# 4 things today

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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!)
• 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:
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