# 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?

https://brainmass.com/statistics/factor-analysis/perform-manova-test-three-different-versions-608072

#### Solution Preview

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.

I run the SPPS to get the following table of descriptive statistics:

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

I also create the following histogram for each of LDL and HDL:

b. Give a one to two paragraph write up of the data once you have done this.

From the above table of descriptive statistics, we find that drug B has the highest mean levels of cholesterol for both HDL and LDL groups.

c. Create an APA style table that ...

#### Solution Summary

The solution gives detailed steps on performing MANOVA to test three different versions of the new medication and then post hoc tests for further research. All outputs are generated from SPSS.