Perform MANOVA to test three different versions

In this experiment, the researcher is testing three different versions of the new medication. In data file "Activity 8.sav" you will find the following variables:
• Drug (0=control, 1=Drug A, 2=Drug B, 3=Drug C),
• LDL and HDL (cholesterol numbers of participants after 12 weeks).
Using a MANOVA, try to determine which version of the drug (A, B or C) shows the most promise. Perform the following analyses, and paste the SPSS output into your document.
1. Exploratory Data Analysis.
a. Perform exploratory data analysis on the relevant variables in the dataset. When possible, include appropriate graphs to help illustrate the dataset.
b. Give a one to two paragraph write up of the data once you have done this.
c. Create an APA style table that presents descriptive statistics for the sample.

Case Processing Summary
group Cases
Valid Missing Total
N Percent N Percent N Percent
Low-density Lipoprotein Control 10 100.0% 0 0.0% 10 100.0%
Drug A 10 100.0% 0 0.0% 10 100.0%
Drug B 10 100.0% 0 0.0% 10 100.0%
Drug C 10 100.0% 0 0.0% 10 100.0%
High-density Lipoprotein Control 10 100.0% 0 0.0% 10 100.0%
Drug A 10 100.0% 0 0.0% 10 100.0%
Drug B 10 100.0% 0 0.0% 10 100.0%
Drug C 10 100.0% 0 0.0% 10 100.0%

Descriptivesa,b,c,d,e,f
group Statistic Std. Error Bootstrapg
Bias Std. Error 95% Confidence Interval
Lower Upper
Low-density Lipoprotein Control Mean 101.10 3.114 -.01h 3.11h 94.75h 107.43h
95% Confidence Interval for Mean Lower Bound 94.05
Upper Bound 108.15
5% Trimmed Mean 101.11 -.04j 3.06j 95.00j 107.48j
Median 101.00 -.05h 2.33h 97.50h 106.50h
Variance 96.989 -10.367h 47.692h 8.266h 193.136h
Std. Deviation 9.848 -.943h 2.708h 2.875h 13.897h
Minimum 82
Maximum 120
Range 38
Interquartile Range 8 4j 7j 3j 27j
Skewness .015 .687 .025h 1.063h -2.152h 2.162h
Kurtosis 1.917 1.334 -.570j 2.142j -2.160j 6.347j
Drug A Mean 86.20 2.149 .13i 2.13i 82.14i 90.27i
95% Confidence Interval for Mean Lower Bound 81.34
Upper Bound 91.06
5% Trimmed Mean 86.33 .11k 2.26k 81.94k 90.50k
Median 88.50 -1.04i 3.88i 79.00i 92.00i
Variance 46.178 -4.908i 11.992i 13.694i 62.800i
Std. Deviation 6.795 -.460i 1.067i 3.701i 7.925i
Minimum 76
Maximum 94
Range 18
Interquartile Range 14 -2k 3k 4k 16k
Skewness -.415 .687 -.062i .727i -2.062i .903i
Kurtosis -1.687 1.334 .802k 1.749k -2.523k 4.754k
Drug B Mean 121.40 3.110 .09h 3.10h 115.50h 127.88h
95% Confidence Interval for Mean Lower Bound 114.37
Upper Bound 128.43
5% Trimmed Mean 121.39 .12h 3.28h 115.11h 128.06h
Median 120.50 1.11h 4.59h 113.00h 130.00h
Variance 96.711 -9.531h 29.509h 28.783h 144.957h
Std. Deviation 9.834 -.648h 1.673h 5.365h 12.040h
Minimum 107
Maximum 136
Range 29
Interquartile Range 19 -2h 5h 6h 26h
Skewness -.057 .687 -.002h .584h -1.231h 1.144h
Kurtosis -1.162 1.334 .410h 1.221h -2.324h 2.441h
Drug C Mean 83.20 1.405 -.01 1.37 80.83 86.17
95% Confidence Interval for Mean Lower Bound 80.02
Upper Bound 86.38
5% Trimmed Mean 82.83 .14k 1.34k 80.78k 86.09k
Median 82.50 -.08 1.36 80.00 84.00
Variance 19.733 -1.882 11.421 2.696 42.565
Std. Deviation 4.442 -.468 1.434 1.642 6.524
Minimum 79
Maximum 94
Range 15
Interquartile Range 5 1k 3k 2k 14k
Skewness 1.726 .687 -.701i .867i -.762i 2.361i
Kurtosis 3.743 1.334 -2.444k 2.644k -2.357k 6.552k
High-density Lipoprotein Control Mean 58.70 1.921 .00h 1.92h 54.83h 62.42h
95% Confidence Interval for Mean Lower Bound 54.35
Upper Bound 63.05
5% Trimmed Mean 58.78 -.03j 2.01j 54.70j 62.50j
Median 59.50 -.18h 2.54h 53.00h 64.00h
Variance 36.900 -3.941h 11.891h 8.984h 57.704h
Std. Deviation 6.075 -.441h 1.107h 2.997h 7.596h
Minimum 49
Maximum 67
Range 18
Interquartile Range 11 -1j 3j 3j 16j
Skewness -.322 .687 .032h .612h -1.616h 1.122h
Kurtosis -.933 1.334 .416j 1.436j -2.306j 3.531j
Drug A Mean 53.70 1.096 -.03i 1.09i 51.67i 55.90i
95% Confidence Interval for Mean Lower Bound 51.22
Upper Bound 56.18
5% Trimmed Mean 53.56 .02k 1.10k 51.61k 55.91k
Median 52.50 .42i 1.19i 51.50i 56.00i
Variance 12.011 -1.336i 5.242i 2.125i 20.900i
Std. Deviation 3.466 -.311i .852i 1.458i 4.572i
Minimum 49
Maximum 61
Range 12
Interquartile Range 5 0k 2k 1k 9k
Skewness .996 .687 -.250i .681i -.596i 2.125i
Kurtosis 1.036 1.334 -.590k 1.925k -2.091k 5.300k
Drug B Mean 68.60 .991 -.01h .96h 66.67h 70.57h
95% Confidence Interval for Mean Lower Bound 66.36
Upper Bound 70.84
5% Trimmed Mean 68.61 -.02h .98h 66.62h 70.68h
Median 68.50 .05h .92h 66.50h 70.50h
Variance 9.822 -1.075h 4.200h 1.861h 18.093h
Std. Deviation 3.134 -.268h .730h 1.364h 4.254h
Minimum 63
Maximum 74
Range 11
Interquartile Range 3 1h 2h 1h 9h
Skewness -.105 .687 .077h .816h -1.816h 1.984h
Kurtosis .501 1.334 .021h 1.824h -1.988h 5.085h
Drug C Mean 64.70 1.274 .05 1.25 62.11 67.14
95% Confidence Interval for Mean Lower Bound 61.82
Upper Bound 67.58
5% Trimmed Mean 64.78 .04k 1.32k 61.90k 67.22k
Median 65.50 -.25 1.64 61.50 68.50
Variance 16.233 -1.744 5.616 3.620 26.407
Std. Deviation 4.029 -.302 .775 1.903 5.139
Minimum 58
Maximum 70
Range 12
Interquartile Range 7 -1k 2k 2k 11k
Skewness -.504 .687 .054i .608i -1.659i .796i
Kurtosis -.712 1.334 .366k 1.484k -2.381k 3.610k
a. Low-density Lipoprotein is constant when group = Drug A in one or more split files. It has been omitted.
b. High-density Lipoprotein is constant when group = Drug A in one or more split files. It has been omitted.
c. Low-density Lipoprotein is constant when group = Control in one or more split files. It has been omitted.
d. High-density Lipoprotein is constant when group = Control in one or more split files. It has been omitted.
e. Low-density Lipoprotein is constant when group = Drug B in one or more split files. It has been omitted.
f. High-density Lipoprotein is constant when group = Drug B in one or more split files. It has been omitted.
g. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples
h. Based on 998 samples
i. Based on 999 samples
j. Based on 993 samples
k. Based on 995 samples

Tests of Normalityc,d,e,f,g,h
group Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
Low-density Lipoprotein Control .224 10 .170 .939 10 .540
Drug A .204 10 .200* .886 10 .154
Drug B .116 10 .200* .958 10 .758
Drug C .229 10 .148 .835 10 .038
High-density Lipoprotein Control .154 10 .200* .946 10 .618
Drug A .188 10 .200* .925 10 .404
Drug B .224 10 .168 .959 10 .769
Drug C .131 10 .200* .944 10 .602
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
c. Low-density Lipoprotein is constant when group = Drug A in one or more split files. It has been omitted.
d. High-density Lipoprotein is constant when group = Drug A in one or more split files. It has been omitted.
e. Low-density Lipoprotein is constant when group = Control in one or more split files. It has been omitted.
f. High-density Lipoprotein is constant when group = Control in one or more split files. It has been omitted.
g. Low-density Lipoprotein is constant when group = Drug B in one or more split files. It has been omitted.
h. High-density Lipoprotein is constant when group = Drug B in one or more split files. It has been omitted.

2. Perform a MANOVA. Using the "Activity 8.sav" data set perform a MANOVA. "Group" is your fixed factor, and LDL and HDL are your dependent variables. Be sure to include simple contrasts to distinguish between the drugs (group variable). In the same analysis, include descriptive statistics, and parameter estimates. Finally, be certain to inform SPSS that you want post-hoc test to help you determine which drug works best.
d. Is there any statistically significant difference in how the drugs perform? If so, explain the effect. Use the post hoc tests as needed.
e. Write up the results using APA style and interpret them
Bootstrap Specifications
Sampling Method Simple
Number of Samples 1000
Confidence Interval Level 95.0%
Confidence Interval Type Percentile

General Linear Model
Warnings
Post hoc tests are not performed for group in split file $bootstrap_split=21 because at least one group has fewer than two cases.
Post hoc tests are not performed for group in split file $bootstrap_split=353 because at least one group has fewer than two cases.

Between-Subjects Factors
Value Label N
group 0 Control 10
1 Drug A 10
2 Drug B 10
3 Drug C 10

Descriptive Statistics
group 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

Box's Test of Equality of Covariance Matricesa
Box's M 15.168
F 1.515
df1 9
df2 14851.910
Sig. .136
Tests the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups.
a. Design: Intercept + Group

Multivariate Testsa
Effect Value F Hypothesis df Error df Sig. Partial Eta Squared Noncent. Parameter Observed Powerd
Intercept Pillai's Trace .997 6049.563b 2.000 35.000 .000 .997 12099.125 1.000
Wilks' Lambda .003 6049.563b 2.000 35.000 .000 .997 12099.125 1.000
Hotelling's Trace 345.689 6049.563b 2.000 35.000 .000 .997 12099.125 1.000
Roy's Largest Root 345.689 6049.563b 2.000 35.000 .000 .997 12099.125 1.000
Group Pillai's Trace 1.347 24.749 6.000 72.000 .000 .673 148.493 1.000
Wilks' Lambda .087 27.921b 6.000 70.000 .000 .705 167.526 1.000
Hotelling's Trace 5.520 31.277 6.000 68.000 .000 .734 187.665 1.000
Roy's Largest Root 4.379 52.548c 3.000 36.000 .000 .814 157.645 1.000
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.
d. Computed using alpha = .05

Levene's Test of Equality of Error Variancesa
F df1 df2 Sig.
Low-density Lipoprotein 1.691 3 36 .186
High-density Lipoprotein 1.954 3 36 .138
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a. Design: Intercept + Group

Parameter Estimates
Dependent Variable Parameter B Std. Error t Sig. 95% Confidence Interval Partial Eta Squared Noncent. Parameter Observed Powerb
Lower Bound Upper Bound
Low-density Lipoprotein Intercept 83.200 2.548 32.658 .000 78.033 88.367 .967 32.658 1.000
[Group=0] 17.900 3.603 4.968 .000 10.593 25.207 .407 4.968 .998
[Group=1] 3.000 3.603 .833 .411 -4.307 10.307 .019 .833 .128
[Group=2] 38.200 3.603 10.603 .000 30.893 45.507 .757 10.603 1.000
[Group=3] 0a . . . . . . . .
High-density Lipoprotein Intercept 64.700 1.369 47.261 .000 61.924 67.476 .984 47.261 1.000
[Group=0] -6.000 1.936 -3.099 .004 -9.927 -2.073 .211 3.099 .854
[Group=1] -11.000 1.936 -5.682 .000 -14.927 -7.073 .473 5.682 1.000
[Group=2] 3.900 1.936 2.014 .051 -.027 7.827 .101 2.014 .500
[Group=3] 0a . . . . . . . .
a. This parameter is set to zero because it is redundant.
b. Computed using alpha = .05

Tests of Between-Subjects Effects
Source Dependent Variable Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared Noncent. Parameter Observed Powerc
Corrected Model Low-density Lipoprotein 9154.475a 3 3051.492 47.016 .000 .797 141.049 1.000
High-density Lipoprotein 1293.075b 3 431.025 22.998 .000 .657 68.995 1.000
Intercept Low-density Lipoprotein 383964.025 1 383964.025 5915.988 .000 .994 5915.988 1.000
High-density Lipoprotein 150921.225 1 150921.225 8052.711 .000 .996 8052.711 1.000
Group Low-density Lipoprotein 9154.475 3 3051.492 47.016 .000 .797 141.049 1.000
High-density Lipoprotein 1293.075 3 431.025 22.998 .000 .657 68.995 1.000
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)
c. Computed using alpha = .05

Bootstrap for Parameter Estimates
Dependent Variable Parameter B Bootstrapa
Bias Std. Error Sig. (2-tailed) 95% Confidence Interval
Lower Upper
Low-density Lipoprotein Intercept 83.200 .140 1.415 .001 80.903 86.399
[Group=0] 17.900 -.212 3.465 .001 10.775 24.395
[Group=1] 3.000 -.187 2.467 .240 -2.249 7.208
[Group=2] 38.200 -.324 3.505 .001 30.865 44.649
[Group=3] 0 0 0 0 0
High-density Lipoprotein Intercept 64.700 -.122 1.281 .001 62.000 67.000
[Group=0] -6.000 .132 2.294 .017 -10.312 -1.286
[Group=1] -11.000 .122 1.686 .001 -14.100 -7.548
[Group=2] 3.900 .212 1.642 .024 .900 7.356
[Group=3] 0 0 0 0 0
a. Unless otherwise noted, bootstrap results are based on 1000 bootstrap samples

Estimated Marginal Means
group
Dependent Variable group Mean Std. Error 95% Confidence Interval
Lower Bound Upper Bound
Low-density Lipoprotein Control 101.100 2.548 95.933 106.267
Drug A 86.200 2.548 81.033 91.367
Drug B 121.400 2.548 116.233 126.567
Drug C 83.200 2.548 78.033 88.367
High-density Lipoprotein Control 58.700 1.369 55.924 61.476
Drug A 53.700 1.369 50.924 56.476
Drug B 68.600 1.369 65.824 71.376
Drug C 64.700 1.369 61.924 67.476

Post Hoc Tests

group
Multiple Comparisons
LSD
Dependent Variable (I) group (J) group Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
Low-density Lipoprotein Control Drug A 14.90* 3.603 .000 7.59 22.21
Drug B -20.30* 3.603 .000 -27.61 -12.99
Drug C 17.90* 3.603 .000 10.59 25.21
Drug A Control -14.90* 3.603 .000 -22.21 -7.59
Drug B -35.20* 3.603 .000 -42.51 -27.89
Drug C 3.00 3.603 .411 -4.31 10.31
Drug B Control 20.30* 3.603 .000 12.99 27.61
Drug A 35.20* 3.603 .000 27.89 42.51
Drug C 38.20* 3.603 .000 30.89 45.51
Drug C Control -17.90* 3.603 .000 -25.21 -10.59
Drug A -3.00 3.603 .411 -10.31 4.31
Drug B -38.20* 3.603 .000 -45.51 -30.89
High-density Lipoprotein Control Drug A 5.00* 1.936 .014 1.07 8.93
Drug B -9.90* 1.936 .000 -13.83 -5.97
Drug C -6.00* 1.936 .004 -9.93 -2.07
Drug A Control -5.00* 1.936 .014 -8.93 -1.07
Drug B -14.90* 1.936 .000 -18.83 -10.97
Drug C -11.00* 1.936 .000 -14.93 -7.07
Drug B Control 9.90* 1.936 .000 5.97 13.83
Drug A 14.90* 1.936 .000 10.97 18.83
Drug C 3.90 1.936 .051 -.03 7.83
Drug C Control 6.00* 1.936 .004 2.07 9.93
Drug A 11.00* 1.936 .000 7.07 14.93
Drug B -3.90 1.936 .051 -7.83 .03
Based on observed means.
The error term is Mean Square(Error) = 17.859.
*. The mean difference is significant at the .05 level.

3. Reflect on your experience throughout the course. In your document, include a brief assessment of what you have learned. In 2-3 paragraphs, cover the following:
a. What were the three most important things you learned?
b. How will the material in this course help you in your dissertation work?
c. What would you like to have seen covered that wasn't?