Conceptual Understanding

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 • H0: P = C =R =M • H1: The four population means are not all equal

14. Step 2: Find F-Critical • Step 2.1 • Need to first find dfbetween and dfwithin • Dfbetween = 3 (k = number of groups) • dfwithin = 12 (N = total number of observations) • dftotal = 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 • X2 = 937 • Tj2 = 3671 • N = 16 • n = 4

17. X = 121 X2 = 937 Tj2= 3671 N = 16 n = 4 Step 3.2: Calculate SS • SStotal

18. X = 121 X2 = 937 Tj2= 3671 N = 16 n = 4 Step 3.2: Calculate SS • SStotal 121 21.94 937 16

19. X = 121 X2 = 937 Tj2= 3671 N = 16 n = 4 Step 3.2: Calculate SS • SSWithin

20. X = 121 X2 = 937 Tj2= 3671 N = 16 n = 4 Step 3.2: Calculate SS • SSWithin 3671 19.25 937 4

21. X = 121 X2 = 937 Tj2= 3671 N = 16 n = 4 Step 3.2: Calculate SS • SSBetween

22. X = 121 X2 = 937 Tj2= 3671 N = 16 n = 4 Step 3.2: Calculate SS • SSBetween 2.69 3671 121 4 16

23. Step 3.2: Calculate SS • Check! • SStotal = SSBetween + SSWithin

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

25. Step 3.3: Calculate MS

26. Step 3.3: Calculate MS 2.69 .90 3

27. Calculating this Variance Ratio

28. Step 3.3: Calculate MS 19.25 1.60 12

29. Step 3.4: Calculate the F value

30. Step 3.4: Calculate the F value .90 .56 1.60

31. Step 4: Decision • If F value > than F critical • Reject H0, and accept H1 • If F value < or = to F critical • Fail to reject H0

32. Step 4: Decision F value = .56 F crit = 5.95 • If F value > than F critical • Reject H0, and accept H1 • If F value < or = to F critical • Fail to reject H0

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? • H0: 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.

38. tobs = 4.257 • tcrit = 2.101 • Age does seem to “affect” 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