Descriptive Statistics: Manova, Reflection and Post Test

Do you need this or any other assignment done for you from scratch?
We have qualified writers to help you.
We assure you a quality paper that is 100% free from plagiarism and AI.
You can choose either format of your choice ( Apa, Mla, Havard, Chicago, or any other)

NB: We do not resell your papers. Upon ordering, we do an original paper exclusively for you.

NB: All your data is kept safe from the public.

Click Here To Order Now!

SPSS Assignment

Exploratory Data Analysis

Box plot depicting the distribution of low-density lipoprotein in various treatment groups.
Figure 1: Box plot depicting the distribution of low-density lipoprotein in various treatment groups.
Box plot depicting the distribution of high-density lipoprotein in various treatment groups.
Figure 2: Box plot depicting the distribution of high-density lipoprotein in various treatment groups.

Table 1. Descriptive Statistics of LDL and HDL of Each Group.

Groups Low-density Lipoprotein High-density Lipoprotein
Control Mean 101.10 58.70
Std. Deviation 9.848 6.075
Median 101.00 59.50
Minimum 82 49
Maximum 120 67
N 10 10
Drug A Mean 86.20 53.70
Std. Deviation 6.795 3.466
Median 88.50 52.50
Minimum 76 49
Maximum 94 61
N 10 10
Drug B Mean 121.40 68.60
Std. Deviation 9.834 3.134
Median 120.50 68.50
Minimum 107 63
Maximum 136 74
N 10 10
Drug C Mean 83.20 64.70
Std. Deviation 4.442 4.029
Median 82.50 65.50
Minimum 79 58
Maximum 94 70
N 10 10

The distributions of low-density lipoprotein (LDL) and high-density lipoprotein (HDL) shows skewness and the presence of outliers. Figure 1 shows that LDL of the control group has two extreme outliers (82 and 120) whereas that of the group treated with drug C has a less extreme outlier (94). The distribution of LDL appears to violate the assumption of the normality in group A due to negative skew and group B owing to positive skew. The box plot (Figure 2) for HDL has less extreme outliers, 63 and 74, which distort the distribution of data. The control group and the treatment group C violates the assumption of normality caused by the negative skew of the distribution of HDL. In contrast, treatment groups A and B depict the existence of a positive skew in the distribution of HDL.

According to descriptive statistics (Table 1) , when compared to the level of LDL in the control group (M = 101.10, SD = 9.848), groups treated with drug A (M = 86.20, SD = 6.795) and C (M = 83.20, SD = 4.442) had lower mean levels of LDL, whereas the group treated with drug B had a higher mean level of LDL (M = 121.40, SD = 9.834). Similarly, the mean level of HDL in the group treated with drug B (M = 68.60, SD = 3.134) was higher while those of groups treated with drug A (M = 53.70, SD = 3.466) and drug C (M = 64.70, SD = 4.029) were lower than in the control group (M = 58.70, SD = 6.075).

MANOVA

Descriptive statistics (Table 2) point out that drug A (M = 86.20, SD =6.975) and drug C (M = 97.98, SD = 4.442) decreased LDL levels as expected, but drug B (M = 12.40, SD = 9.834) increased the LDL level an unexpectedly. Comparatively, drug B (M = 68.70, SD = 3.134) and drug C (M = 64.70, SD = 4.029) increased HDL levels as predicated, but drug A decreased the HDL level unpredictably.

Table 2. Descriptive Statistics.

Groups Mean Std. Deviation N
Low-density Lipoprotein Control 101.10 9.848 10
Drug A 86.20 6.795 10
Drug B 121.40 9.834 10
Drug C 83.20 4.442 10
Total 97.98 17.165 40
High-density Lipoprotein Control 58.70 6.075 10
Drug A 53.70 3.466 10
Drug B 68.60 3.134 10
Drug C 64.70 4.029 10
Total 61.43 7.103 40

The multivariate test (Table 3) reveals that drugs have statistically significant effect on cholesterol among patients, F(6,70) = 27.921, p = 0.000; Wilk’s Λ = 0.087. Comprehensive MANOVA outputs are in the appendix section.

Table 3. Multivariate Tests.

Effect Value F Hypothesis df Error df Sig.
Wilks’ Lambda .087 27.921 6.000 70.000 .000

Table 4 indicates that drugs have statistically significant effect on both LDL (F(3,36) = 47.016, p = 0.000) and HDL (F(3,36) = 22.998, p = 0.000).

Table 4. Tests of Between-Subjects Effects.

Source Dependent Variable Type III Sum of Squares df Mean Square F Sig.
Group Low-density Lipoprotein 9154.475 3 3051.492 47.016 .000
High-density Lipoprotein 1293.075 3 431.025 22.998 .000
Error Low-density Lipoprotein 2336.500 36 64.903
High-density Lipoprotein 674.700 36 18.742
Total Low-density Lipoprotein 395455.000 40
High-density Lipoprotein 152889.000 40

Parameter estimates (Table 5) compare the levels of cholesterol to that of group C treated with the promising drug. The LDL level of the control group is statistically significantly higher than that of the group treated with drug C (b = 17.9, p = 0.000). Moreover, the HDL level of the control group is statistically significantly lower than that of the group treated with Drug C (b = -6.0, p = 0.04).

Table 5. Parameter Estimates.

Dependent Variable Parameter B Std. Error t Sig. 95% Confidence Interval
Lower Bound Upper Bound
Low-density Lipoprotein Intercept 83.200 2.548 32.658 .000 78.033 88.367
[Group=0] 17.900 3.603 4.968 .000 10.593 25.207
[Group=1] 3.000 3.603 .833 .411 -4.307 10.307
[Group=2] 38.200 3.603 10.603 .000 30.893 45.507
[Group=3] 0a . . . . .
High-density Lipoprotein Intercept 64.700 1.369 47.261 .000 61.924 67.476
[Group=0] -6.000 1.936 -3.099 .004 -9.927 -2.073
[Group=1] -11.000 1.936 -5.682 .000 -14.927 -7.073
[Group=2] 3.900 1.936 2.014 .051 -.027 7.827
[Group=3] 0a . . . . .
a. This parameter is set to zero because it is redundant.

Post Hoc Analysis

Post hoc analysis (Table 6) shows that the levels of both LDL and HDL are statistically significant between the control group and the treatment groups of drug A, drug B, and drug C (p < 0.05). Drug C, which is the most promising drug, reduced the level of LDL (M = 83.20) in a statistically significant way when compared to the control group (M = 101.10). Additionally, drug C increased the level of HDL (M = 64.70) in a statistically significant manner when compared to the control group (M = 58.70).

Table 6. Pairwise Comparisons.

Dependent Variable (I) group (J) group Mean Difference (I-J) Std. Error Sig.b 95% Confidence Interval for Difference
Lower Bound Upper Bound
Low-density Lipoprotein Control Drug A 14.900* 3.603 .000 7.593 22.207
Drug B -20.300* 3.603 .000 -27.607 -12.993
Drug C 17.900* 3.603 .000 10.593 25.207
High-density Lipoprotein Control Drug A 5.000* 1.936 .014 1.073 8.927
Drug B -9.900* 1.936 .000 -13.827 -5.973
Drug C -6.000* 1.936 .004 -9.927 -2.073

Reflection

Scales of measurement, exploratory data analysis, and inferential statistics are the three most important areas of statistics that I have learned throughout the course. A scale of measurement determines the nature of statistical analyses because ordinal and nominal scales favor non-parametric tests, whereas interval and ratio scales are robust for parametric tests (Pallant, 2016). Exploratory data analysis summarizes data by establishing the existence of specific patterns and trends.

Moreover, exploratory data analysis aids in evaluating whether the distribution of data meets or violates applicable assumptions. Inferential statistics allow the determination of the statistical significance of noticeable trends and patterns of data.

The understanding of scales of measurement would greatly help me in formulating a questionnaire and collecting relevant data tailored to specific analyses in my dissertation work. The exploratory data analysis would enable me to describe trends and patterns in my dissertation, as well as assess if they meet the assumptions of inferential tests. Eventually, inferential statistics would assist in hypothesis testing and drawing of valid conclusions from my dissertation work.

Critical analysis of the course shows that it did not cover factor analysis, which is essential to the design and development of Likert scales. Fundamentally, factors analysis creates principal components and removes redundant variables.

Reference

Pallant, J. (2016). SPSS survival manual: A step-by-step guide to data analysis using SPSS (6th ed.). Maidenhead, England: Open University Press.

Appendices

Multivariate Tests
Effect Value F Hypothesis df Error df Sig.
Intercept Pillai’s Trace .997 6049.563b 2.000 35.000 .000
Wilks’ Lambda .003 6049.563b 2.000 35.000 .000
Hotelling’s Trace 345.689 6049.563b 2.000 35.000 .000
Roy’s Largest Root 345.689 6049.563b 2.000 35.000 .000
Group Pillai’s Trace 1.347 24.749 6.000 72.000 .000
Wilks’ Lambda .087 27.921b 6.000 70.000 .000
Hotelling’s Trace 5.520 31.277 6.000 68.000 .000
Roy’s Largest Root 4.379 52.548c 3.000 36.000 .000
a. Design: Intercept + Group
b. Exact statistic
c. The statistic is an upper bound on F that yields a lower bound on the significance level.
Tests of Between-Subjects Effects
Source Dependent Variable Type III Sum of Squares df Mean Square F Sig.
Corrected Model Low-density Lipoprotein 9154.475a 3 3051.492 47.016 .000
High-density Lipoprotein 1293.075b 3 431.025 22.998 .000
Intercept Low-density Lipoprotein 383964.025 1 383964.025 5915.988 .000
High-density Lipoprotein 150921.225 1 150921.225 8052.711 .000
Group Low-density Lipoprotein 9154.475 3 3051.492 47.016 .000
High-density Lipoprotein 1293.075 3 431.025 22.998 .000
Error Low-density Lipoprotein 2336.500 36 64.903
High-density Lipoprotein 674.700 36 18.742
Total Low-density Lipoprotein 395455.000 40
High-density Lipoprotein 152889.000 40
Corrected Total Low-density Lipoprotein 11490.975 39
High-density Lipoprotein 1967.775 39
a. R Squared =.797 (Adjusted R Squared =.780)
b. R Squared =.657 (Adjusted R Squared =.629)
Pairwise Comparisons
Dependent Variable (I) group (J) group Mean Difference (I-J) Std. Error Sig.b 95% Confidence Interval for Difference
Lower Bound Upper Bound
Low-density Lipoprotein Control Drug A 14.900* 3.603 .000 7.593 22.207
Drug B -20.300* 3.603 .000 -27.607 -12.993
Drug C 17.900* 3.603 .000 10.593 25.207
Drug A Control -14.900* 3.603 .000 -22.207 -7.593
Drug B -35.200* 3.603 .000 -42.507 -27.893
Drug C 3.000 3.603 .411 -4.307 10.307
Drug B Control 20.300* 3.603 .000 12.993 27.607
Drug A 35.200* 3.603 .000 27.893 42.507
Drug C 38.200* 3.603 .000 30.893 45.507
Drug C Control -17.900* 3.603 .000 -25.207 -10.593
Drug A -3.000 3.603 .411 -10.307 4.307
Drug B -38.200* 3.603 .000 -45.507 -30.893
High-density Lipoprotein Control Drug A 5.000* 1.936 .014 1.073 8.927
Drug B -9.900* 1.936 .000 -13.827 -5.973
Drug C -6.000* 1.936 .004 -9.927 -2.073
Drug A Control -5.000* 1.936 .014 -8.927 -1.073
Drug B -14.900* 1.936 .000 -18.827 -10.973
Drug C -11.000* 1.936 .000 -14.927 -7.073
Drug B Control 9.900* 1.936 .000 5.973 13.827
Drug A 14.900* 1.936 .000 10.973 18.827
Drug C 3.900 1.936 .051 -.027 7.827
Drug C Control 6.000* 1.936 .004 2.073 9.927
Drug A 11.000* 1.936 .000 7.073 14.927
Drug B -3.900 1.936 .051 -7.827 .027
Based on estimated marginal means
*. The mean difference is significant at the.05 level.
b. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).
Do you need this or any other assignment done for you from scratch?
We have qualified writers to help you.
We assure you a quality paper that is 100% free from plagiarism and AI.
You can choose either format of your choice ( Apa, Mla, Havard, Chicago, or any other)

NB: We do not resell your papers. Upon ordering, we do an original paper exclusively for you.

NB: All your data is kept safe from the public.

Click Here To Order Now!