ANOVA Model - R & D Expenditure per Employee
· Problem Statement
· Raw Data
· SPSS
· SPSS Output & Interpretation of Results:
o Descriptive Statistics
o ANOVA - Homogeneity of Variance Assumption Test
o ANOVA - Main Test
o ANOVA - Post-Hoc Test
Problem Statement:
Research and development is essential to maintaining a competitive edge in the marketplace for many businesses. However, the importance of innovation may be more critical in some industries than in others. One measure of a company’s commitment to R&D is dollars spend per employee. This reflects the firm’s R&D investment in relation to its size. The figures below show sample data for U.S. companies in four basic industries for the year 1978.
R&D Expenditures per Employee ($100)
Information
Aerospace Chemicals Drugs Processing
6.1 3.0 36.1 21.7
6.5 22.0 24.3 33.2
17.8 25.0 56.2 21.3
13.5 28.5 14.0 16.5
10.7 33.8 33.1
6.1
Is there a significant difference, at the 0.05 level, between the four industry samples? State the null and research hypotheses for this test.
Raw Data
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1 1 6.10
2 1 6.50
3 1 17.80
4 1 13.50
5 2 3.00
6 2 22.00
7 2 25.00
8 2 28.50
9 2 10.70
10 2 6.10
11 3 36.10
12 3 24.30
13 3 56.20
14 3 14.00
15 3 33.80
16 4 21.70
17 4 33.20
18 4 21.30
19 4 16.50
20 4 33.10
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SPSS
è SPSS - Variable View
è Analyze
è Compare Means
è One-Way ANOVA
èClick Post Hoc
è Click Options
SPSS Output
Oneway
[DataSet0] G:\My Web Sites\class\05_lssu\mgmt_375\biz_analytics\anova\r_d_per_emp\r_d_per_emp.sav
Descriptives /R&D $ per emp /
/ N / Mean / Std. Deviation / Std. Error / 95% Confidence Interval for Mean / Minimum / Maximum /
/ Lower Bound / Upper Bound /
Aerospace / 4 / 10.9750 / 5.67883 / 2.83942 / 1.9387 / 20.0113 / 6.10 / 17.80 /
Chemicals / 6 / 15.8833 / 10.66085 / 4.35227 / 4.6955 / 27.0712 / 3.00 / 28.50 /
Drugs / 5 / 32.8800 / 15.69322 / 7.01822 / 13.3943 / 52.3657 / 14.00 / 56.20 /
Info Process / 5 / 25.1600 / 7.57549 / 3.38786 / 15.7538 / 34.5662 / 16.50 / 33.20 /
Total / 20 / 21.4700 / 13.03142 / 2.91391 / 15.3711 / 27.5689 / 3.00 / 56.20
Test of Homogeneity of Variances /
R&D $ per emp /
Levene Statistic / df1 / df2 / Sig. /
1.271 / 3 / 16 / .318
Hypothesis:
H0: σ21 = σ22 = σ23 = σ24 (variances are all equal among four industries)H1: Not all variances are equal
Where σ21 = the population variance of R&D expenditures in Aerospace Industry
Interpretation of Results:
Since p-value (0.318) > 0.05, we accept H0.Chances are 19 out of 20 that data supports that all variances are assumed to be equal. So we can proceed the ANOVA model for testing the main hypothesis.
ANOVA /
R&D $ per emp /
/ Sum of Squares / df / Mean Square / F / Sig. /
Between Groups / 1346.866 / 3 / 448.955 / 3.822 / .031 /
Within Groups / 1879.676 / 16 / 117.480 /
Total / 3226.542 / 19
Main Hypothesis:
H0: µ1 = µ2 = µ3 = µ4(Each population mean average is equal among 4 industries = No significant difference)
H1: Not all means are equal (significant difference).
Where µ1 = the population mean average of R&D expenditure per employee in the aerospace industry.
Interpretation of Results:
Since p-value (0.031) < 0.05, we reject H0.Chances are 19 out 20 that evidence shows that there exist significant differences of R&D expenditures per employee among four industries. We need to investigate further to find out which industry makes significant impact, using the post-hoc analysis.
Post Hoc Tests
R&D $ per emp
Tukey HSD /
(I) industry / (J) industry / Mean Difference (I-J) / Std. Error / Sig. / 95% Confidence Interval /
Lower Bound / Upper Bound /
Aerospace / Chemicals / -4.90833 / 6.99642 / .895 / -24.9252 / 15.1086 /
Drugs / -21.90500* / 7.27089 / .037 / -42.7072 / -1.1028 /
Info Process / -14.18500 / 7.27089 / .247 / -34.9872 / 6.6172 /
Chemicals / Aerospace / 4.90833 / 6.99642 / .895 / -15.1086 / 24.9252 /
Drugs / -16.99667 / 6.56322 / .083 / -35.7742 / 1.7808 /
Info Process / -9.27667 / 6.56322 / .509 / -28.0542 / 9.5008 /
Drugs / Aerospace / 21.90500* / 7.27089 / .037 / 1.1028 / 42.7072 /
Chemicals / 16.99667 / 6.56322 / .083 / -1.7808 / 35.7742 /
Info Process / 7.72000 / 6.85506 / .679 / -11.8925 / 27.3325 /
Info Process / Aerospace / 14.18500 / 7.27089 / .247 / -6.6172 / 34.9872 /
Chemicals / 9.27667 / 6.56322 / .509 / -9.5008 / 28.0542 /
Drugs / -7.72000 / 6.85506 / .679 / -27.3325 / 11.8925 /
*. The mean difference is significant at the 0.05 level.
Interpretation:
Post-hoc analysis reveals that there exists a statistically significant difference between Drug industry and aerospace industry (p = 0.037), and substantial differences between drug and chemical industry (p = 0.083). Aerospace industry, chemical industry, and info processing industry are not making significant differences in terms of R&D expenditure per employee.