Descriptive Statistics: Manova, Reflection and Post Test Essay

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Updated: Feb 5th, 2024

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.

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GroupsLow-density LipoproteinHigh-density Lipoprotein
ControlMean101.1058.70
Std. Deviation9.8486.075
Median101.0059.50
Minimum8249
Maximum12067
N1010
Drug AMean86.2053.70
Std. Deviation6.7953.466
Median88.5052.50
Minimum7649
Maximum9461
N1010
Drug BMean121.4068.60
Std. Deviation9.8343.134
Median120.5068.50
Minimum10763
Maximum13674
N1010
Drug CMean83.2064.70
Std. Deviation4.4424.029
Median82.5065.50
Minimum7958
Maximum9470
N1010

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.

GroupsMeanStd. DeviationN
Low-density LipoproteinControl101.109.84810
Drug A86.206.79510
Drug B121.409.83410
Drug C83.204.44210
Total97.9817.16540
High-density LipoproteinControl58.706.07510
Drug A53.703.46610
Drug B68.603.13410
Drug C64.704.02910
Total61.437.10340

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.

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EffectValueFHypothesis dfError dfSig.
Wilks’ Lambda.08727.9216.00070.000.000

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.

SourceDependent VariableType III Sum of SquaresdfMean SquareFSig.
GroupLow-density Lipoprotein9154.47533051.49247.016.000
High-density Lipoprotein1293.0753431.02522.998.000
ErrorLow-density Lipoprotein2336.5003664.903
High-density Lipoprotein674.7003618.742
TotalLow-density Lipoprotein395455.00040
High-density Lipoprotein152889.00040

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 VariableParameterBStd. ErrortSig.95% Confidence Interval
Lower BoundUpper Bound
Low-density LipoproteinIntercept83.2002.54832.658.00078.03388.367
[Group=0]17.9003.6034.968.00010.59325.207
[Group=1]3.0003.603.833.411-4.30710.307
[Group=2]38.2003.60310.603.00030.89345.507
[Group=3]0a.....
High-density LipoproteinIntercept64.7001.36947.261.00061.92467.476
[Group=0]-6.0001.936-3.099.004-9.927-2.073
[Group=1]-11.0001.936-5.682.000-14.927-7.073
[Group=2]3.9001.9362.014.051-.0277.827
[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) groupMean Difference (I-J)Std. ErrorSig.b95% Confidence Interval for Difference
Lower BoundUpper Bound
Low-density LipoproteinControlDrug A14.900*3.603.0007.59322.207
Drug B-20.300*3.603.000-27.607-12.993
Drug C17.900*3.603.00010.59325.207
High-density LipoproteinControlDrug A5.000*1.936.0141.0738.927
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.

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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
EffectValueFHypothesis dfError dfSig.
InterceptPillai’s Trace.9976049.563b2.00035.000.000
Wilks’ Lambda.0036049.563b2.00035.000.000
Hotelling’s Trace345.6896049.563b2.00035.000.000
Roy’s Largest Root345.6896049.563b2.00035.000.000
GroupPillai’s Trace1.34724.7496.00072.000.000
Wilks’ Lambda.08727.921b6.00070.000.000
Hotelling’s Trace5.52031.2776.00068.000.000
Roy’s Largest Root4.37952.548c3.00036.000.000
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
SourceDependent VariableType III Sum of SquaresdfMean SquareFSig.
Corrected ModelLow-density Lipoprotein9154.475a33051.49247.016.000
High-density Lipoprotein1293.075b3431.02522.998.000
InterceptLow-density Lipoprotein383964.0251383964.0255915.988.000
High-density Lipoprotein150921.2251150921.2258052.711.000
GroupLow-density Lipoprotein9154.47533051.49247.016.000
High-density Lipoprotein1293.0753431.02522.998.000
ErrorLow-density Lipoprotein2336.5003664.903
High-density Lipoprotein674.7003618.742
TotalLow-density Lipoprotein395455.00040
High-density Lipoprotein152889.00040
Corrected TotalLow-density Lipoprotein11490.97539
High-density Lipoprotein1967.77539
a. R Squared =.797 (Adjusted R Squared =.780)
b. R Squared =.657 (Adjusted R Squared =.629)
Pairwise Comparisons
Dependent Variable(I) group(J) groupMean Difference (I-J)Std. ErrorSig.b95% Confidence Interval for Difference
Lower BoundUpper Bound
Low-density LipoproteinControlDrug A14.900*3.603.0007.59322.207
Drug B-20.300*3.603.000-27.607-12.993
Drug C17.900*3.603.00010.59325.207
Drug AControl-14.900*3.603.000-22.207-7.593
Drug B-35.200*3.603.000-42.507-27.893
Drug C3.0003.603.411-4.30710.307
Drug BControl20.300*3.603.00012.99327.607
Drug A35.200*3.603.00027.89342.507
Drug C38.200*3.603.00030.89345.507
Drug CControl-17.900*3.603.000-25.207-10.593
Drug A-3.0003.603.411-10.3074.307
Drug B-38.200*3.603.000-45.507-30.893
High-density LipoproteinControlDrug A5.000*1.936.0141.0738.927
Drug B-9.900*1.936.000-13.827-5.973
Drug C-6.000*1.936.004-9.927-2.073
Drug AControl-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 BControl9.900*1.936.0005.97313.827
Drug A14.900*1.936.00010.97318.827
Drug C3.9001.936.051-.0277.827
Drug CControl6.000*1.936.0042.0739.927
Drug A11.000*1.936.0007.07314.927
Drug B-3.9001.936.051-7.827.027
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).
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