
Within conditions df = 15
Between conditions df = 2
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
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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
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Anova summary table, p. 128
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
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15
28
1.87
Total
17
328
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
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Reading the F table
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
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Check out . . .
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 |
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Check out, also . . .
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 |
[email protected]
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R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
[email protected]
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Interaction effects
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 |
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An Experiment
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
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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 |
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balloon
doorknob
minivan
meatloaf
teacher
zebra
pillow
barn
sidewalk
coffin
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
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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 |
[email protected]
i
forget
interest
anger
imagine
fortitude
smart
peace
effort
hunt
focus
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
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List A again
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 |
[email protected]
i
balloon
doorknob
minivan
meatloaf
teacher
zebra
pillow
barn
sidewalk
coffin
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
[email protected]
i
balloon
doorknob
minivan
meatloaf
teacher
zebra
pillow
barn
sidewalk
coffin
forget
interest
anger
imagine
fortitude
smart
peace
effort
hunt
focus
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
[email protected]
i
I’ll collect the data via a show of hands.
R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471
7046 |
[email protected]
i