Oxnard Petro, Ltd., has three interdisciplinary project development teams that f
ID: 3128192 • Letter: O
Question
Oxnard Petro, Ltd., has three interdisciplinary project development teams that function on an ongoing basis. Team members rotate from time to time. Every 4 months (three times a year) each department head rates the performance of each project team (using a 0 to 100 scale, where 100 is the best rating). Are the main effects significant? Is there an interaction?
Fill in the missing data. (Round your Table of Means values to 1 decimal place, SS and F values to 2 decimal places, MS values to 3 decimal places and p-value to 4 decimal places.)
Oxnard Petro, Ltd., has three interdisciplinary project development teams that function on an ongoing basis. Team members rotate from time to time. Every 4 months (three times a year) each department head rates the performance of each project team (using a 0 to 100 scale, where 100 is the best rating). Are the main effects significant? Is there an interaction?
Explanation / Answer
Two way ANOVA
Oxnard Petro, Ltd., has three interdisciplinary project development teams that function on an ongoing basis. Team members rotate from time to time. Every 4 months (three times a year) each department head rates the performance of each project team (using a 0 to 100 scale, where 100 is the best rating). Are the main effects significant? Is there an interaction?
Solution
Here, we have to test the hypothesis whether there is significant main effects and interaction in the scores of the three interdisciplinary projects in the three years. For checking this claim, we have to use the two way analysis of variance. First of all, we need to arrange the data in a following manner.
Score
Year
Discipline
86
2007
Marketing
85
2007
Marketing
82
2007
Marketing
85
2009
Marketing
81
2009
Marketing
80
2009
Marketing
82
2011
Marketing
82
2011
Marketing
81
2011
Marketing
78
2007
Engineering
84
2007
Engineering
79
2007
Engineering
83
2009
Engineering
76
2009
Engineering
77
2009
Engineering
79
2011
Engineering
79
2011
Engineering
75
2011
Engineering
86
2007
Finance
89
2007
Finance
91
2007
Finance
91
2009
Finance
88
2009
Finance
93
2009
Finance
91
2011
Finance
99
2011
Finance
81
2011
Finance
The ANOVA test is given as below:
The mean scores for the given three years are given as below:
Year
Average score
2007
84.4
2009
83.8
2011
83.2
The mean scores for the given three interdisciplinary projects are given as below:
Discipline
Average Score
Engineering
78.9
Finance
89.9
Marketing
82.7
The ANOVA table is given as below:
Two-way ANOVA: Score versus Year, Discipline
Analysis of Variance for Score
Source DF SS MS F P
Year 2 6.7 3.4 0.22 0.802
Discipli 2 562.3 281.1 18.65 0.000
Interaction 4 23.7 5.9 0.39 0.811
Error 18 271.3 15.1
Total 26 864.1
For the variable year we get the p-value as 0.802 which is greater than the level of significance 0.05, so we do not reject the hypothesis that there is no any significant effect due to the year. For the variable discipline we get the p-value as 0.00 which is less than the level of significance 0.05, so we reject the null hypothesis that there is no any significant effect due to the discipline. For the combined interaction for the year and discipline, the p-value is given as 0.811 which is greater than the given level of significance 0.05, so we do not reject the null hypothesis that there is no any significant interaction present.
Score
Year
Discipline
86
2007
Marketing
85
2007
Marketing
82
2007
Marketing
85
2009
Marketing
81
2009
Marketing
80
2009
Marketing
82
2011
Marketing
82
2011
Marketing
81
2011
Marketing
78
2007
Engineering
84
2007
Engineering
79
2007
Engineering
83
2009
Engineering
76
2009
Engineering
77
2009
Engineering
79
2011
Engineering
79
2011
Engineering
75
2011
Engineering
86
2007
Finance
89
2007
Finance
91
2007
Finance
91
2009
Finance
88
2009
Finance
93
2009
Finance
91
2011
Finance
99
2011
Finance
81
2011
Finance
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