# 1. A study examined whether adding a fragrance to a window cleaner

1. A study examined whether adding a fragrance to a window cleaner led people to believe that it cleans better than an unscented product. There were 12 subjects in each group: scented or unscented. The mean cleaning effectiveness rating for the group getting the scented cleaner was 7.42. The mean cleaning effectiveness rating for the group getting the unscented cleaner was 6.00. The standard deviation for cleaning effectiveness ratings across all subjects was 1.369. A t test showed that the scented cleaner was rated as a significantly more effective cleaner (p < .01).

a. Calculate the Cohen’s d effect size for this study:

b. Interpret the result: Do you believe there was a practical difference in cleaning effectiveness between scented and unscented cleaners? Explain your answer.

2. A study examined whether male or female college students studied more. There were 10 males and 10 females in the study. The mean study time for males was 11.1 hours/week. The mean study time for females was 10.9 hours/week. The standard deviation for study time across both males and females was 2.81. A t test showed no significant difference in study time between males and females (p .10).

a. Calculate the Cohen’s d effect size for this study:

b. Interpret the result: Do you believe there was a practical difference in study time between males and females? Explain your answer.

3. When the Power is 84%, what is the Type 2 Error?

4. When the Type 2 Error is 12%, what is the Power?

For question 5-8, use the following table: (Note: this table represents a significance level of .05 for a two-sample independent t test.)

Cohens d

.10

.20(small)

.30

.40

.50 (medium)

.60

.70

.80 (large)

.90

1.00

.80 power

1571

393

175

99

64

45

33

26

17

12

5. You are designing a study and want .80 power. You expect Cohen’s d to be about .80. How many subjects will you need per group?

6. You are designing a study and able to obtain 65 subjects per group. Approximately what will Cohen’s d have to be for you to obtain .80 power?

7. You are designing a study and want .80 power. You expect Cohen’s d to be about .65. Approximately how many subjects will you need per group?

8. You are designing a study and able to obtain 25 subjects per group. Approximately what will Cohen’s d have to be for you to obtain .80 power?

a. Calculate the Cohen’s d effect size for this study:

b. Interpret the result: Do you believe there was a practical difference in cleaning effectiveness between scented and unscented cleaners? Explain your answer.

2. A study examined whether male or female college students studied more. There were 10 males and 10 females in the study. The mean study time for males was 11.1 hours/week. The mean study time for females was 10.9 hours/week. The standard deviation for study time across both males and females was 2.81. A t test showed no significant difference in study time between males and females (p .10).

a. Calculate the Cohen’s d effect size for this study:

b. Interpret the result: Do you believe there was a practical difference in study time between males and females? Explain your answer.

3. When the Power is 84%, what is the Type 2 Error?

4. When the Type 2 Error is 12%, what is the Power?

For question 5-8, use the following table: (Note: this table represents a significance level of .05 for a two-sample independent t test.)

Cohens d

.10

.20(small)

.30

.40

.50 (medium)

.60

.70

.80 (large)

.90

1.00

.80 power

1571

393

175

99

64

45

33

26

17

12

5. You are designing a study and want .80 power. You expect Cohen’s d to be about .80. How many subjects will you need per group?

6. You are designing a study and able to obtain 65 subjects per group. Approximately what will Cohen’s d have to be for you to obtain .80 power?

7. You are designing a study and want .80 power. You expect Cohen’s d to be about .65. Approximately how many subjects will you need per group?

8. You are designing a study and able to obtain 25 subjects per group. Approximately what will Cohen’s d have to be for you to obtain .80 power?

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