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Sheet1

WEEK 7 EXCEL ASSIGNMENT 2, CHAPTER 8 ANALYSIS OF VARIANCE-EXERCISE 7
A large health maintenance organization is interested in the prescribing patterns of physicians.
Suppose that we selected a random sample of three patients for four diagnoses by three
physicians. If a = 0.05, determine whether differences among the treatment, block and
interactive effects are significant..
Anova: Two-Factor With Replication
Physician Analysis of Variance with Replication or Interaction Summary
Diagnosis A B C Physician
1 11,7,9 8,6,7, 5,4,7 Diagnosis A B C 1 A B C Total
2 14,10,11 10,9,8 6,8,7 11 8 5 Count 3 3 3 9 The data is reported in five main sections. The first four of these respond to the
3 4,5,3 5,5,6 3,4,2 1 7 6 4 Sum 27 21 16 64 mean of each sample, grouped by diagnosis and physician, and to the mean of each
4 10,9,7 6,7,4 5,6,3 9 7 7 Average (Mean) 9 7 5.33 7.11 block or prescribed treatment. For example, the mean of each sample and row
14 10 6 Variance 4 1 2.33 4.36 appears in boldface. In the first section, the mean of the samples selected for diagnosis
2 10 9 8 1 and physicians A,B, and C were 9, 7, and 5.33 respectively. The mean difference
11 8 7 among prescribed treatment with diagnosis 1 was 7.11. The fifth section of the
4 5 3 2 3 3 3 9 summary reports the results that are derived for each column or physician. In the
3 5 5 4 Sum 35 27 21 83 last row of the summary data, the mean difference for physicians A, B, and C were
3 6 7 Average (Mean) 11.67 9 7 9.22 8.33,6.75, and 5.42 respectively.
10 6 5 Variance 4.33 1 1 5.69
4 9 7 6
7 4 3 3
Count 3 3 3 9
Sum 12 16 14 42
Average (Mean) 4 5.33 4.67 4.67
Variance 1 0.33 4.33 1.75
4
Count 3 3 3 9
Sum 26 17 14 57
4 Average (Mean) 8.67 5.67 4.67 6.33
Variance 2.33 2.33 2.33 5.00
Total
Count 12 12 12
Sum 100 81 65
Average (Mean) 8.33 6.75 5.42
Variance 10.42 3.11 2.81
ANOVA The ANOVA table is interpreted as follows. The source of
Source of Variation SS df MS F P-value F crit variation identified as "sample" corresponds to the block effects
Sample 96.56 3 32.19 14.67 0.00001 3.01 or diagnoses, whereas the source identified as "columns" refers
Columns 51.17 2 25.58 11.66 0.00029 3.40 to the prescribed treatments by or physician effects. The row
Interaction 30.61 6 5.10 2.32 0.06529 2.51 identified as "interaction" contains results that pertain to the
Within 52.67 24 2.19 interactive effects whereas the row identified as "within" refers
to the error term. A comparison of the calculated value of F
Total 231 35 with the critical value was used to reach the following conclusion:
Testing of hypothesis on interaction between physicians and diagnoses
(H0): There is no effect of interaction between the physicians and the diagnoses of the patients.
H1: There is an effect of interaction between the physicians and the diagnoses.
F = MS (interaction)/MS (within) 2.32
Test statistic is equal to 2.32
The p value is 0.089 which is more than 0.05 significance level therefore we shall not reject the
null hypothesis. Conclusively, there is adequate evidence to support the claim that there is no
interaction effect between the diagnoses and the physicians prescribed treatments.
Testing the null hypothesis of the diagnosis effect on patients
H0: There are no diagnosis effects on patients.
H1: There are diagnosis effects on patients.
F = MS(sample)/MS (within) 14.67
Test statistic equals to 14.67
The p value of 0.016 is less than the 0.05 significance level therefore the null hypothesis is
rejected. It can be concluded that there is adequate evidence to support that there are
diagnosis effects on patients.
Testing the Physicians Effects on the Patients
H0: there is no physicians effect on patients.
H1: There is physicians effect on patients.
F = MA(Sample/MS(within) 14.67
Test statistic equals to 14.67
The p value of 0.023 is less than the significance level of 0.05 therefore, the null hypothesis is
rejected. It is concluded that there is adequate evidence to claim that the physicians have an
effect on patients.

Sheet2

WEEK 7 EXCEL ASSIGNMENT 1: REGRESSION ANALYSIS: CHAPTER 10, QUESTION 1
Use Regression and the data presented in Exercise 2 of Chapter 9 to estimate the linear relation between the number
of visits and the age of the patient. Examine the results of the analysis by:
1. Interpreting the coefficient of determination.
2. interpreting the square root of the coefficient of determination.
3. interpreting findings presented in the ANOVA table.
4. Determining wheter the intercept and slope of the sample regression line are significant.
Data from Chapter 9, exercise 2
Visits 3 5 4 2 1 3 6 7 4 5 10 1 2 3 8
Ages 28 45 50 19 16 27 54 63 32 42 68 19 23 30 61