u04a1– Related-Samples t Tests, ANOVA, and the Tukey HSD Test

Complete the following problems within this Word document (do not submit other files). Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. (You may want to highlight your answer or use a different type of color to set it apart.)

Problem Set 4.1: t Test with Related Samples

• Criterion: Differentiate between independent samples, repeated measures, and matched samples.• Data: o Scenario A: A researcher wants to know whether men or women spend more money at the movie concession stand. He asks the concession clerk to identify the customer as male or female based on each saved receipt.o Scenario B: A CPR instructor wants to know if her students are learning anything during her 90-minute training. She decides to quiz her students at the beginning of class and again at the end of class.• Instruction: For each of the two scenarios, identify whether independent samples, repeated measures, or matched samples would be used. Explain how you can make the determination.

Problem Set 4.2: Paired Samples t Test in SPSS

• Criterion: Calculate a paired samples t test in SPSS.• Data: Dr Statistics wanted to test how her learners scored on a problem set when she presented the problems sequentially versus when she presented the problems randomly. She had 10 learners who scored the following:

Learner

Sequential

Random

1

92

90

2

85

89

3

77

85

4

86

80

5

93

96

6

72

75

7

99

91

8

84

80

9

63

71

10

94

95

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• Instruction: Complete the following steps:a. Open SPSS and create a New DataSet.b. Click the Variable View tab.c. Enter Sequential in row 1 and Random in row 2.d. Click the Data View tab. Enter the data for each learner.e. In the Toolbar, click Analyze, select Compare Means, and then select Paired-Samples T Test.f. Click Sequential and then click Arrow to send it over to the Variable 1 box.g. Click Random and then click Arrow to send it over to the Variable 2 box.h. Click OK and copy and paste the output into the Word document below.

Problem Set 4.3: Paired Samples t Test in SPSS

• Criterion: Analyze a paired samples t test to make a decision about the null hypothesis.• Data: Use the data from Problem Set 4.2.• Instruction: Complete the following:o Compare t with the one-tailed critical t at the .01 α level. o Answer this: Did the learners who received sequenced problem sets score significantly higher? Why or why not?o State your decision about the null hypothesis.

Problem Set 4.4: Confidence Intervals

• Criterion: Calculate a confidence interval based on the results of a independent samples t test.• Data: Use the data from Problem Set 4.2.• Instruction: Answer this: Based on that output, what is the 95 percent confidence interval of the difference?

Problem Set 4.5: ANOVA Logic: Sum of Squares

• Criterion: Calculate sum of squares.• Data: The within-group (error) sum of squares is 108.45 and the between-group sum of squares is 48.68.• Instruction: Calculate the sum of squares total.

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Problem Set 4.6: ANOVA Logic: From Mean Squares to F

• Criterion: Calculate F from Mean Squares values.• Data: MSBG = 80 and MSE = 20.• Instruction: Answer this: What is F?

Problem Set 4.7: ANOVA Summary Table

• Criterion: Analyze the results of an ANOVA summary table and report findings.• Data: ANOVA summary table:

SS

df

MS

F

Between Groups

283.32

4

70.83

8.16

Within groups (error)

390.60

45

8.68

Total

673.92

49

• Instruction: Answer questions a–d using the ANOVA summary table above.

a.How many groups participated?

b.How many participants were in each group (assuming equal number of participants per group)?

c.Refer to the F table. What is the critical value of F(4,45) at the .01 level?

d.Given a significant result at the .01 level, how confident are you (0 to 100 percent) that rejecting the null hypothesis is not due to chance? Additionally, what is the probability that you made a Type 1 error?

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Problem Set 4.8: One-Way ANOVA in SPSS

• Criterion: Calculate an ANOVA in SPSS.• Data: Tyrone is testing out dye strength after washing dyed fabric for his new fabric line. He dyes his fabrics blue, green, and yellow and washes the fabric one time. The following are the dye strength results for 10 pieces of fabric in each color after one wash:

Blue

Green

Yellow

98

55

66

96

53

71

92

57

73

92

60

71

88

52

76

86

54

72

89

62

74

92

53

69

94

54

68

90

65

70

• Instruction: Complete the following steps:a. Open SPSS and create a New DataSet.b. Click the Variable View tab and enter Color and DyeStrength as the variables. Click the Values box for the Color row and define 1 as blue, 2 as green, and 3 as yellow.c. Enter the data.d. In the Toolbar, click Analyze, select Compare Means, and then select One-Way ANOVA.e. Click DyeStrength and then click Arrow to send it over to the Dependent List box.f. Click Color and then click Arrow to send it over to the Factor box.g. Click OK and copy and paste the output below.

Problem Set 4.9: One-Way ANOVA results in APA style

• Criterion: Report ANOVA results in APA format.• Data: Use the Dye Strength data from Problem Set 4.8.• Instruction: Complete the following:

a.State the null hypothesis.

b.Report your results in APA format (as you might see them reported in a journal article).

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Problem Set 4.10: Tukey HSD Test in SPSS

• Criterion: Calculate post hoc analyses in SPSS.• Data: Use the SPSS from Problem Set 4.4.• Instruction: Complete the following steps:a. In the Toolbar, click Analyze, select Compare Means, and then select One-Way ANOVA.b. Click Dye Strength and then click Arrow to send it over to the Dependent List box.c. Click Color and then click Arrow to send it over to the Factor box.d. Click Post Hoc and then mark the box Tukey. Click Continue.e. Click OK and copy and paste the output to your Word document.

Problem Set 4.7: Tukey HSD Interpretation

• Criterion: Interpret Tukey HSD results from SPSS output.• Data: Use your output from Problem Set 4.10. • Instruction: Identify where significant differences exist at the .05 level between your colors.

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