LIS 397.1Introduction to Research in Library and Information ScienceSummer, 2003Thoughtful 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) • 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."
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/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.html
Homework Lots more reading. Midterm Thursday. See you Tuesday.