Comparison of multiple outcome variables (MANOVA)
A researcher is interested in testing new medication designed to improve cholesterol levels. Low-density lipoproteins (LDL) are also called the “bad” cholesterol and low numbers (below 100) are considered optimal. High-density lipoprotein (HDL) is also known as “good” cholesterol and numbers above 60 are considered optimal. This paper provides an exploratory data analysis on data collected by the researcher. In addition, a MANOVA has been conducted to ascertain which version of the drugs (A, B, or C) shows the most promise.
Exploratory data analysis
The mean low-density lipoprotein (LDL) in the control group (N = 10) of treatment was 101.10 with a standard deviation of 9.49 while the mean high-density lipoprotein (HDL) for the same control group was 58.70 with a standard deviation of 6.08 (Table 1). In the 10 patients who received Drug A treatment, the mean LDL was 86.20 with a standard deviation of 6.80 while the mean HDL was 53.70 with a standard deviation of 3.47 (Table 2).
For the 10 patients who were treated with Drug B, the mean LDL was 121.40 with a standard deviation of 9.83 while the mean LDL level for patients who received the same Drug B was 68.60 with a standard deviation of 3.13 (Table 3). In the 10 patients who received Drug C for treatment of cholesterol, the mean LDL level was 83.20 with a standard deviation of 4.42 while the mean HDL level after the same treatment was 64.70, with a standard deviation of 4.03 (Table 4).
Figure 1 is a clustered bar chart indicating the mean LDL and HDL levels after treatment with the control, Drug A, Drug B, and Drug C. The highest LDL levels were recorded after treatment with Drug B (121), followed by the control treatment (101), Drug A (86) treatment while Drug C recorded the lowest LDL levels (83). For HDL levels, Drug B treatment resulted in the highest HDL levels (69), followed by Drug C (65), the control (59) while Drug A resulted to the lowest HDL levels (54). From Figure 1, Drug C appears to be the most promising in reducing levels of LDL while raising levels of HDL hence most effective in improving cholesterol levels.
MANOVA
A multivariate analysis was conducted to determine which drug (Drug A, B and C) works best in improving cholesterol levels. All the treatment groups (for Drug A, B, and C) had 10 participants each as shown in Table 5. As indicated in Table 7, equality of variance can be assumed for this model since the Box’s M value is not significant, Box’s M = 15.17, F = 1.52, df =9 and p =.136. The multivariate analysis for this model is shown in Table 8.
According to Table 8, there was a main effect for the drug used in the treatment of cholesterol levels as indicated by the entire test for group of drug (Pillai’s Trace, Wilks’ Lambda, Hotelling’s Trace and Roy’s Largest Root). The Wilks’ Lambda for instance is significant, Wilks’ Lambda =.087, F(6, 70) = 27.92, p =.001 whereas Pillai’s Trace is significant, Pillai’s Trace = 1.35, F (6, 72) = 24.78, p =.001. It, therefore, implies that the type of drug users among the three drugs that were under test had an influence in the outcome of LDL and HDL levels.
The Levene’s test is not significant, F (3, 36) = 1.69, p>.05 and F (3, 36) = 1.95, p >.05 for LDL and HDL indicating that the variances are assumed to be homogenous (Table 9).
The tests of between-subjects effects shows that the treatments had a main effect on the levels of low-density lipoproteins, F (3, 36) = 47.02, p =.001 and also on high-density lipoproteins, F (3, 36) = 23.00, p =.001. The adjusted R squared for LDL is.780 which can be converted to a percentage this becoming 78.0%. This implies that the type of drug used had a contribution of 78.0% changes in LDL levels when all other factors (other drugs other than the one at test) are held constant. On the other hand, Table 10 shows that the R squared value for HDL was.629 (62.9%) indicating that the type of drug used contributed 62.9% of the changes in HDL when all other factors (all other drugs) are held content.
Table 11 indicates parameter estimates for each drug in treating cholesterol levels. It is evident that Drug A (group 1) had a non-significant effect on the improvement of LDL , B =3.00, t =.833, p =.411 and a 95% CI range of between -4.31 and 10.37. However, Drug B (group 2) had a significant effect on LDL levels, B = 3.60, t = 10.60, p =.001 with a 95% CI ranging from 30.89 and 45.51. There was the contribution of Drug C in improving cholesterol levels. For HDL, Drug A was found to have a significant effect on HDL levels, B = -11.00, t = -5.68, p =.004 with a 95% CI of between -14.93 and -7.07. The effect of Drug B (group 2) was almost exact as indicated by B value of 3.90, t = 2.01, p =.051 with a 95% CI of -027 to 7.83. Table 11 also shows that there was a significant effect of Drug C in improving HDL levels.
On performing simple group contrasts, it was possible to contrast Drugs A and Drug B against Drug C in improving both LDL and HDL (Table 12). According to Table 12, Drug A resulted in a higher LDL compared to Drug C with a contrast estimate of 3.00 which was not significant (p =.411) at 95% CI. However, Drug A resulted in a lower HDL compared to Drug C with a contrast estimate of -11.00 and this was significant (p =.001) at 95% CI (-14.93 – -7.07).
On contrasting Drug B and Drug C on their promise in improving cholesterol levels, Drug B led to an increase of LDL compared to Drug C with a contrast estimate of 38.20 and this was significant (p =.001) at 95% CI (30.89 – 45.51). There was also an increase in HDL when comparing Drug B with Drug C in improving HDL levels. The contrast estimate, in this case, was 3.90 which is close to exact ( p =.051) with a 95% CI (-.027 – 7.83). The contrast results show that Drug B led to the highest increase in LDL while Drug A led to the highest decrease in HDL.
The univariate test shows that the effect of the type of drug was significant for both LDL and HDL levels. The contrast for LDL is significant, F = 47.02, df 3 and p =.001 which is the same case with contrast for HDL, F = 23.00, df =3 and p =.001 (Table 14). This indicates that all the drugs had an effect on the levels of both LDL and HDL.
To determine which drug worked well in the improvement of cholesterol, post-hoc tests (Tukey HSD, Games-Howell and Dunnett test) were conducted and the results were presented in Table 15. Tukey’s HSD test shows that Drug A had a significant contribution in the improvement of LDL compared to Drug B, mean difference = -35.20, p =.001, CI (-44.90 – -25.50). However, there was no significant promise in improving LDL levels when comparing Drug A with Drug C, mean difference = 3.00, p =.839, CI (-6.70 – 12.70). When comparing Drug B with Drug C, there was a significant promise in improvement of LDL with a mean difference of 38.20, p =.001, CI (28.50 – 47.90).
Drug C showed a significant improvement in LDL levels when comparing the drug with the rest of the treatments. The Games-Howell test also indicated similar results with Drug C showing significant improvement in LDL levels against all the other drugs with Drug A having a non-significant (p =.655) improvement in LDL compared to Drug C. The Dunnett test also indicates similar results with Drug A’s contribution being non-significant (p =.742)in improving LDL.
Tukey’s HSD test to identify which drug showed more promise in improving HDL showed that Drug A led to a significant improvement (p =.001) in HDL compared to Drug B and Drug C. However, Drug B had a non-significant contribution (p =.202) in improving HDL compared to Drug C. Drug B is therefore less promising in improving HDL levels whereas Drug C appears to be most promising. These findings are also in line with Games-Howell test Drug B has a non-significant (p =.112) improvement in HDL compared to Drug C (95% CI = -.69 to 8.49). Dunnett test also shows that there is a statistically significant improvement in HDL with all other drugs except with Drug B versus Drug C (p =.127, CI = -.85 – 8.65).
From the post-hoc tests, it is evident that the most promising drug in improvement of both LDL and HDL is Drug C since it is capable of reducing LDL while increasing HDL levels. It is also evident that Drug A is the worst in improving LDL whereas Drug B is the least efficient in improving HDL. It would therefore be recommendable to use Drug C in treatment of cholesterol since it is not only promising for LDL levels but also for improvement of HDL levels.
Reflection
By the beginning of this course, I was not sure of what I was expected to learn and I was filled with not only uncertainty but also fear that the course would be hard to understand. However, this has not been the case as I have not only understood many aspects of this course but I am also well positioned to utilize these skills in practical studies. One of the most important thins I have learnt in this course is the aspect of coding information into data that can then be fed into SPSS data editor for subsequent analysis. One particular aspect of coding that was most intriguing and undoubtedly important was to know the various scales of measurement including ordinal variables, nominal variables, and scale variables.
Other than coding and entering data in SPSS, I have gained a wealth of experience on how to perform exploratory data analysis and the reasons behind performing exploratory data analysis as one of the first tasks before carrying any analysis on data. From this, I have learnt to check for normality of data as well as the various descriptives performed on data to check their distribution.
Other than the overall understanding of how to perform various analyses using SPSS, I have particularly learnt how to test hypotheses using t-test as well as how to analyze relationships between various variables under study. As such, the skills of performing and interpreting correlation and regression analyses have been indispensable. It has been a good experience to have a clear understanding of the difference between a dependent variable (DV) and an independent variable (IV). Understanding these differences has given me an easy time in carrying out most analysis and more so ANOVA, ANCOVA and MANOVA.
The third most important thing I have learnt throughout this course is how to apply the various analytical skills offered by SPSS in a study. This was achieved through constant review of how the various tests would be utilized in my area of research interest. It is from this background that I believe I will competently develop a hypothesis for my dissertation and successfully test it by analyzing the collected data appropriately using SPSS. I believe this course has eased by data analysis and interpretation section of my dissertation. As a conclusion, I would suggest that this course cover other tests such as MANCOVA and Odds Ratio as well as logit and probit models.
Appendix
Table 1: Descriptive Statistics for Control Drug.
Table 2: Descriptive Statistics for Drug A.
Table 3: Descriptive Statistics for Drug B.
Table 4: Descriptive Statistics for Drug C.
Table 5: Between-Subjects Factors for MANOVA Design.
Table 6: Descriptive Statistics for LDL and HDL.
Table 7: Test of Equality of Covariance (Sphericity) Matrices.
Table 8: Multivariate Tests for MANOVA.
Table 9: Levene’s Test of Equality of Error Variances.
Table 10: Tests of Between-Subjects Effects.
Table 11: Parameter Estimates for LDL and HDL.
Table 12: Simple Contrast Results.
Table 13: Multivariate Tests Results.
Table 14: Univariate Test Results.
Table 15: Post-hoc Tests (Tukey HSD, Games-Howell and Dunnett Test).
