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Psyc 235: Introduction to Statistics

Psyc 235: Introduction to Statistics. DON’T FORGET TO SIGN IN FOR CREDIT!. http://www.psych.uiuc.edu/~jrfinley/p235/. Reminders:. Assessment: Comments? Concerns? Thursday: office hours hands-on help with specific problems Special lab sections:

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Psyc 235: Introduction to Statistics

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  1. Psyc 235:Introduction to Statistics DON’T FORGET TO SIGN IN FOR CREDIT! http://www.psych.uiuc.edu/~jrfinley/p235/

  2. Reminders: • Assessment: Comments? Concerns? • Thursday: office hours • hands-on help with specific problems • Special lab sections: • May receive an invitation: same penalties for missing apply • Review some trouble topics • Hypothesis Testing • As always, contact us for specific requests…

  3. Where we are… • Last week, Jason reviewed Hypothesis Testing… • If you haven’t completed those sections… • Check out the online lecture slides • print decision trees • Print selecting a distribution • Attend Office Hours • Attend Special Labs which will review hyp testing • Let us know how we can help!

  4. Review: ANOVA(analysis of variance) • Last week, Jason gave you specific definitions and some example problems. (See slides on-line for review) • Today, we’re going to work through another problem and spend some more time talking about the underlying model in ANOVA. • Then we’ll move on to Chi-Square Tests.

  5. Example: Eysenck (1974) • Craik & Lockhart (1972) suggest that memory for verbal material is a function of how well it was processed when it was originally presented. • To test this Eysenck, divided 50 subjects into 5 conditions: • Counting • Rhyming • Adjective • Imagery • Intentional If learning involves merely being exposed to the material, there should be no differences between groups (equal recall). If level of processing is important, should be differences between group means.

  6. Data!!… Now What? • What’s our Null hypothesis? • H0 = 1 = 2 = 3 = 4 = 5 • What test do we use? • What model?

  7. ANOVA: Underlying Model • First let’s think generally about the underlying model with a concrete example: • Suppose average U.S. height is 5’7” • And males tend to be 2” taller • And suppose you are an adult male… • You could think of your height as being composed of 3 parts • The mean height • Adjustment for being male • Your own unique contribution • So, Height = 5’7” + 2” + uniqueness • In general terms, we could write this model as • Xij =  + male +you

  8. Underlying Model & Assumptions • In our lvls of processing example, what should our model look like? • Xij =  + j +ij • Basic Assumptions in ANOVA: • Homogeniety of variance of each population • Scores are Normally Distributed around mean • Observations are independent • So, we assume the same shape and distribution of each group… What is the only way left for them to differ? (Hint: Jason drew this on the board last week)

  9. Eysenck Computations SStotal = (Xij - X..)2 = (9-10.06) 2 + (8-10.06)2 +…+(11-10.06) 2 = 786.82 SStreat = n(Xj - X..)2= 10((7-10.06) 2 + (6.9-10.06)2 +…+(12-10.06) 2 = 351.52 SSerror = Sstotal - Sstreat = 786.82-351.52 = 435.3

  10. ANOVA Summary Table Review: Where are df from? We calculated SS, how do we get MS? What is the F-Ratio? What does it mean?

  11. Chi - Square Goodness of Fit • How do we do hypothesis testing on categorical data? • Is there a “good fit” between what we found and what we would expect to find under the Null?

  12. Example: Tolman, Ritchie, and Kalish (1946) So, it looks like the rats chose D more, but how can we be sure?

  13. Chi Square • Observed Frequencies: the frequencies you actually observed in the data • Expected Frequencies: the frequencies you would expect if the null hypothesis were true (whatever it is) • In this case, expected was that each rat would randomly choose a tunnel (so N * p= 32 *1/4=8)

  14. Chi-Square Test 2 = (O-E)2 E  • Intuitively, this should make some sense. • Start with the numerator: • If Null is true, O-E should be small (even squared) • Denominator: • To keep the difference between observed and expected in proportion we divide by expected.

  15. In our example… 2 = 9.25 df = k-1 (where k is # cells) defer to ALEKS

  16. Goodness of Fit • Note that you can compare your observed data to any reasonable set of expected values… • Prior data • Distributions (Normal, Uniform, Bimodal, etc)

  17. Two-Way Chi Square (contingency tables) Pugh(1983) Rape Convictions How could we compute expected frequency? • - What’s our Null hypothesis? • H0 = Verdict is not related to implied fault. • = They’re independent!! Eij = RiCj N

  18. Let’s Compute the Expected Values Finally, we use the same formula to compute 2 ~ 2 df 2 = (O-E)2 E = 35.93  Where, df = (R-1)(C-1)

  19. Questions? • Remember: • Keep Working • Let us know how we can help!

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