4 things today

1. LIS 397.1Introduction to Research in Library and Information ScienceSummer, 2003Thoughtful Thursday -- Day 5

2. 4 things today • NEW equation for σ • z scores and “area under the curve” • Probabilities – Take 2 • In-class practice exercises

3. 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.

4. 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.

5. 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.

7. 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?

8. 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 . . .

9. 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.

10. 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."

11. Let’s try with Venn diagrams

12. Practice Exercises

13. 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

14. Homework Lots more reading. Midterm Thursday. See you Tuesday.