R. G. Bias | School of Information | SZB 562BB | Phone: | i 1 INF397C Introduction to Research in Information Studies Spring, 2005 Day 13

R. G. Bias | School of Information | SZB 562BB | Phone: | i 2 More resources -- SE Dr. Phil Doty’s 26-minute online tutorial on standard error of the mean. Very helpful: m 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, 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:

R. G. Bias | School of Information | SZB 562BB | Phone: | i 3 More resources - Probability Jim asked for a visual demonstration of probability and outliers (or some such). Here’s a good one: moApplet.html moApplet.html Here’s a better one: html html Here’s another: bility.htmlhttp:// bility.html

R. G. Bias | School of Information | SZB 562BB | Phone: | i 4 More resources – Assorted things 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?! NormHiLite.htm StandardNormal.htm Play with the standard deviation slider bar! StandardNormal.htm stat.stanford.edu/~naras/jsm/NormalDensity/N ormalDensity.html

R. G. Bias | School of Information | SZB 562BB | Phone: | i 5 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... – for an example of some t tests. – 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.

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

R. G. Bias | School of Information | SZB 562BB | Phone: | i 7 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) = CI = / (5.0/SQRT 25) = / = – “The odds are 95 out of 100 that the population mean falls between and ” (NOTE: This is NOT the same as “95% of the scores fall within this range!!!)

R. G. Bias | School of Information | SZB 562BB | Phone: | i 8 Another CI example Hinton, p. 89. t test not sig. What if we did this via confidence intervals?

R. G. Bias | School of Information | SZB 562BB | Phone: | i 9 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.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 10 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.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 11 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

R. G. Bias | School of Information | SZB 562BB | Phone: | i 12 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”).

R. G. Bias | School of Information | SZB 562BB | Phone: | i 13 ANOVA (cont’d.) Let’s work through the Hinton example on p. 111.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 14 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.)

R. G. Bias | School of Information | SZB 562BB | Phone: | i 15 Check out... ANOVA summary table on p This is for a ONE FACTOR anova (i.e., one IV). (Maybe MANY levels.) Sample ANOVA summary table on p 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 (No, I’m only kidding.)

R. G. Bias | School of Information | SZB 562BB | Phone: | i 16 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.)

R. G. Bias | School of Information | SZB 562BB | Phone: | i 17 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.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 18 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.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 19 Correlation (cont’d.) Go to the McGraw-Hill statistics primer hill.com/sites/ /student_view0/stati stics_primer.html hill.com/sites/ /student_view0/stati stics_primer.html and click on “Correlational Statistics.” Read the three sub-sections. I will NOT ask you to calculate a product moment correlation nor a coefficient of determination, but these are good concepts to know, and these few pages describe it well.

R. G. Bias | School of Information | SZB 562BB | Phone: | i 20 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, –Several other articles

R. G. Bias | School of Information | SZB 562BB | Phone: | i 21 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

R. G. Bias | School of Information | SZB 562BB | Phone: | i 22 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)

R. G. Bias | School of Information | SZB 562BB | Phone: | i 23 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