2. Dr. Sinn, PSYC301, The joy of 1-way ANOVA1 Unit 3 Outline Day 1: Introduce F Return Tests (20) Power (20) Matching variance with data, ranking Fs (20) SPSS Example (15) – up to F value Day 2: Clean-up F: Practice F in class Finish SPSS Example (10) Post-hoc, alternative outcomes, practical significance (15) Explain where F comes from (15) Hypothesis Testing Steps ANOVA Example #2: (20) Practice conducting ANOVAs and writing up. (Dep. Therapies) Homework: Explain….Write up 1 ANOVA outcome (Typing) – two outcomes. Day 3: Write-ups Fs, Team Events Review Homework (10) Understanding F ratio – curves on graph paper (15) Pick the stat (20) Regression Review (30) Day 4: Practice test selection & write-ups Pick the stat Homework: Stats for Breakfast + regression.

3. Dr. Sinn, PSYC301, The joy of 1-way ANOVA2 Lecture Overview on ANOVA Review hypothesis testing; inferential statistics z-test, t-test, independent & dependent t-test New Stuff Power – Ability to reject Ho ANOVA Analysis of Variance Done with 3 or more groups Playground Exercise Complete SPSS Example

4. Dr. Sinn, PSYC301, The joy of 1-way ANOVA3 Power Review: Hypothesis Testing Errors Wrongly rejecting Ho: Chance of Type I error: α Wrongly retaining Ho: Chance of Type II error: β Power Opposite of β Power = 1- β Ability to reject Ho (when Ho should be rejected). Researchers want Power! Want ability to reject Ho; Show you were right to suspect a difference. Want to show IV affects your DV.

5. Dr. Sinn, PSYC301, The joy of 1-way ANOVA4 Error Areas α area (where we reject the Ho, and we shouldn’t) beyond t critical under Ho β area (where we retain the Ho, and we shouldn’t) inside t critical under Ha Ho: μ=55 tctc tctc αα β Ha: μ>55 tctc

6. Dr. Sinn, PSYC301, The joy of 1-way ANOVA5 Increasing Power #1: Increase Treatment: Increase difference between groups (μ’s) β Reality: μ=57 tctc β tctc H 0 : μ=55 Reality: μ=72 tctc tctc β β #2: Decrease Sampling Error: Decrease differences within groups.

7. Dr. Sinn, PSYC301, The joy of 1-way ANOVA6 Examples of increasing power #1 Increase Treatment Effect (Increase BG differences) Rat study 0,3,or 6 mg 0,10,or 20 mg Therapy study 10 therapy sessions 1 therapy session #2 Decrease Sampling Error (Decrease WG differences) Rat study Different strains of rats Same strain of rat Rats allowed to eat freely Rats all unfed for 24 hours Therapy study Diff. types of Therapy Same type of Therapy Rat Study: IV :Caffeine Level DV :Amt. Food Found Therapy Study: IV:Therapy (drug, talk, drug+talk, or control) DV: Improvement ]

8. Dr. Sinn, PSYC301, The joy of 1-way ANOVA7 1-Way ANOVA ANOVA Analysis of Variance 1-way means 1 Independent Variable (IV) Purpose: ANOVA allows hypothesis testing with 3+ sample means Imagine study on interventions to help frosh make friends Three IV levels: Standard courses, interactive courses, clustered courses. ANOVA uses F-test Strategy: Compare variability within group to variability between groups. F is ratio between two values:

9. Dr. Sinn, PSYC301, The joy of 1-way ANOVA8 ANOVA Playground (Download from Website)

10. Dr. Sinn, PSYC301, The joy of 1-way ANOVA9 Matching Exercise

11. Dr. Sinn, PSYC301, The joy of 1-way ANOVA10 Playground Exercises Do the following and record what happens to F: Make the means (approximately) 2, 4, and 6 without changing the WG variability. Now double the WG variability, trying to keep the means about the same (2,4,6). Now change the means to approximately 6, 4, 2. Now change the means to approximately 12, 7, and, 2. Play with the following: Make F as big as possible. Make F as close to 1 as possible.

12. Dr. Sinn, PSYC301, The joy of 1-way ANOVA11 Draw Conclusions from Playground  What does a large F mean?  What two things will make F large?

13. Dr. Sinn, PSYC301, The joy of 1-way ANOVA12 Partitioning Variance Partition fancy word for “divide up” ANOVA partitions variance (MS means variance) Types of variance Total variance = MS WG + MS BG MS WG = sampling error (background noise) MS BG = sampling error + treatment (includes effect of Independent Variable) If just error  F tends toward 1.0 If treatment effect  F gets larger

14. Dr. Sinn, PSYC301, The joy of 1-way ANOVA13 Example of 1-way ANOVA Studying effect of caffeine on productivity Does caffeine help or hurt? IV: Level of Caffeine: 0, 10, 20 mg DV: Number of Food Pellets Found 0 mg10 mg20 mg 2314223142 1231212312 444455444455 Number of Food Pellets Found

15. Dr. Sinn, PSYC301, The joy of 1-way ANOVA14 SPSS Data Entry DV IV Label levels of IV so output is easier to read.

16. Dr. Sinn, PSYC301, The joy of 1-way ANOVA15 SPSS Analysis Go to Analyze, Compare Means, & select One-way ANOVA Put IV here. Put DV here.

17. Dr. Sinn, PSYC301, The joy of 1-way ANOVA16 SPSS Analysis, Part #2 Conducts “after the fact” test to compare all pairs of sample means. Select this to get descriptive statistics like sample means & standard deviations. Gives you a line graph of the sample means Alpha level still set to.05, just like it was with t- tests.

18. Dr. Sinn, PSYC301, The joy of 1-way ANOVA17 SPSS Output Source of Variation Table Sample means from 3 groups, plus mean amount of food found overall.

19. Dr. Sinn, PSYC301, The joy of 1-way ANOVA18 Where does F come from? MS WG = SS WG /df WG = Sum of Squares / degrees of freedom MS BG = SS BG /df BG = Sum of Squares / degrees of freedom Degrees of freedom df WG : N T – K (Total # of subjects - # of groups) df BG : K-1 (# of groups – 1) df TOTAL : N T – 1 (Total # of subjects – 1) Expectations: If I give you df and SS, you can calculate F You don’t have to get any SS by hand.

20. Dr. Sinn, PSYC301, The joy of 1-way ANOVA19 SPSS Output –Post Hoc Test No Sig. Diff. Between 0 & 10mg Rats at 20 mg found significantly more food than rats on 0 or 10 mg of caffeine.

21. Dr. Sinn, PSYC301, The joy of 1-way ANOVA20 SPSS Output– Practical Significance η 2 (“eta squared”) Effect size statistic – indicates % of variance explained Measures impact of IV on DV We can explain 68% of the variance in how much food a rat finds if we know the level of caffeine.

22. Dr. Sinn, PSYC301, The joy of 1-way ANOVA21 Hypothesis Testing Steps 1.Comparison: cf. three sample means. 2.Hypothesis: Ho: μ 1 = μ 2 = μ 3 Ha: Not all μ’s equal 3.Set-up: α=.05, df bg = K-1= 2, df wg = N T -K = 16-3=13, Fcrit = 3.80 4.F obt = 13.653 5.Reject Ho. The hypothesis was largely supported. Rats found sig. more food on 20mg of caffeine (M=4.33) than on 0mg (M=2.40) or 10mg (M=1.80), F(2,13) = 13.653, p <=.05. Caffeine has a large effect on food finding behavior, accounting for about 68% of the variance, η 2 =.6775.

23. Dr. Sinn, PSYC301, The joy of 1-way ANOVA22 F-table df Between Groups df Within Groups

24. Dr. Sinn, PSYC301, The joy of 1-way ANOVA23 Lab #8: 1-way ANOVA TV Problem: The hypothesis was supported. Light TV users provided more community service (M = 6.13) than did moderate users (M = 4.00), who provided more than heavy users (M = 1.75), F(2,21) = 15.963, p ≤.05. TV accounts for about 60% of the variance in community service, η 2 =.6032.

25. Dr. Sinn, PSYC301, The joy of 1-way ANOVA24 Follow-up Questions Q1: Variance within group? MS wg = 2.399 Q2: Variance between groups? MS bg =38.292 Q3: Replacing heavy scores with 4,5,4,5,6,5,4,3 would decrease the difference between groups because the heavy users would then difference less from the other groups. Q4: Decreasing between group differences (decreasing treatment) would decrease F.

26. Dr. Sinn, PSYC301, The joy of 1-way ANOVA25 Problem #2: Post Hoc Explanation

27. Dr. Sinn, PSYC301, The joy of 1-way ANOVA26 Problem #2: Post Hoc Explanation

28. Dr. Sinn, PSYC301, The joy of 1-way ANOVA27 Problem #2: The hypothesis was supported. People commuting 0 minutes participated significantly more (M=3.4 hours) than people commuting 45 (M=1.2) or 60 minutes (M=1.6), F (3,16) = 7.256, p≤.05. Commuting accounted for a large amount of variance in community involvement, η 2 =.5764.

29. Dr. Sinn, PSYC301, The joy of 1-way ANOVA28 Follow-up Questions Q1: Variance within group? MS wg =.650 Q2: Variance between groups? MS bg =4.717 Q3: Replacing 30 minute commuting scores with 1,4,1,4,3 would increase the within group variability. Q4: Increasing sampling error would decrease F.

30. Dr. Sinn, PSYC301, The joy of 1-way ANOVA29 Review Partitioning Study: Does alcohol affect reaction time? Identify the treatment effect in this case. Explain how sampling error might arise. No Alcohol 2 Beers4 Beers 101520 2515 30 102040 14 23 26 Sample Means μ na =?? μ 2b =?? μ 4b =?? Population Means

31. Dr. Sinn, PSYC301, The joy of 1- way ANOVA30 One-Way ANOVA Part 2!!

32. Dr. Sinn, PSYC301, The joy of 1-way ANOVA31 Review Partitioning Study: Does alcohol affect reaction time? within groups What accounts for variability within groups? What accounts for variability between groups? What’s the Formula for F? No Alcohol 2 Beers4 Beers 101520 2515 30 102040

33. Dr. Sinn, PSYC301, The joy of 1-way ANOVA32 Review Partitioning Study: Does alcohol affect reaction time? If the alcohol content of the beers is not held constant, what happens to F? a.increases b.decreases c.neither No Alcohol 2 Beers4 Beers 101520 2515 30 102040 If the alcohol content of the beers is not held constant, what happens? a.error increases b.error decreases c.treatment effect increases d.treatment effect decreases

34. Dr. Sinn, PSYC301, The joy of 1-way ANOVA33 Hypothesis Testing Steps 1.Comparison: cf. three sample means. 2.Hypothesis: Ho: μ 1 = μ 2 = μ 3 Ha: Not all μ’s equal 3.Set-up: α=.05, df bg =K-1=3-1=2, df wg =N T -K=12-3=9, Fcrit = 4.26 now do one-way ANOVA on SPSS

35. Dr. Sinn, PSYC301, The joy of 1-way ANOVA34 SPSS Output - Charts

36. Dr. Sinn, PSYC301, The joy of 1-way ANOVA35 SPSS Output - Graphs

37. Dr. Sinn, PSYC301, The joy of 1-way ANOVA36 Hypothesis Testing Steps 1.Comparison: cf. three sample means. 2.Hypothesis: Ho: μ 1 = μ 2 = μ 3 Ha: Not all μ’s equal 3.Set-up: α=.05, df bg =K-1=3-1=2, df wg =N T -K=12-3=9, Fcrit = 4.26 4.F obt = 2.633 5.Retain Ho. The hypothesis was not supported. The reaction times following no alcohol (M=13.75), two beers (M=22.50), and four beers (M=26.25) did not differ significantly, F(2,9) = 2.633, n.s..

38. Dr. Sinn, PSYC301, The joy of 1-way ANOVA37 Numb. of Words Recalled: Dataset A Bet. Group Varib: L M H MS bg : _______ With. Group Varib:L M H MS wg : _______ 4812 5910 4911 5812

39. Dr. Sinn, PSYC301, The joy of 1-way ANOVA38 Numb. of Words Recalled: Dataset B Bet. Group Varib: L M H MS bg : _______ With. Group Varib:L M H MS wg : _______ 8410 9512 9511 8412

40. Dr. Sinn, PSYC301, The joy of 1-way ANOVA39 Numb. of Words Recalled: Dataset C Bet. Group Varib: L M H MS bg : _______ With. Group Varib:L M H MS wg : _______ 739 10613 7610 313

41. Dr. Sinn, PSYC301, The joy of 1-way ANOVA40 Numb. of Words Recalled: Dataset D Bet. Group Varib: L M H MS bg : _______ With. Group Varib:L M H MS wg : _______ 767 1087 7612 10 12

42. Dr. Sinn, PSYC301, The joy of 1-way ANOVA41 Numb. of Words Recalled: Dataset E Bet. Group Varib: L M H MS bg : _______ With. Group Varib:L M H MS wg : _______ 767 1087 7612 10 12 767 1087 7612 10 12

43. Dr. Sinn, PSYC301, The joy of 1-way ANOVA42 Numb. of Words Recalled: Dataset F Bet. Group Varib: L M H MS bg : _______ With. Group Varib:L M H MS wg : _______