Name that tune.

1. Name that tune.  Song title?  Performer(s)?

2. Scientific Method and Statistics(continued) “Finding New Information” 3/28/2010

3. Objectives • Continue experimental design and statistics. • Randolph – remember to take roll. • Who thinks there are two people in this classroom with the same birthday? (Month and day – not year.) http://www.nytimes.com/2009/08/06/technology/06stats.html

4. To summarize

5. Let me work an example all the way through.

6. Summary • An experiment is “personkind’s way of asking nature a question.” • I manipulate some variables (IVs), control other variables, count on random assignment to wash out the effects of all the rest of the variables, and look for an effect on the DVs. • Independent Groups = Between-subjects design • Repeated Measures = Within-subjects design • Natural Groups Design = Pseudoexperiment = NO inference of causality • I start with a null hypothesis and an alternate hypothesis. • If I find a difference (in my DV), I infer it was caused by the IV (the treatment) and I reject my H0 and accept my HA. • If I find no difference I do NOT accept the H0, rather I say that we do not have any evidence to reject it at this time. (NOTE how hard it is to prove the absence of something!)

7. Role of Data Analysis in Exps. • Primary goal of data analysis is to determine if our observations support a claim about behavior. Is that difference really different? • We want to draw conclusions about populations, not just the sample. • Two different ways – statistics and replication.

8. Scales • The data we collect can be represented on one of FOUR types of scales: • Nominal • Ordinal • Interval • Ratio • “Scale” in the sense that an individual score is placed at some point along a continuum.

9. Nominal Scale • Describe something by giving it a name. (Name – Nominal. Get it?) • Mutually exclusive categories. • For example: • Gender: 1 = Female, 2 = Male • Marital status: 1 = single, 2 = married, 3 = divorced, 4 = widowed • Make of car: 1 = Ford, 2 = Chevy . . . • Thinks sex is a good thing: 1 = Yes, 2 = No • The numbers are just names.

10. Ordinal Scale People “Sue” has ever wanted to have sex with, by height: 1 = Vern 2 = Joe 3 = Mick 4 = Tim • An ordered set of objects. • But no implication about the relative SIZE of the steps. • Example: • The 50 states in order of population: • 1 = California • 2 = Texas • 3 = New York • . . . 50 = Wyoming

11. Interval Scale • Ordered, like an ordinal scale. • Plus there are equal intervals between each pair of scores. • With Interval data, we can calculate means (averages). • However, the zero point is arbitrary. • Examples: • Temperature in Fahrenheit or Centigrade (of the room where someone had sex) • IQ scores

12. Ratio Scale • Interval scale, plus an absolute zero. • Sample: • Distance, weight, height, time (but not years – e.g., the year 2002 isn’t “twice” 1001). • Number of times “Mary” thought about sex.

13. Scales (cont’d.) It’s possible to measure the same attribute on different scales. Say, for instance, your midterm test. I could: • Give you a “1” if you don’t finish, and a “2” if you finish. • “1” for highest grade in class, “2” for second highest grade, . . . . • “1” for first quarter of the class, “2” for second quarter of the class,” . . . • Raw test score (100, 99, . . . .). • (NOTE: A score of 100 doesn’t mean the person “knows” twice as much as a person who scores 50, he/she just gets twice the score.)

14. Scales (cont’d.)

15. Critical Skepticism • Remember the Rabbit Pie example from earlier? • The “critical consumer” of statistics asked “what do you mean by ’50/50’”? • Let’s look at some other situations and claims. • From How to Lie with Statistics.

16. Company is hurting. • We’d like to ask you to take a 50% cut in pay. • But if you do, we’ll give you a 75% raise next month. OK? • Problem: Base rate.

17. Sale! • “Save 100%” • I doubt it.

18. Probabilities • “It’s safer to drive in the fog than in the sunshine.” (Kinda like “Most accidents occur within 25 miles of home.” Doesn’t mean it gets safer once you get to San Marcos.) • Navy literature around WWI: • “The death rate in the Navy during the Spanish-American war was 9/1000. For civilians in NYC during the same period it was 16/1000. So . . . Join the Navy. It’s safer.”

19. Are all results reported? • “In an independent study [ooh, magic words], people who used Doakes toothpaste had 23% fewer cavities.” • How many studies showed MORE cavities for Doakes users?

20. Sampling problems • “Average salary of 1999 UT grads – “$41,000.” • How did they find this? I’ll bet it was average salary of THOSE WHO RESPONDED to a survey. • Who’s inclined to respond?

21. Correlation ≠ Causation • Around the turn of the 20th century, there were relatively MANY deaths of tuberculosis in Arizona. • What’s up with that?

22. Remember . . . • I do NOT want you to become cynical. • Not all “media bias” is intentional. • Just be sensible, critical, skeptical. • As you “consume” statistics, ask some questions . . .

23. Ask yourself. . . • Who says so?(A Zest commercial is unlikely to tell you that Irish Spring is best.) • How does he/she know?(That Zest is “the best soap for you.”) • What’s missing?(One year, 33% of female grad students at Johns Hopkins married faculty.) • Did somebody change the subject?(“Camrys are bigger than Accords.” “Accords are bigger than Camrys.”) • Does it make sense?(“Study in NYC: Working woman with family needed $40.13/week for adequate support.”)

24. Claims • “Better chance of being struck by lightening than being bitten by a shark.” • Tom Brokaw – Tranquilizers.

25. The Normal Distribution(From Jaisingh [2000])

27. Notice • Many things influence how easy or hard it is to discover a difference. • How big the real difference is. • How much variability there is in the population distribution(s). • How much error variance there is. • Let’s talk about variance.

28. Sources of variance • Systematic vs. Error • Real differences • Error variance • What would happen to the DV if our measurement apparatus was a little inconsistent? • There are OTHER sources of error variance, and the whole point of experimental design is to try to minimize ‘em. Get this: The more error variance, the harder for real differences to “shine through.”

29. Z distribution

30. Probability • VERY little of life is certain. • It is PROBABILISTIC. (That is, something might happen, or it might not.)

31. Prob. (cont’d.) • Life’s a gamble! • Just about every decision is based on probable outcomes. • None of you is a “statistical wizard.” 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.

32. 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%.)

33. 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,” . . . .

34. Let’s talk about socks

35. 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 = .167 • 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) = ?

36. Yet more prob. • http://www.midcoast.com.au/~turfacts/maths.html • The product or multiplication rule. "If two chances are mutually exclusive the chances of getting both together, or one immediately after the other, is the product of their respective probabilities.“ • the addition rule. "If two or more chances are mutually exclusive, the probability of making ONE OR OTHER of them is the sum of their separate probabilities."

37. What’s the probability . . . • That the next card is a king? • That the next card is a heart? • That the next card is a spade? • That the next card is a club and a king? • That the next card is a spade OR a heart? • That the next two cards are kings?

38. 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?

39. 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

40. Happy B’day to Us • But we had 50. • Probability that the first person has a birthday: 1.00. • 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 + 1/365 – the chances of all three of them having the same birthday.

41. Sooooo . . . • http://en.wikipedia.org/wiki/Birthday_paradox

42. References • Hinton, P. R. Statistics explained. • Shaughnessy, Zechmeister, and Zechmeister. Experimental methods in psychology.

43. http://highered.mcgraw-hill.com/sites/0072494468/student_view0/statistics_primer.htmlhttp://highered.mcgraw-hill.com/sites/0072494468/student_view0/statistics_primer.html • Click on Statistics Primer.