1. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 1 INF397C Introduction to Research in Information Studies Spring, 2005 Day 13

2. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 2 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%.

3. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 3 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!!!)

4. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 4 Another CI example Hinton, p. 89. t-test not sig. What if we did this via confidence intervals?

5. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 5 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 in the butt. b)You multiply your chances of making a Type I error.

6. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 6 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.

7. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 7 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

8. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 8 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”).

9. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 9 ANOVA (cont’d.) Let’s work through the Hinton example on p. 111.

10. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 10 F is... F is the variance ratio. F is –between conditions variance/error variance –(systematic differences + error variance) /error variance –Between conditions variance/within conditions variance (This from Hinton, p. 112, p. 119.)

11. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 11 Check out... ANOVA summary table on p. 120. This is for a ONE FACTOR anova (i.e., one IV). (Maybe MANY levels.) Sample ANOVA summary table on p. 124. Don’t worry about unequal sample sizes – interpretation of the summary table is the same. 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. 146 and 150.) Note, in Chapter 15, that as factors (IVs) increase, the comparisons (the number of F ratios) multiply. See p. 167, 174. What happens when you have 3 levels of an IV, and you get a significant F? Memorize the table on p. 177. (No, I’m only kidding.)

12. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 12 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. 157, 158.)

13. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 13 Correlation With correlation, we return to DESCRIPTIVE statistics. (This is counterintuitive. To me.) (Well, it’s BOTH descriptive and inferential.) We are describing the strength and direction of the relationship between two variables. And how much one variable predicts the other.

14. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 14 Correlation Formula – –Hinton, p. 259, or –S, Z, & Z, p. 393 Two key points: –How much predictability does one variable provide, for another. –NOT causation. Let’s work two trivial examples.

15. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 15 Let’s talk about the final Here’s what you’ve read: –Huff (How to lie with statistics) –Dethier (To know a fly) –Hinton: Ch. 1 – 15, 20 –S, Z, & Z: Ch. 1-8, 10-13 –Several other articles

16. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 16 For the final, EMPHASIZE… Descriptive stat –Measures of central tendency, dispersion –Z scores (both ways!) –Frequency distributions, tables, graphs –Correlation (interpret, not calculate) Inferential stat –Hypothesis testing –Standard error of the mean –t-test (calculate one, for one sample; interpret others) –Confidence intervals (maybe calculate one) –Chi square (maybe one) –ANOVA – interpret summary table –Type I and II errors –Effect size (book only – concept, not calculate)

17. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 17 Emphasize... Experimental design –IV, DV, controls, confounds, counterbalancing –Repeated measures, Independent groups –Sampling –Operational definitions –Individual differences variable –Ethics of human study –Possible sources of bias and error variance and how to minimize/eliminate Qualitative methods –Per Rice Lively, Gracy, Doty –Survey generation (from SZZ, Ch. 5)

18. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 18 De-emphasize Complicated probability calculations APA ethical standard (S,Z, & Z, Ch. 3) Content analysis (SZZ, Ch. 6) Calculating an ANOVA. Nonequivalent control group design (SZZ, Ch. 11) (Indeed, de-emphasize all Ch. 11) Hinton, Ch. 12

19. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 19 Sample Problems With answers – hand out.

20. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 20 Experiment 1 I’ll present 10 word, 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?

21. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 21 balloon doorknob minivan meatloaf teacher zebra pillow barn sidewalk coffin

22. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 22 balloon doorknob minivan meatloaf teacher zebra pillow barn sidewalk coffin

23. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 23 Experiment 2 Now, 10 new words. 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?

24. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 24 forget interest anger imagine fortitude smart peace effort hunt focus

25. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 25 forget interest anger imagine fortitude smart peace effort hunt focus

26. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 26 Course Evaluation

27. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 27 See you Monday! Don’t hesitate to call or shoot me an email if you have any questions.