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LIS 397.1 Introduction to Research in Library and Information Science Summer, 2003 Thoughtful Thursday -- Day 5. 4 things today. NEW equation for σ z scores and “area under the curve” Probabilities – Take 2 In-class practice exercises. NEW equation for σ. σ = SQRT( Σ (X - µ) 2 /N)
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LIS 397.1Introduction to Research in Library and Information ScienceSummer, 2003Thoughtful Thursday -- Day 54 things today
  • NEW equation for σ
  • z scores and “area under the curve”
  • Probabilities – Take 2
  • In-class practice exercises
  • NEW equation for σ
  • 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.
  • z scores – table values
  • 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.
  • Going into the table
  • You need to remember a few things:
  • 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.
  • 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?
  • 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 . . .
  • 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.
  • 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."
  • Let’s try with Venn diagramsPractice ExercisesAdditional 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/tutorials.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.htmlHomeworkLots more reading.Midterm Thursday.See you Tuesday.
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