# STATS Chapter 12 Assignment 2015

August 30, 2017

Question
Chapter 12 Assignment Name

Description of the Data: The data set contains part of the data for a study of oral condition of cancer patients conducted at the Mid-Michigan Medical Center. The oral conditions of the patients were measured and recorded at the initial stage, at the end of the second week, at the end of the fourth week, and at the end of the sixth week. The variables age, initial weight and initial cancer stage of the patients were recorded. Patients were divided into two groups at random: one group received a placebo and the other group received aloe juice treatment.
Sample size:, n = 25 patients with neck cancer. The treatment is Aloe Juice. (See the Excel File “Chapter 12 Dataset” to complete the questions below.)

Variable Names:

ID- Patient ID

TRT- treatment group: 0 = placebo; 1 = aloe juice

AGE- patient’s age in years

WEIGHTIN- patient’s weight at the initial stage

STAGE- initial cancer stage, coded 1 through 4

TOTALCIN- oral condition at the initial stage

TOTALCW2- oral condition at the end of week 2

TOTALCW4- oral condition at the end of week 4

TOTALCW6- oral condition at the end of week 6

Research Question: Does using aloe juice affect the oral condition of patients with neck cancer after controlling for weight, age, and cancer stage? Is there a change in oral condition from week 1 to week 2 to week 4 to week 6?

1. What type of test will we perform?

2. What are the independent variables, dependent variables, and covariates?

Independent variable:

Dependent variables:

Covariates:

3. List the assumptions for this type of test.

4. Are the dependent variables a continuous measurement?

5. Is the independent variable categorical? What are the categories?

6. Identify the null and alternative hypothesis.

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Now, let’s perform our analysis.

Refer to the output below to answer the questions.

Multivariate Testsb

Effect

Value

F

Hypothesis df

Error df

Sig.

week

Pillai’s Trace

.018

.097a

3.000

16.000

.960

Wilks’ Lambda

.982

.097a

3.000

16.000

.960

Hotelling’s Trace

.018

.097a

3.000

16.000

.960

Roy’s Largest Root

.018

.097a

3.000

16.000

.960

week * AGE

Pillai’s Trace

.065

.374a

3.000

16.000

.773

Wilks’ Lambda

.935

.374a

3.000

16.000

.773

Hotelling’s Trace

.070

.374a

3.000

16.000

.773

Roy’s Largest Root

.070

.374a

3.000

16.000

.773

week * WEIGHIN

Pillai’s Trace

.038

.209a

3.000

16.000

.888

Wilks’ Lambda

.962

.209a

3.000

16.000

.888

Hotelling’s Trace

.039

.209a

3.000

16.000

.888

Roy’s Largest Root

.039

.209a

3.000

16.000

.888

week * STAGE

Pillai’s Trace

.167

1.066a

3.000

16.000

.391

Wilks’ Lambda

.833

1.066a

3.000

16.000

.391

Hotelling’s Trace

.200

1.066a

3.000

16.000

.391

Roy’s Largest Root

.200

1.066a

3.000

16.000

.391

week * TRT

Pillai’s Trace

.018

.099a

3.000

16.000

.960

Wilks’ Lambda

.982

.099a

3.000

16.000

.960

Hotelling’s Trace

.018

.099a

3.000

16.000

.960

Roy’s Largest Root

.018

.099a

3.000

16.000

.960

a. Exact statistic

b. Design: Intercept + AGE + WEIGHIN + STAGE + TRT

Within Subjects Design: week

Mauchly’s Test of Sphericityb

Measure:MEASURE_1

Within Subjects Effect

Mauchly’s W

Approx. Chi-Square

df

Sig.

Epsilona

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

dimension1

week

.672

6.657

5

.248

.789

1.000

.333

Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.

a. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.

b. Design: Intercept + AGE + WEIGHIN + STAGE + TRT

Within Subjects Design: week

Tests of Within-Subjects Effects

Measure:MEASURE_1

Source

Type III Sum of Squares

df

Mean Square

F

Sig.

week

Sphericity Assumed

2.109

3

.703

.134

.939

Greenhouse-Geisser

2.109

2.368

.890

.134

.905

Huynh-Feldt

2.109

3.000

.703

.134

.939

Lower-bound

2.109

1.000

2.109

.134

.718

week * AGE

Sphericity Assumed

5.577

3

1.859

.355

.786

Greenhouse-Geisser

5.577

2.368

2.354

.355

.738

Huynh-Feldt

5.577

3.000

1.859

.355

.786

Lower-bound

5.577

1.000

5.577

.355

.559

week * WEIGHIN

Sphericity Assumed

5.138

3

1.713

.327

.806

Greenhouse-Geisser

5.138

2.368

2.169

.327

.758

Huynh-Feldt

5.138

3.000

1.713

.327

.806

Lower-bound

5.138

1.000

5.138

.327

.574

week * STAGE

Sphericity Assumed

25.527

3

8.509

1.626

.194

Greenhouse-Geisser

25.527

2.368

10.778

1.626

.205

Huynh-Feldt

25.527

3.000

8.509

1.626

.194

Lower-bound

25.527

1.000

25.527

1.626

.218

week * TRT

Sphericity Assumed

2.756

3

.919

.176

.912

Greenhouse-Geisser

2.756

2.368

1.164

.176

.873

Huynh-Feldt

2.756

3.000

.919

.176

.912

Lower-bound

2.756

1.000

2.756

.176

.680

Error(week)

Sphericity Assumed

282.539

54

5.232

Greenhouse-Geisser

282.539

42.632

6.627

Huynh-Feldt

282.539

54.000

5.232

Lower-bound

282.539

18.000

15.697

7. According to the output, does our dataset satisfy the requirement of sphericity?

8. Identify the appropriate test statistic and p-value for testing the claim that aloe juice is an effective treatment for improving oral condition in neck cancer patients.

Test statistic:

p-value:

9. If appropriate, use post hoc tests to determine if there is a change in oral condition from week 1 to week 2 to week 4 to week 6. If not, explain why. State your conclusion and reasons for your decision.

10. Use APA style reporting to write up your results of this analysis.

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