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## Statistics in Healthcare Research Exercise For Dependent Groups: Questions to be graded

### Solution 1

The design of the study was conducted on a pretest-posttest design, where 25 women were involved in a health promotion program, with 21 of them completing the test. The calculated ratios are shown in Tables 2 and 3 reflect the significance of the change in various variables specified in the test between the pretest time to 3 months period and between the pretest time to 6 months period.

Even though this was a pretest-posttest design, we could say that there were two following categories of dependent results under investigation: results between the pretest to 3 months period, and results between the pretest to 6 months period.

### Solution 2

The greatest standardized change in the total risk behavior from the pretest to 3 months period is . This t ratio is statistically significant at a 5% significance level since it contains the (*) sign. Therefore, we reject the null hypothesis in this case, which states that the health promotion intervention did not affect the total risk behavior.

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### Solution 3 is the smallest ratio presented in Table 3. This ratio is not significant because it does not contain the (*) sign. Therefore, it implies that the p-value at this calculated t ratio is more than a 5% significance level. Hence, we do not have sufficient evidence to reject the null hypothesis which states that the health promotion intervention did not affect stress management.

### Solution 4

Assumptions for conducting a t-test for dependent groups are:

a) There is a normal or approximately normal distribution of the scores.

b) Measurement of dependent variables was done in intervals.

c) There is the dependence of groups examined for changes.

d) There is the independence of scores between the differences.

This study fulfilled the following assumptions:

e) Normal or approximately normal distribution of the scores the women were selected randomly. Thus, the mean score for various variables was random and assumed normal distribution.

f) Interval measurements of dependent variables the mean scores of variables were measured at the interval of 3 and 6 months.

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g) Dependence of groups examined for changes results in the two intervals were taken from one group pretest-posttest study design, hence dependent.

h) Independence of scores between the differences changes in the first interval does not influence the differences in the second interval, hence independent.

### Solution 5

The long-term change on the variable exercise is expected to become progressively insignificant. Between pre-test to 3 months interval, the t ratio is , while the one to 6 months interval is. Even though the changes for both intervals are significant, the value of the t ratio is reducing. The relationship between the t ratio and the p-value is inversely proportional. Therefore, as the t ratio decreases, the p-value will increase. Eventually, if the increase goes beyond the 5% level of significance, then the null hypothesis that the health promotion intervention did not affect the Exercise variable will be accepted.

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### Solution 6

t = 2.03*, p t ratio listed in Table 2. The 2.03 is the smallest t ratio with an *, indicating that change in the Cholesterol level was statistically significant from pretest to 3 months interval at 5% level of significance.

### Solution 7

Larget ratios indicate that large relative changes in the variables measured at various intervals are statistically different, especially when the sample size of the study is small. The calculated t ratios are inversely proportional to the observed p values. Therefore, the likelihood of failing to reject the null hypothesis when the t ratios decrease progressively is high since the groups are not significantly different.

### Solution 8

No. The health-promotion program intervention did not have any effect on Systolic blood pressure (BP). t = 1.57 (3 months) and t = 1.66 (6 months). At 3 months, the change in the Systolic blood pressure (BP) from the pretest was statistically insignificant with t = 1.57. At 6 months, the change in Systolic blood pressure (BP) from the pretest was still statistically insignificant with t = 1.66.

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### Solution 9

The pretest mean for Systolic BP is 121.7. This means decreased to 117.3 after 3 months and to 115.6 after 6 months. The pre-test Systolic BP standard deviation is 14.6. It decreased to 12.3 after three months and increased to 13.4 after 6 months. These results are clinically insignificant since the calculated t ratios for both do not contain the (*) sign, hence insignificant at the 5% level. Therefore, the null hypothesis that the health promotion program did not affect the Systolic BP of the subjects is rejected.

### Solution 10

This quasi-experimental design is weak since determining the effects of treatment is difficult without a comparison of a separate control group.

## Solution for the bonus Question

Yes. The calculated t value for change in the first interval is and the second interval is . Therefore, the changes for both periods were significant. Consequently, the null hypothesis that the health promotion intervention program did not affect the total risk score is rejected. Hence, if I were the health care provider, I could implement the intervention program.

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Solutions for worksheet 1: Hypothesis Excel Worksheet

b) c) d) We calculate the p-value of the calculated z.

This p-value is less than the significance level of 0.05. Therefore, the null hypothesis that the treatment did not have a significant effect is rejected. Hence the treatment had a significant effect.

If N=16,

P-value

This value is more than the level of significance of 0.05. Hence there is enough evidence to fail to reject the null hypothesis. Therefore, the treatment did not have a significant effect.

Since the critical , the value 4 lies in the region of rejection. Therefore, the two-sample means are sufficient to conclude that the educational models are significantly different.

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Solutions for worksheet two: InteliBoard Assessment

Answers for multiple choice question 1 to 10

1. D

2. B

3. C

4. B

5. D

6. D

7. A

8. B

9. D

10. A

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