2. Conceptual Understanding Complete the above table for an ANOVA having 3 levels of the independent variable and n = 20. Test for significant at.05.

3. Conceptual Understanding Fcrit = 3.18 Complete the above table for an ANOVA having 3 levels of the independent variable and n = 20. Test for significant at.05. Fcrit (2, 57) = 3.15

5. Conceptual Understanding Under what circumstance will the F ratio, over the long run, approach 1.00? Under what circumstances will the F ratio be greater than 1.00?

6. Conceptual Understanding Under what circumstance will the F ratio, over the long run, approach 1.00? Under what circumstances will the F ratio be greater than 1.00? F ratio will approach 1.00 when the null hypothesis is true F ratio will be greater than 1.00 when the null hypothesis is not true

7. Conceptual Understanding Without computing the SS within, what must its value be? Why?

8. Conceptual Understanding The SS within is 0. All the scores within a group are the same (i.e., there is NO variability within groups)

10. Practice You are interested in comparing the taste preference of four sodas. Subjects drank one of four sodas and asked to rank it on a 1-10 scale of how much they liked the taste.

11. Results

12. Practice Is there a significant (.01) difference in how much these sodas were liked?

13. Step 1: State the Hypothesis H 0 :  P =  C =  R =  M H 1: The four population means are not all equal

14. Step 2: Find F-Critical Step 2.1 Need to first find df between and df within Df between = 3 (k = number of groups) df within = 12 (N = total number of observations) df total = 15 Check yourself 15 = 3 + 12

15. Step 2: Find F-Critical Step 2.2 Look up F-critical using table F on pages 370 - 373. F (3,12) = 5.95

16. Step 3.1: Ingredients  X = 121  X 2 = 937  T j 2 = 3671 N = 16 n = 4

17. Step 3.2: Calculate SS  X = 121  X 2 = 937  T j 2 = 3671 N = 16 n = 4 SS total

18. Step 3.2: Calculate SS SS total 937 121 16 21.94  X = 121  X 2 = 937  T j 2 = 3671 N = 16 n = 4

19. Step 3.2: Calculate SS SS Within  X = 121  X 2 = 937  T j 2 = 3671 N = 16 n = 4

20. Step 3.2: Calculate SS SS Within 937 3671 4 19.25  X = 121  X 2 = 937  T j 2 = 3671 N = 16 n = 4

21. Step 3.2: Calculate SS SS Between  X = 121  X 2 = 937  T j 2 = 3671 N = 16 n = 4

22. Step 3.2: Calculate SS SS Between 3671 4 121 16 2.69  X = 121  X 2 = 937  T j 2 = 3671 N = 16 n = 4

23. Step 3.2: Calculate SS Check! SS total = SS Between + SS Within

24. Step 3.2: Calculate SS Check! 21.94 = 2.69+ 19.25

25. Step 3.3: Calculate MS

26. 2.69 3.90

27. Calculating this Variance Ratio

28. Step 3.3: Calculate MS 19.25 12 1.60

29. Step 3.4: Calculate the F value

30. .90 1.60.56 Step 3.4: Calculate the F value

31. Step 4: Decision If F value > than F critical –Reject H 0, and accept H 1 If F value < or = to F critical –Fail to reject H 0

32. Step 4: Decision If F value > than F critical –Reject H 0, and accept H 1 If F value < or = to F critical –Fail to reject H 0 F value =.56 F crit = 5.95

33. Step 5: Create the Summary Table

34. Step 6: Put answer into words Question: Is there a significant (.01) difference in how much these sodas were liked? H 0 :  P =  C =  R =  M There was not a significant difference in how much these sodas were liked. On average, they were all liked equally as well.

35. Practice Odometers measure automobile mileage. Suppose 12 cars drove exactly 10 miles and the following mileage figures were recorded. Determine if, on average, the odometers were accurate (Alpha =.05). 9.8, 10.1, 10.3, 10.2, 9.9, 10.4, 10.0, 9.9, 10.3, 10.0, 10.1, 10.2

36. One-sample t-test H1 = Mean not equal to 10 H0 = Mean = 10 t critical (11) = 2.201 t obs = 1.86 The odometers did not record a siginficantly different distance than what was driven.

37. Practice A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30) were given a life satisfaction test with high scores indicative of high life satisfaction. Determine if age has an affect (.05) on life satisfaction. Older AdultsYounger Adults Mean = 44.5Mean = 28.1 S = 8.68S = 8.54

38. t obs = 4.257 t crit = 2.101 Age does seem to “effect” life satisfaction.

39. Review Compare one sample to another value –One sample t-test Compare two independent samples to each other –Two sample independent t-test (equal or unequal n) Compare two dependent samples to each other –Two sample dependent t-test Compare two or more independent samples to each other –One-way ANOVA