Expert answer:Anova Application

Solved by verified expert:ANOVA is a hypothesis testing technique used to compare the equality of means for two or more groups; for example, it can be used to test that the mean number of computer chips produced by a company on each of the day, evening, and night shifts is the same. Give an example of an application of ANOVA in an industrial, operations, or manufacturing setting that is different from the examples provided in the overview that is attached and discuss.
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Module Six introduced hypotheses and hypothesis testing on a single population mean.
Module Seven compares several population means through a statistical procedure called
analysis of variance (ANOVA). One-way ANOVA, also referred to as one-factor ANOVA or
completely randomized design, is a part of Design of Experiments, a larger subset of
statistics used extensively in the automotive, chemical, and medicinal drug industries.
How does the ANOVA test work? To determine whether the various sample means came
from a single population or populations with different means, you actually compare these
sample means through their variances. For example, a general manager of a chemical plant
may wish to determine whether a difference exists in the annual salaries of his shift
supervisors, assistant plant managers, and maintenance managers. Within-group variation
exists among salaries in each of the three groups, and between-group variation is present
across the three groups. ANOVA uses a ratio of between-group variation to within-group
variation to form an F statistic. If the F statistic results in a p value that is less than or equal
to a given significance level (typically 5%), then he may conclude that the salaries of shift
supervisors, assistant plant managers, and maintenance managers are significantly
different. If the p value exceeds the significance level, then the annual salaries of the three
groups are not significantly different.
Note that probability computation for an F statistic is based on an F distribution. There is not
a single F distribution but a family of F distributions. A particular member of the family is
determined by two parameters: the degrees of freedom in the numerator and the degrees of
freedom in the denominator.
Consider another example of ANOVA. A professor taught four small sections of Quantitative
Analysis last semester, which resulted in the following data on student scores by section:
Section 1 Section 2 Section 3 Section 4
94
75
70
68
90
68
73
70
85
77
76
72
80
83
78
65
88
80
74
68
65
65
QSO 510 Module Seven
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The professor would like to know whether there is a difference in the mean scores for
students in the four sections. Using statistical software to analyze the data with ANOVA
provides the following results:
ANOVA
Source of
Variation
Between
Groups
Within
Groups
Total
SS
df
MS
F
P value
F crit
440.4933 3
146.8311 2.530122 0.089662 3.159908
1044.598 18
58.0332
1485.091 21
Note that F = 2.53 and p = 0.089662. At a significance level of 0.05, H0 will not be rejected
and we conclude that the mean scores of students in the four sections of the course are not
significantly different.
Additional applications of ANOVA may include a researcher using ANOVA to test for a
difference in the effectiveness of three drugs in treating Alzheimer’s disease. Or, an
automotive engineer may use ANOVA to test for a difference in three fuel blends on the
performance of the company’s new engine. An operations manager may use ANOVA to test
for a difference in delivery times for the company’s products over four routes.
2
QSO 510 Module Seven
…
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