Q1) For this analysis, what is H0:
Paired sample t-test is used in evaluating the difference between means of two groups (Norusis, 2006). Thus, the null hypothesis (H0) is as shown below:
H0: There is no difference between the average of pre-treatment scores and the average of the follow-up scores
H1: There is a difference between the average of pre-treatment scores and the average of the follow-up scores
Q2) Based on the paired t-test results, what can you say about an overall treatment effect? Do people get better over time?
From table 1 it can be seen that the mean of the pre-treatment scores is 20.81 ± 7.16 while the mean of the follow-up treatment is 15.04 ± 7.26.
From table 2, it is seen that the pre-treatment scores and the follow-up scores are moderately and positively correlated (r = 0.556, p < 0.05)
There was a significant mean difference between pre-treatment scores and follow-up scores (t5.696, p < 0.05). Thus, we fail to accept the null hypothesis and conclude that there is a difference between the mean of pre-treatment scores and the follow-up scores. Consequently, it is evident that on average, the pre-treatment score was 5.768 higher than the follow-up scores (95% CI [3.727, 7.809]).
From this, it can be deduced that the overall treatment has a significant impact. By conducting frequent follow up, the stress scores were seen to reduce significantly. Thus people get better with time as their stress levels continue to decline after undergoing the treatment.
Q3) Write the H0: for the ANOVA comparing 3 groups at follow up
A one-way ANOVA is used in finding the differences between the means of two or more groups (Heiberger & Neuwirth, 2009). The null hypothesis and the alternate hypothesis of the One-Way ANOVA is as shown below:
H0: The is no difference between the averages of the three groups
H1: There is a difference between the averages of the three groups
Q4) What can you say about the groups one month after treatment (at followup)?
Based on table 4 above, it is evident that there was a significant difference between the groups as evaluated by the one-way ANOVA (F(2,44) = 11.602, p < 0.05)
Q5) Is there a need to do Post Hoc tests (i.e., do we have an overall difference between groups, where we will need to find which individual groups are different)? If so, report which groups differ significantly from each other, along with the significance level (p value).
There was a need to perform a Post Hoc Test in order to confirm where the difference between the groups occurs (Keppel & Wickens, 2004). The results of the Post Hoc Test are as shown in the table below:
From the Tukey post hoc test in table 6 above, it is evident that the follow-up scores were statistically significant lower during the low exercises (21.44 ± 6.18, p = 0.000) and moderate exercises (14.58 ± 5.795, p = 0.009) compared to the high exercises (10.19 ± 5.999). There was no statistically significant difference between the high exercises and low exercises and also high exercises and moderate exercises.
Q6) Is there a significant interaction effect of group and exercise on PTSD scores at follow up?
The two way ANOVA was conducted to determine the effect of exercises and group therapy in the reduction in PSTD severity (Lu, Liu & Koestler, 2017). According to table 6, it was found out that there was no statistically significant interaction between the effects of exercises and group therapy in the reduction in PSTD severity, F (6,33) = 0.654, p > 0.05.
Q7) Based on the first plot where you have separate lines for exercise, what do you see is happening for the different levels of exercise?
Based on figure 1 above, it is evident that there is an interaction between the moderate exercises and the high exercises at the supportive counselling therapy group. At no point does the low exercise interact with either the high exercises or the moderate exercises.
Q8) Based on the second plot where you have separate lines for group, what do you see is happening for the different levels of therapygroup?
From figure 2, it can be seen that there is an interaction of the wait list, prolonged exposure, and supportive counselling therapy group at the moderate level of exercise. Conversely there is an interaction between the wait list and the stress inoculation therapy group at the low level of exercise.
Q9) Is there a significant main effect of therapy group on PTSD scores at follow up?
It was found out that there was no main effect of therapy group, F (3, 33) = 0.918, P > 0.05.
Q10) Is there a significant main effect of exercise on PTSD scores at follow up?
It was found out that there was a main effect of exercises, F (2, 33) = 6.350, P < 0.05.
Q11) Write up the results as if you were writing up a results section. Describe what you have found so far in your study.
To study the impact of treatment for PSTD, various statistical measures were carried out. They include the paired sample t-test, the one way ANOVA and the two-way ANOVA. The paired sample t-test was carried out to determine if there was a difference or not between the means of pre-treatment scores and the mean of the follow-up scores. It was found out that there was a statically significant difference between the mean of the pre-treatment scores and the mean of the follow-up scores (t5.696, p < 0.05). Since the mean of the pre-treatment score (20.81 ± 7.159) was higher than the mean of the follow-up score (15.04 ± 7.256), then it was evident that the rehabilitation process was effective since the stress levels decreased significantly.
The One-way ANOVA was carried out to determine if there were any differences between the mean of the three exercise groups (High, Moderate, and Low). It was found out that there was a statistically significant difference between the three groups (F (2, 44) = 11.602, p < 0.05). from the descriptive statistics, it was observed that the mean of the low exercise group (21.44 ± 6.18) was the highest, followed by the mean of the moderate group (14.58 ± 5.795) and then the mean of the high exercise group (10.19 ± 5.999). However, based on the post hoc test, it was evident that follow-up scores were statistically significant lower during the low exercises (21.44 ± 6.18, p = 0.000) and moderate exercises (14.58 ± 5.795, p = 0.009) compared to the high exercises (10.19 ± 5.999).
The two-way ANOVA was carried out to determine the effect of exercises and group therapy in the reduction of PSTD severity. Evidently, there was no significant interaction between the effects of exercises and group therapy in the efforts in the reduction of PSTD severity (F (6, 33) = 0.654, p > 0.05). Since the interaction was insignificant, we determine the significant main effects by putting the scores of the individual variables into consideration. From this, it was seen that there was no significant main effect of therapy group on PSTD scores (F (3, 33) = 0.918, P > 0.05). However, it was observed that there was a significant main effect of exercises on PSTD scores (F (2, 33) = 6.350, P < 0.05). Thus, form the estimated marginal means of follow-up (figure 2), interactions were seen at moderate exercises (prolonged exposure, supportive exposure and supportive counseling) and at the low exercise (wait list and stress inoculation).
Reference:
Heiberger, R. M., & Neuwirth, E. (2009). One-way anova. In R through excel (pp. 165-191). Springer, New York, NY.
Keppel, G., & Wickens, T. D. (2004). Simultaneous comparisons and the control of type I errors. Design and analysis: A researcher’s handbook. 4th ed. Upper Saddle River (NJ): Pearson Prentice Hall. p, 111-130.
Lu, P., Liu, J., & Koestler, D. (2017). pwr2: power and sample size analysis for one-way and two-way ANOVA models.
Norušis, M. J. (2006). SPSS 14.0 guide to data analysis. Upper Saddle River, NJ: Prentice Hall.
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