# t-TEST FOR DEPENDENT GROUPS

EXERCISE 31 *t*-TEST FOR DEPENDENT GROUPS

STATISTICAL TECHNIQUE IN REVIEW

The ** t-test for dependent groups** is a parametric analysis technique used to determine statistical differences between two related samples or groups. Groups are dependent or related because they were matched as part of the design to ensure similarities between the two groups and thus reduce the effect of extraneous variables. For example, two groups might be matched on gender so an equal number of males and females are in each group, thus reducing the extraneous effect of gender on the study results. The researcher’s decision to match groups is determined by the study being conducted and is detailed in the study design. In previous research, groups have most commonly been matched for age, gender, ethnicity, diagnoses, and status of illness. Matching the groups strengthens the study design by reducing the effect of extraneous variables controlled by matching. Groups are also dependent when scores used in the analysis are obtained from the same subjects under different conditions, such as pretest and posttest study design. In this type of design, a single group of subjects is exposed to pretest, treatment, and posttest. Subjects are referred to as serving as their own control during the pretest that is then compared with the posttest scores following the treatment. This is a weak quasi-experimental design since it is difficult to determine the effects of a treatment without comparison to a separate control group. The assumptions for the

*t*-test for dependent groups are:

1. The distribution of scores is normal or approximately normally distributed.

2. The dependent variable(s) is (are) measured at interval or ratio levels.

3. The groups examined for differences are dependent based on matching or subjects serving as their own control.

4. The differences between the paired scores are independent (Burns & Grove, 2005).

RESEARCH ARTICLE

**Source:** Kim, C., Junes, K., & Song, R. (2003). Effects of a health-promotion program on cardiovascular risk factors, health behaviors, and life satisfaction in institutionalized elderly women. *International Journal of Nursing Studies, 40* (4), 375–81.

Introduction

Kim, Junes, and Song (2003) conducted a quasi-experimental study with a one group pretest-posttest design. “A convenient sample of 21 elderly women was recruited from a home for elderly people.” (Kim et al., 2000, p. 376). The purpose of the study was to determine the health benefits of a 3-month health-promotion program for institutionalized elderly women on cardiovascular risk factors, health behaviors, and life satisfaction. These researchers found the following positive effects from the program: reductions in total risk score, improved health behaviors, and improved life satisfaction. However, Kim et al. (2003) noted a decrease in these positive effects 3 months after the completion of the health-promotion program.

Relevant Study Results

A total of 25 women were enrolled in the health-promotion program and 21 subjects completed the program with three sets of outcome assessments at pretest, 3 months, and 6 months. The mean age of the subjects was 77 years, and 90% of them had been diagnosed with one or more chronic diseases. The significance level of the study was set at a = 0.05. The results from the study are presented in the two tables that follow. Table 2 describes the health-promotion program’s effects on cardiovascular risk factors, and Table 3 describes the effects on health behaviors. The third dependent variable of this study was life satisfaction, which was significantly improved from pretest to the end of the health-promotion program at 3 months and at 6 months follow-up.

TABLE 2 Program Effects on Cardiovascular Risk Factors

PRETEST

3 MONTHS

6 MONTHS

Variable

M (*SD*)

M (*SD*)

Paired *t*^{a}

M (*SD*)

Paired *t*^{b}

Total risk score

20.1 (4.5)

16.8 (3.2)

4.14*

18.1 (4.0)

2.56*

Cholesterol

200.2 (29.1)

189.6 (25.3)

2.03*

192.7 (22.1)

1.73

Triglyceride

164.2 (42.0)

150.4 (44.1)

2.58*

142.9 (53.5)

2.20*

BMI

22.7 (3.0)

22.1 (3.0)

3.44*

22.9 (3.0)

-0.80

Systolic BP

121.7 (14.6)

117.2 (12.3)

1.57

115.6 (13.4)

1.66

Kim, C., Junes, K., & Song, R. (2003). Effects of a health-promotion program on cardiovascular risk factors, health behaviors, and life satisfaction in institutionalized elderly women. International Journal of Nursing Studies, 40(4), p. 378

.

BMI

(body mass index), *BP* (blood pressure)

* *p*

a Paired *t*-test results between the pretest and 3-month measures.

b Paired *t*-test results between the pretest and 6-month measures.

TABLE 3 Program Effects on Health Behaviour

PRETEST

3 MONTHS

6 MONTHS

Variable

M (*SD*)

M (*SD*)

Paired *t*^{a}

M (*SD*)

Paired *t*^{b}

Total health behavior

66.3 (8.1)

69.7 (5.0)

-3.02*

68.1 (5.1)

-1.34

Health responsibility

2.19 (0.5)

2.13 (0.3)

1.03

2.29 (0.3)

-1.39

Exercise

1.88 (0.3)

2.58 (0.3)

-7.75*

2.29 (0.4)

-3.93*

Diet behavior

3.41 (0.3)

3.47 (0.2)

-0.93

3.26 (0.3)

2.00

Stress management

2.39 (0.4)

2.44 (0.3)

-0.65

2.45 (0.3)

-0.70

Smoking behavior

2.85 (0.8)

2.92 (0.8)

-1.45

3.01 (0.7)

-0.96

* *p*

a Paired *t*-test results between the pretest and 3-month measures.

b Paired *t*-test results between the pretest and 6-month measures.

Kim, C., Junes, K., & Song, R. (2003). Effects of a health-promotion program on cardiovascular risk factors, health behaviors, and life satisfaction in institutionalized elderly women. International Journal of Nursing Studies, 40(4), p. 379

.

STUDY QUESTIONS

1. What clues do you have that this study had “dependent groups?”

2. Which *t* ratio or value in Table 3 is the greatest for the 6-month follow-up? Which variable is being examined for differences between the pretest and 6-month follow-up by this *t* ratio?

3. Which *t* ratio or value listed in Table 2 is the smallest in determining the difference between the pretest and 6-month follow-up? This *t* ratio was calculated to determine the change in which variable from pretest to 6 months after the intervention?

4. *t* = -0.93 is the result for what variable in this study? Is this *t* ratio significant? Provide a rationale for your answer.

5. Compare the pretest to 3 months and 6 months *t* ratios for BMI from Table 2. What is your conclusion regarding the effects of the health-promotion intervention on the BMI long term?

6. The *t*-test for dependent groups is conducted in research for what purpose?

7. What is the smallest, significant *t* ratio listed in Table 3? Provide a rationale for your answer.

8. Why do you think that the smaller *t* ratios are not statistically significant?

9. How would you describe the result *t* = -1.45 in this study?

ANSWERS TO STUDY QUESTIONS

1. This study was conducted using a *one group* pretest-posttest design in which the subjects serve as their own control. The subjects’ outcomes at 3 and 6 months were compared with their pretest values. The single sample pretest-posttest design indicates that the groups were dependent or related. In Tables 2 and 3 the *t*-tests are identified as paired *t*-tests, which are conducted on dependent groups.

2. *t* = -3.93 (Exercise) is the largest *t* ratio at 6 months, as listed in Table 3.

3. *t* = -0.80 (BMI) represents the smallest *t*-ratio at 6 months, as listed in Table 2.

4. *t* = -0.93 indicates the difference in Diet behavior from pretest to 3 months. This *t*-ratio does not have an asterisk (*) next to it in Table 3; therefore, it is not statistically significant. The asterisk directs the reader to the footnotes at the bottom of the table where the asterisk is said to represent *p*

5. *t* = 3.44* (3 months) and *t* = -0.80 (6 months). At 3 months, the difference in BMI (body mass index) from pretest was statistically significant with *t* = 3.44*, *p* *t* = -0.80. These results indicate that although initially the BMI decreased significantly from the pretest (mean = 22.7) to 3 months (mean = 22.1), the BMI actually increased at 6 months (mean = 22.9). Thus, the health-promotion intervention did not have a positive long-term effect on the subject’s BMI, since the subjects demonstrated an increase in BMI versus a decrease.

6. The *t*-test for dependent groups is conducted to determine statistical differences between two related or dependent groups. The *t*-test can be used to determine differences between two dependent groups following a treatment and also for comparing and contrasting two groups for a selected variable. Paired *t*-test is another name for the *t*-test for dependent groups.

7. *t* = -3.02*, *p* *t* ratio listed in Table 3. The -3.02 is the smallest *t* ratio with an *, indicating that Total health behavior was statistically significant from pretest to 3 months in this study at *p*

8. The small *t* ratios indicate small relative differences between the two groups that are usually not statistically significantly different, especially in small sample studies. The larger the calculated *t* ratios, the smaller the observed *p* values and the more likely one will reject the null hypothesis, since the groups are significantly different.

9. The result *t* = -1.45 indicates that there is no statistically significant difference in Smoking behavior from pretest to 3 months in this sample. Thus, the null hypothesis would be accepted, which states the health-promotion intervention did not have an effect on Smoking behavior.

Name:____________________________________________ Class: ____________________

Date: _________________________________________________________________________________

_ EXERCISE 31 Questions to be Graded

1. What are the two groups whose results are reflected by the *t* ratios in Tables 2 and 3?

2. Which *t* ratio in Table 2 represents the greatest relative or standardized difference between the pretest and 3 months outcomes? Is this *t*ratio statistically significant? Provide a rationale for your answer.

3. Which *t* ratio listed in Table 3 represents the smallest relative difference between the pretest and 3 months? Is this *t* ratio statistically significant? What does this result mean?

4. What are the assumptions for conducting a *t*-test for dependent groups in a study? Which of these assumptions do you think were met by this study?

5. Compare the 3 months and 6 months *t* ratios for the variable Exercise from Table 3. What is your conclusion about the long-term effect of the health-promotion intervention on Exercise in this study?

6. What is the smallest, significant *t* ratio listed in Table 2? Provide a rationale for your answer.

7. Why are the larger *t* ratios more likely to be statistically significant?

8. Did the health-promotion program have a statistically significant effect on Systolic blood pressure (BP) in this study? Provide a rationale for your answer.

9. Examine the means and standard deviations for Systolic BP at pretest, 3 months (completion of the treatment), and 6 months. What do these results indicate? Are these results clinically important? Provide a rationale for your answer.

10. Is this study design strong or weak? Provide a rationale for your answer.

BONUS QUESTION

Would you, as a health care provider, implement this intervention at your facility based on the Total Risk Score results? Provide a rationale for your answer.

(Grove 231)

Grove, Susan K.. *Statistics for Health Care Research: A Practical Workbook*. W.B. Saunders Company, 022007. .

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