2. Practice Does drinking milkshakes affect (alpha =.05) your weight? To see if milkshakes affect a persons weight you collected data from 5 sets of twins. You randomly had one twin drink water and the other twin drank milkshakes. After 3 months you weighed them.

3. Results Water Twin A186 Twin B200 Twin C190 Twin D162 Twin E175 Milkshakes 195 202 196 165 183

4. Hypothesis Two-tailed Alternative hypothesis –H 1 :  water =  milkshake Null hypothesis –H 0 :  water =  milkshake

5. Step 2: Calculate the Critical t N = Number of pairs df = N - 1 5 - 1 = 4  =.05 t critical = 2.776

6. Step 3: Draw Critical Region t crit = 2.776t crit = -2.776

7. Step 4: Calculate t observed t obs = (X - Y) / S D

8. 3.04 = (D) -9 -2 -6 -3 -8  D = -28  D 2 =194 N = 6 -28 194 5 5 - 1

9. Step 4: Calculate t observed t obs = (X - Y) / S D 1.36=3.04 / 5 N = number of pairs

10. Step 4: Calculate t observed -4.11 = (182.6 – 188.2) / 1.36 X = 182.6 Y = 188.2 S D = 1.36

11. Step 5: See if t obs falls in the critical region t crit = 2.776t crit = -2.776 t obs = -4.11

12. Step 6: Decision If t obs falls in the critical region: –Reject H 0, and accept H 1 If t obs does not fall in the critical region: –Fail to reject H 0

13. Step 7: Put answer into words Reject H 0, and accept H 1 Milkshakes significantly (  =.05) affect a persons weight.

15. What if... You were asked to determine if psychology and sociology majors have significantly different class attendance (i.e., the number of days a person misses class) You would simply do a two-sample t-test –two-tailed Easy!

16. But, what if... You were asked to determine if psychology, sociology, and biology majors have significantly different class attendance You can’t do a two-sample t-test –You have three samples No such thing as a three sample t-test!

17. One-Way ANOVA ANOVA = Analysis of Variance This is a technique used to analyze the results of an experiment when you have more than two groups

18. Example You measure the number of days 7 psychology majors, 7 sociology majors, and 7 biology majors are absent from class You wonder if the average number of days each of these three groups was absent is significantly different from one another

19. Hypothesis Alternative hypothesis (H 1 ) H 1: The three population means are not all equal

20. Hypothesis Alternative hypothesis (H 1 )  socio =  bio

21. Hypothesis Alternative hypothesis (H 1 )  socio =  psych

22. Hypothesis Alternative hypothesis (H 1 )  psych =  bio

23. Hypothesis Alternative hypothesis (H 1 )  psych =  bio =  soc

24. Hypothesis Alternative hypothesis (H 1 ) –Notice: It does not say where this difference is at!!

25. Hypothesis Null hypothesis (H 0 )  psych =  socio =  bio –In other words, all three means are equal to one another (i.e., no difference between the means)

26. Results X = 3.00X = 2.00X = 1.00

27. Logic Is the same as t-tests 1) calculate a variance ratio (called an F; like t-observed) 2) Find a critical value 3) See if the the F value falls in the critical area

28. Between and Within Group Variability Two types of variability Between –the differences between the mean scores of the three groups –The more different these means are, the more variability!

29. Results X = 3.00X = 2.00X = 1.00

30. Between Variability X = 3.00X = 2.00X = 1.00 S 2 =.66

31. Between Variability X = 3.00X = 2.00X = 1.00 + 5

32. Between Variability X = 8.00X = 2.00X = 1.00

33. Between Variability X = 8.00X = 2.00X = 1.00 S 2 = 9.55

34. Between Group Variability What causes this variability to increase? 1) Effect of the variable (college major) 2) Sampling error

35. Between and Within Group Variability Two types of variability Within –the variability of the scores within each group

36. Results X = 3.00X = 2.00X = 1.00

37. Within Variability X = 3.00X = 2.00X = 1.00 S 2 =.57

38. Within Variability X = 3.00X = 2.00X = 1.00 S 2 =.57S 2 =1.43S 2 =.57

39. Within Group Variability What causes this variability to increase? 1) Sampling error

40. Between and Within Group Variability Between-group variability Within-group variability

41. Between and Within Group Variability sampling error + effect of variable sampling error

42. Between and Within Group Variability sampling error + effect of variable sampling error Thus, if null hypothesis was true this would result in a value of 1.00

43. Between and Within Group Variability sampling error + effect of variable sampling error Thus, if null hypothesis was not true this value would be greater than 1.00