LIS 397'1 Introduction to Research in Library and Information Science Summer, 2003 Thoughtful Thursd

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LIS 397.1Introduction to Research in Library and
Information ScienceSummer, 2003Thoughtful
Thursday -- Day 5
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4 things today

• NEW equation for s
• z scores and area under the curve
• Probabilities Take 2
• In-class practice exercises

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NEW equation for s

• s SQRT(S(X - µ)2/N)
• HARD to calculate when you have a LOT of scores.
  Gotta do that subtraction with every one!
• New, computational equation
• s SQRT((S(X2) (SX)2/N)/N)
• Lets convince ourselves it gives us the same
  answer.

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z scores table values

• z (X - µ)/s
• 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.

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Going into the table

• You need to remember a few things
• Were 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 itll help you to draw a picture.
• So, with that, lets try some exercises.

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z table practice

• 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?

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Probabilities Take 2

• 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 . . .

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Prob (II)

• 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.

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Prob (II)

• http//www.midcoast.com.au/turfacts/maths.html
• 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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Lets try with Venn diagrams
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Practice Exercises
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Additional Resources

• 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/tutor
  ials.html
• 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.ht
  ml

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Homework

• Lots more reading.
• Midterm Thursday.
• See you Tuesday.