1. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 1 INF 397C Fall, 2003 Days 12 & 13

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

3. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 3 Power of the Test The power of a statistical test refers to its ability to find a difference in distributions when there really is one there. Things that influence the power of a test: –Size of the effect. –Sample size. –Variability. –Alpha level.

4. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 4 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.

5. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 5 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.

6. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 6 ANOVA Hinton, pp. 104-128, 141-200 SZZ, pp. 415 - 439

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 –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. 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 Homework http://www.environ.wa.gov.au/community/results.asp http://www.yogapoint.com/info/research.htm http://www.main.nc.us/bcsc/Chess_Research_Study_I.htm http://www.econ.upenn.edu/Centers/CARESS/CARESSpdf/00- 15.pdfhttp://www.econ.upenn.edu/Centers/CARESS/CARESSpdf/00- 15.pdf http://www.georgetowncollege.edu/departments/education/portfoli os/Franzen/research_paper.htmhttp://www.georgetowncollege.edu/departments/education/portfoli os/Franzen/research_paper.htm http://www.pbats.com/articles/foot/Foot_Postures.pdf http://www.cwrl.utexas.edu/currents/spring02/wakefield.html http://www.neuhaus.org/paper3.htm

14. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 14 Other “T scores” http://www.rehabinfo.net/rrtc/publications /research_summaries/neropsychfunction /default.asphttp://www.rehabinfo.net/rrtc/publications /research_summaries/neropsychfunction /default.asp “T scores” – “Standardized T scores for the WAIS-R, WISC-R, and HRB” http://collection.nlc- bnc.ca/100/201/300/cdn_medical_associ ation/cim/vol-21/issue-2/0094.htmhttp://collection.nlc- bnc.ca/100/201/300/cdn_medical_associ ation/cim/vol-21/issue-2/0094.htm Yet new “T scores.”

15. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 15 Other measures Confidence intervals http://www.hortnet.co.nz/publications/nzp ps/proceedings/95/95_294.htmhttp://www.hortnet.co.nz/publications/nzp ps/proceedings/95/95_294.htm Anova http://www.ischool.utexas.edu/~adillon/p ublications/empirical.htmlhttp://www.ischool.utexas.edu/~adillon/p ublications/empirical.html

16. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 16 Chi-squared Hinton, p. 239

17. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 17 Chi square test Let’s work an example in Hinton. Just know that you use the chi square test when you have FREQUENCY data.

18. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 18 Correlation With correlation, we return to DESCRIPTIVE statistics. (This is counterintuitive. To me.) We are describing the strength and direction of the relationship between two variables. And how much one variable predicts the other.

19. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 19 Hinton, p. 259

20. R. G. Bias | School of Information | SZB 562BB | Phone: 512 471 7046 | rbias@ischool.utexas.edu i 20 Let’s talk about the final Next week – Nov.20 – wrap up loose ends – correlation, Chi-squared, look at your research examples you sent me, hand in your Methods Section assignment (hard copy). Q-and-A session, Monday, December 1, 5:30 – 6:30, place TBD. Sample problems handed out next week.