1. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 1 INF397C Introduction to Research in Information Studies Fall, 2009 Week 12

2. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 2 From Blink, by Malcolm Gladwell P. 32. The author is talking about negative emotions that tend to predict subsequent break-ups of marriages: “... there is one emotion that [Dr. Gottman] considers the most important of all: contempt. If Gottman observes one or both partners in a marriage showing contempt for one another, he considers it the single most important sign that the marriage is in trouble.”

3. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 3 p. 33 “Gottman has found, in fact, that the presence of contempt in a marriage can even predict such things as how many colds a husband or wife gets; in other words, having someone you love express contempt toward you is so stressful that it begins to affect the functioning of your immune system.”

4. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 4 More resources – Assorted things http://www.stat.berkeley.edu/~stark/Java/Html/ NormHiLite.htm Use the slider bars! Man, don’t you wish you had had access to this tool for the last question on the midterm?!http://www.stat.berkeley.edu/~stark/Java/Html/ NormHiLite.htm http://www.stat.berkeley.edu/~stark/Java/Html/ StandardNormal.htm Play with the standard deviation slider bar!http://www.stat.berkeley.edu/~stark/Java/Html/ StandardNormal.htm http://www- stat.stanford.edu/~naras/jsm/NormalDensity/N ormalDensity.html

5. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 5 More resources -- SE Dr. Phil Doty’s 26-minute online tutorial on standard error of the mean. Very helpful: http://cobra.gslis.utexas.edu:8080/ramgen/Content2/faculty/doty/research/dsmbb.r m http://cobra.gslis.utexas.edu:8080/ramgen/Content2/faculty/doty/research/dsmbb.r m –Note, I had not talked of “expected value.” When you hear that “M is the expected value of µ,” you can substitute “M is used to estimate µ.” –Note also we have not talked about “CV,” though last week I did say to expect that S is kinda of the same general order of magnitude, but smaller than, M. Same idea. –Don’t forget Dr. Doty’s page of tutorials, http://www.gslis.utexas.edu/~lis397pd/fa2002/tutorials.html http://www.gslis.utexas.edu/~lis397pd/fa2002/tutorials.html where you will find also an eight-minute introduction to inferential statistics, two tutorials on confidence intervals, and one on Chi squared. I think one thing you’ll find interesting in these tutorials is that here is a second professor, using a different text book (Spatz), who studied at a different school, who’s never heard me lecture (nor I him)... and we use much the same language to describe things. The point is, this stuff (descriptive and inferential statistics) is universal. Two pages of explanation of standard error of the mean: http://davidmlane.com/hyperstat/A103735.html http://davidmlane.com/hyperstat/A103735.html

6. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 6 More resources - Probability A visual demonstration of probability and outliers (or some such). Here’s a good one: http://www.ms.uky.edu/~mai/java/stat/GaltonM achine.html http://www.ms.uky.edu/~mai/java/stat/GaltonM achine.html Here’s another: http://www.stattucino.com/berrie/dsl/Galton.ht ml http://www.stattucino.com/berrie/dsl/Galton.ht ml http://www.mathgoodies.com/lessons/vol6/intr o_probability.htmlhttp://www.mathgoodies.com/lessons/vol6/intr o_probability.html

7. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 7 http://highered.mcgraw- hill.com/sites/0072494468/student_view0 /statistics_primer.htmlhttp://highered.mcgraw- hill.com/sites/0072494468/student_view0 /statistics_primer.html

8. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 8 t tests Go to the McGraw-Hill statistics primer and read the subsections on Inferential Statistics. Not a lot of meat, there, but it will help you to hear it stated in a slightly different way. For some examples of the use of t tests... –http://www.yogapoint.com/info/research.htm for an example of some t tests.http://www.yogapoint.com/info/research.htm –http://www.main.nc.us/bcsc/Chess_Research_Study_I.htmhttp://www.main.nc.us/bcsc/Chess_Research_Study_I.htm Notice how they continually say “p>.05” rather than “p<.05”! Do NOT, as they suggest at the end, “send a check for $39.95 payable to the American Chess School.” Go find more examples, just for yourself.

9. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 9 Confidence Intervals We calculate a confidence interval for a population parameter. The mean of a random sample from a population is a point estimate of the population mean. But there’s variability! (SE tells us how much.) What is the range of scores between which we’re 95% confident that the population mean falls? Think about it – the larger the interval we select, the larger the likelihood it will “capture” the true (population) mean. CI = M +/- (t.05 )(SE) See Box 12.2 on “margin of error.” NOTE: In the box they arrive at a 95% confidence that the poll has a margin of error of 5%. It is just coincidence that these two numbers add up to 100%.

10. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 10 CI about a mean -- example CI = M +/- (t.05 )(SE) Establish the level of α (two-tailed) for the CI. (.05) M=15.0 s=5.0 N=25 Use Table A.2 to find the critical value associated with the df. –t.05 (24) = 2.064 CI = 15.0 +/- 2.064(5.0/SQRT 25) = 15.0 +/- 2.064 = 12.935 – 17.064 “The odds are 95 out of 100 that the population mean falls between 12.935 and 17.064.” (NOTE: This is NOT the same as “95% of the scores fall within this range!!!)

11. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 11 Another CI example Hinton, p. 89. t test not sig. What if we did this via confidence intervals?

12. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 12 Type I and Type II Errors World  Our decision Null hypothesis is false Null hypothesis is true Reject the null hypothesis Correct decision Type I error (α) Fail to reject the null hypothesis Type II error (β) Correct decision (1-β)

13. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 13 Limitations of t tests Can compare only two samples at a time Only one IV at a time (with two levels) But you say, “Why don’t I just run a bunch of t tests”? a)It’s a pain. b)You multiply your chances of making a Type I error.

14. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 14 ANOVA Analysis of variance, or ANOVA, or F tests, were designed to overcome these shortcomings of the t test. An ANOVA with ONE IV with only two levels is the same as a t test.

15. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 15 ANOVA (cont’d.) Remember back to when we first busted out some scary formulas, and we calculated the standard deviation. We subtracted the mean from each score, to get a feel for how spread out a distribution was – how DEVIANT each score was from the mean. How VARIABLE the distribution was. Then we realized if we added up all these deviation scores, they necessarily added up to zero. So we had two choices: we coulda taken the absolute value, or we coulda squared ‘em. And we squared ‘em. Σ(X – M) 2

16. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 16 ANOVA (cont’d.) Σ(X – M) 2 This is called the Sum of the Squares (SS). And when we add ‘em all up and average them (well – divide by N-1), we get S 2 (the “variance”). We take the square root of that and we have S (the “standard deviation”).

17. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 17 ANOVA (cont’d.) Let’s work through the Hinton example on p. 119.

18. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 18 M =

19. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 19 Total sum of squares = 328 XMX-M(X-M) 2 XMX-M(X-M) 2 XMX- M (X-M) 2 510-5251110111410416 610-41610 001510525 710-3991011710749 510025111011131039 3 -74991011710749 410-63610 001410416 1604164

20. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 20 Within conditions sum of squares = 28 XMX-M(X-M) 2 XMX-M(X-M) 2 XMX-M(X-M) 2 550011101114151 651110 0015 00 75249101171524 55001110111315-24 35 49101171524 45110 0014151 10414

21. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 21 Between conditions sum of squares = 300 XMX-M(X-M) 2 times 6 510525150 10 000 1510525150 50300

22. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 22 So... Total sum of squares = 328 Within conditions SS = 28 Between conditions SS = 300 (Magic!) How about df? –Total = 17 –Within conditions df = 15 –Between conditions df = 2

23. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 23 From Hinton p. 127 Variance ratio (F) = Between condition variance/Error variance Or Variance ratio (F) = Systematic differences + Error variance Error variance Think about it – why is the “within condition variance” called “error variance”? Note, what happens where there are no systematic differences?

24. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 24 Anova summary table, p. 128

25. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 25 So, from our example... Source of variation dfSSMSFp Between conditions 230015080.21<.01 Within conditions 15281.87 Total17328

26. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 26 Reading the F table

27. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 27 Check out... ANOVA summary table on p. 128. This is for a ONE FACTOR anova (i.e., one IV). (Maybe MANY levels.) Sample ANOVA summary table on p. 132. The only thing you need to realize in Chapter 13 is that for repeated measures ANOVA, we also tease out the between subjects variation from the error variance. (See p. 154 and 158.)

28. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 28 Check out, also... Note, in Chapter 15, that as factors (IVs) increase, the comparisons (the number of F ratios) multiply. See p. 172, 179. What happens when you have 3 levels of an IV, and you get a significant F? (As we did in our worked example.) Memorize the table on p. 182. (No, I’m only kidding.)

29. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 29

30. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 30 Interaction effects Here’s what I want you to understand about interaction effects: –They’re WHY we run studies with multiple IVs. –A significant interaction effect means different levels of one IV have different influences on the other IV. –You can have significant main effects and insignificant interactions, or vice versa (or both sig., or both not sig.) (See p. 164, 166.)

31. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 31 An Experiment First, let’s divide into two groups – who has an ODD SSN (last digit is odd). Group 1 – You’ll do List A first, then List B. (Group 2 will keep their eyes closed during List A.) (I’m just sure of it.) Then we’ll all do List B. Then Group B will go back and do List A.

32. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 32 List A I’ll present 10 words, one at a time. Presented visually. After the 10 th I’ll say “go” and you’ll write down as many as you can. Don’t have to remember them in order. Pencils down. (Group 2 – please close your eyes.) Ready?

33. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 33 balloon doorknob minivan meatloaf teacher zebra pillow barn sidewalk coffin

34. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 34 List B Now, 10 new words. Everyone (groups 1 and 2). Same task -- recall them. After the 10 th one I’ll say “Go,” write down as many of the 10 words as you can. Again, don’t have to remember them in order. Pencils down. Ready?

35. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 35 forget interest anger imagine fortitude smart peace effort hunt focus

36. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 36 List A again Now, for Group 2. (Group 1 can keep their eyes open – just don’t participate.) I’ll present 10 words, one at a time. Presented visually. After the 10 th I’ll say “go” and you’ll write down as many as you can. Don’t have to remember them in order. Pencils down. Ready?

37. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 37 balloon doorknob minivan meatloaf teacher zebra pillow barn sidewalk coffin

38. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 38 List A List B balloon doorknob minivan meatloaf teacher zebra pillow barn sidewalk coffin forget interest anger imagine fortitude smart peace effort hunt focus

39. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 39 Calculate your difference score How many did you get right from List A? How many did you get right from List B? I’ll collect the data via a show of hands.

40. R. G. Bias | School of Information | UTA 5.424 | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 40 Was there a true difference?