Transcript Day 5 Slides - School of Information

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LIS 397.1
Introduction to Research in Library and
Information Science
Summer, 2003
Thoughtful Thursday -- Day 5
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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4 things today
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NEW equation for σ
z scores and “area under the curve”
Probabilities – Take 2
In-class practice exercises
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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NEW equation for σ
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• σ = SQRT(Σ(X - µ)2/N)
– HARD to calculate when you have a LOT of
scores. Gotta do that subtraction with every
one!
• New, “computational” equation
– σ = SQRT((Σ(X2) – (ΣX)2/N)/N)
– Let’s convince ourselves it gives us the
same answer.
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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z scores – table values
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• z = (X - µ)/σ
• It is often the case that we want to know
“What percentage of the scores are
above (or below) a certain other score”?
• Asked another way, “What is the area
under the curve, beyond a certain point”?
• THIS is why we calculate a z score, and
the way we do it is with the z table, on p.
306 of Hinton.
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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Going into the table
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• You need to remember a few things:
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We’re ASSUMING a normal distribution.
The total area under the curve is = 1.00
Percentage is just a probability x 100.
50% of the curve is above the mean.
z scores can be negative!
z scores are expressed in terms of (WHAT – this is
a tough one to remember!)
– USUALLY it’ll help you to draw a picture.
• So, with that, let’s try some exercises.
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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z table practice
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What percentage of scores fall above a z score of
1.0?
What percentage of scores fall between the mean
and one standard deviation above the mean?
What percentage of scores fall within two standard
deviations of the mean?
My z score is .1. How many scores did I “beat”?
My z score is .01. How many scores did I “beat”?
My score was higher than only 3% of the class. (I
suck.) What was my z score.
Oooh, get this. My score was higher than only 3%
of the class. The mean was 50 and the standard
deviation was 10. What was my raw score?
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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Probabilities – Take 2
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• From Runyon:
– Addition Rule: The probability of selecting a
sample that contains one or more elements is the
sum of the individual probabilities for each element
less the joint probability. When A and B are
mutually exclusive,
• p(A and B) = 0.
• P(A or B) = p(A) + p(B) – p(A and B)
– Multiplication Rule: The probability of obtaining a
specific sequence of independent events is the
product of the probability of each event.
• P(A and B and . . .) = p(A) x p(B) x . . .
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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Prob (II)
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• From Slavin:
– Addition Rule: If X and Y are mutually
exclusive events, the probability of obtaining
either of them is equal to the probability of X
plus the probability of Y.
– Multiplication Rule: The probability of the
simultaneous or successive occurrence of
two events is the product of the separate
probabilities of each event.
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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Prob (II)
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• http://www.midcoast.com.au/~turfacts/maths.ht
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– 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."
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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Let’s try with Venn diagrams
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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Practice Exercises
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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Additional Resources
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• Phil Doty, from the ISchool, has taught this class
before. He has welcomed us to use his online video
tutorials, available at
http://www.gslis.utexas.edu/~lis397pd/fa2002/tutorials.
html
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Frequency Distributions
z scores
Intro to the normal curve
Area under the normal curve
Percentile ranks, z-scores, and area under the normal curve
• Pretty good discussion of probability:
http://ucsub.colorado.edu/~maybin/mtop/ms16/exp.html
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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Homework
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Lots more reading.
Midterm Thursday.
See you Tuesday.
R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | [email protected]
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