**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

*(Assessment continues on next page.)*

• **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 A**rrow** 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.

* (Assessment continues on next page.)*

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

• **Criterion**: Calculate F from Mean Squares values.• **Data**: *MS*BG = 80 and *MS*E = 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?

*(Assessment* *continues on next page.)*

**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).

*(Assessment* *continues on next page*.*)*

**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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