R. G. Bias | School of Information | SZB 562BB | Phone: | i 1 LIS Introduction to Research in Library and Information Science Summer, 2003 Day 4

R. G. Bias | School of Information | SZB 562BB | Phone: | i 2 Old Business Typo on syllabus –Here’s the REAL reading schedule: –Before week 1 – Nothing –Before week 2 – Huff Best Hinton, Ch. 1, 2, 3 S, Z, & Z, Ch. 1, 2, 3 –Before Week 3 – Dethier Hinton, Ch. 4, 5, 6, 7, 8 S, Z, & Z, Ch. 7, 8, 14 Harris

R. G. Bias | School of Information | SZB 562BB | Phone: | i 3 Updated Reading Sched. (Cont’d.) Before Week 4 – –S, Z, &, Z, Ch. 4, 5, 6, 10, 11 –Cronin –Groman articles Before Week 5 – –Hinton, Ch. 9 – 16, 19 –S, Z, & Z, Ch. 12, 13 Before Week 6 – –MacCoun –(No S, Z, & Z, Ch. 16) Also, I listed the “17 th day of class” wrongly – it’s 7/10/2003.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 4 More Old Business Web site Room Normal curve example

R. G. Bias | School of Information | SZB 562BB | Phone: | i 5 From Jaisingh (2000)

R. G. Bias | School of Information | SZB 562BB | Phone: | i 6

i 7 Calculating percentiles From Runyon et al. (2000)

R. G. Bias | School of Information | SZB 562BB | Phone: | i 8

i 9 Graphs Graphs/tables/charts do a good job (done well) of depicting all the data. But they cannot be manipulated mathematically. Plus it can be ROUGH when you have LOTS of data. Let’s look at your examples.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 10 Some rules For building graphs/tables/charts: –Label axes. –Divide up the axes evenly. –Indicate when there’s a break in the rhythm! –Keep the “aspect ratio” reasonable. –Histogram, bar chart, line graph, pie chart, stacked bar chart, which when? –Keep the user in mind.

R. G. Bias | School of Information | SZB 562BB | Phone: | i o_id=01000US.htmlhttp://factfinder.census.gov/bf/_lang=en_vt_name=DEC_2000_SF3_U_DP3_ge o_id=01000US.html mlhttp:// ml

R. G. Bias | School of Information | SZB 562BB | Phone: | i 12 So far we’ve talked of summarizing ONE distribution of scores. –By ordering the scores. –By organizing them in graphs/tables/charts. –By calculating a measure of central tendency and a measure of dispersion. What happens when we want to compare TWO distributions of scores?

R. G. Bias | School of Information | SZB 562BB | Phone: | i 13 “Now, why would I want to do that”? Is your child taller or heavier? Is this month’s SAT test any easier or harder than last month’s? Is my 91 in my Research Methods class better than my 95 in my Digital Libraries class? Is the new library lay-out better than the old one? Can more employees sign up, more quickly, for benefits with our new intranet site than with our old one? Did my class perform better on the TAKS test than they did on the TAAS test?

R. G. Bias | School of Information | SZB 562BB | Phone: | i 14 Well? COULD it be the case that your 91 in your Research Methods class is better than your 95 in your Digital Libraries class? How?

R. G. Bias | School of Information | SZB 562BB | Phone: | i 15 What if... The mean in Research Methods was 50, and the mean in Digital Libraries was 99? (What, besides the fact that everyone else is trying to drop the Research class!) So: YouMean Res. Meth Dig. Lib.9599

R. G. Bias | School of Information | SZB 562BB | Phone: | i 16 The Point As I said yesterday, you need to know BOTH a measure of central tendency AND a measure of spread to understand a distribution. BUT STILL, this can be convoluted... “Well, daughter, how are you doing in grad school this semester”?

R. G. Bias | School of Information | SZB 562BB | Phone: | i 17 “Well, Mom... “... I have a 91 in Research Methods but the mean is 50 and the standard deviation is 12, but I only have a 95 in Digital Libraries, whereas the mean in that class is 99 with a standard deviation of 1.” Of course, your mom’s reaction will be, “Just call home more often, dear.”

R. G. Bias | School of Information | SZB 562BB | Phone: | i 18 Wouldn’t it be nice if there could be one score we could use for BOTH classes, for BOTH the TAKS test and the TAAS test, for BOTH your child’s height and weight? There is – and it’s called the “standard score,” or “z score.” (Get ready for another headache.)

R. G. Bias | School of Information | SZB 562BB | Phone: | i 19 Standard Score z = (X - µ)/σ “Hunh”? Each score can be expressed as the number of standard deviations it is from the mean of its own distribution. “Hunh”? (X - µ) – This is how far the score is from the mean. (Note: Could be negative! No squaring, this time.) Then divide by the SD to figure out how many SDs you are from the mean.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 20 Z scores (cont’d.) z = (X - µ)/σ Notice, if your score (X) equals the mean, then z is, what? If your score equals the mean PLUS one standard deviation, then z is, what? If your score equals the mean MINUS one standard deviation, then z is, what?

R. G. Bias | School of Information | SZB 562BB | Phone: | i 21 An example Test 1Test 2 Kris76 Robin5286 Marty5880 Terry5890 ΣXΣX µ Mode, median?

R. G. Bias | School of Information | SZB 562BB | Phone: | i 22 Let’s calculate σ – Test 1 XX-µ(X-µ) 2 Kris Robin Marty58-39 Terry58-39 Σ /N6181 σ9

R. G. Bias | School of Information | SZB 562BB | Phone: | i 23 Let’s calculate σ – Test 2 XX-µ(X-µ) 2 Kris Robin8639 Marty80-39 Terry90749 Σ /N8329 σ5.4

R. G. Bias | School of Information | SZB 562BB | Phone: | i 24 So... z = (X - µ)/σ Kris had a 76 on both tests. Test 1 - µ = 61, σ = 9 –So her z score was (76-61)/9 or 15/9 or So we say that Kris’s score was 1.67 standard deviations above the mean. Test 2 - µ = 83, σ = 5.4 –So her z score was (76-83)/5.4 or -7/5.4 or –1.3. So we say that Kris’s score was 1.3 standard deviations BELOW the mean. Given what I said yesterday about two-thirds of the scores being within one standard deviation of the mean....

R. G. Bias | School of Information | SZB 562BB | Phone: | i 25 z = (X - µ)/σ If I tell you that the average IQ score is 100, and that the SD of IQ scores is 16, and that Bob’s IQ score is 2 SD above the mean, what’s Bob’s IQ? If I tell you that your 75 was 1.5 standard deviations below the mean of a test that had a mean score of 90, what was the SD of that test?

R. G. Bias | School of Information | SZB 562BB | Phone: | i 26 Notice... The mean of all z scores (for a particular distribution) will be zero, as will be their sum. With z scores, we transform raw scores into standard scores. These standard scores are RELATIVE distances from their (respective) means. All are expressed in units of σ.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 27 Probability Remember all those decisions we talked about, last week. VERY little of life is certain. –One person wore her new Snoopy shirt because she THOUGHT it would make her feel happy. (Or maybe she thought to herself: “The probability that wearing this shirt will make me happy is ≥.50.”) (But I doubt it.)

R. G. Bias | School of Information | SZB 562BB | Phone: | i 28 Prob. (cont’d.) Life’s a gamble! Just about every decision is based on a probable outcomes. None of you raised your hands last Wednesday when I asked for “statistical wizards.” Yet every one of you does a pretty good job of navigating an uncertain world. –None of you touched a hot stove (on purpose.) –All of you made it to class.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 29 Probabilities Always between one and zero. Something with a probability of “one” will happen. (e.g., Death, Taxes). Something with a probability of “zero” will not happen. (e.g., My becoming a Major League Baseball player). Something that’s unlikely has a small, but still positive, probability. (e.g., probability of someone else having the same birthday as you is 1/365 =.0027, or.27%.)

R. G. Bias | School of Information | SZB 562BB | Phone: | i 30 Just because There are two possible outcomes, doesn’t mean there’s a “50/50 chance” of each happening. When driving to school today, I could have arrived alive, or been killed in a fiery car crash. (Two possible outcomes, as I’ve defined them.) Not equally likely. But the odds of a flipped coin being “heads,”....

R. G. Bias | School of Information | SZB 562BB | Phone: | i 31 Prob (cont’d.) Probability of something happening is –# of “successes” / # of all events –P(one flip of a coin landing heads) = ½ =.5 –P(one die landing as a “2” = 1/6 = 1.67 –P(some score in a distribution of scores is greater than the median) = ½ =.5 –P(some score in a normal distribution of scores is greater than the mean but has a z score of 1 or less is... ? –P(drawing a diamond from a complete deck of cards) = ?

R. G. Bias | School of Information | SZB 562BB | Phone: | i 32 Probability Rules (and Rocks!) Addition Rule (And rule): If there are two or more mutually exclusive outcomes. –Chances of rolling a two or a three, on one die. 1/6 + 1/6 = 2/6 Multiplication Rule (Or rule): Prob. of getting BOTH of two or more independent outcomes. –Chances of rolling a two and THEN a three, on one die. 1/6 x 1/6 = 1/36

R. G. Bias | School of Information | SZB 562BB | Phone: | i 33 Think this through. What are the odds (“what are the chances”) (“what is the probability”) of getting two “heads” in a row? Three heads in a row? Three flips the same (heads or tails) in a row?

R. G. Bias | School of Information | SZB 562BB | Phone: | i 34 So then... WHY were the odds in favor of having two people in our class with the same birthday? Think about the problem! What if there were 367 people in the class. –P(2 people with same b’day) = 1.00

R. G. Bias | School of Information | SZB 562BB | Phone: | i 35 Happy B’day to Us But we had 46. Probability that the first person has a birthday: Prob of the second person having the same b’day: 1/365 Prob of the third person having the same b’day as Person 1 and Person 2 is 1/ /365 – the chances of all three of them having the same birthday.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 36 Sooooo... hday.html

R. G. Bias | School of Information | SZB 562BB | Phone: | i 37 Homework Keep reading. See you tomorrow.