# 2010 05 29 134224 DQ1 and DQ2

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```					DQ #1 "When would you use ANOVA at your place of employment? Give a specific example that includes the
“treatments. Add some thought on what that application might achieve, value, etc.

The purpose of conducting ANOVA is to see if there is any difference between two or more groups on some variable.
ANOVA is a general technique that can be used to test the hypothesis that the means among two or more groups are
equal, under the assumption that the sampled populations are normally distributed.
A one-way analysis of variance requires that the independent variable specify groups or categories and the dependent
variable be interval level.
Where I work, a One-way ANOVA was carried out to see if the display aisles recorded different sales so that more
attention could be paid to those aisles registering lower sales.
Three different aisle locations (three treatments) were considered: Front, Middle, and Rear. A random sample of 18 stores
was selected, with 6 stores randomly assigned to each aisle location. At the end of a one month trial period, the sales
volumes (in thousands of dollars) of the product in each store were recorded to see if there is a significant difference in the
mean sales among the various aisle locations.
Data:
Front Aisle Location Sales: 8.6, 7.2, 5.4, 6.2, 5.0, 4.0
Middle Aisle Sales Location: 3.2, 2.4, 2.0, 1.4, 1.8, 1.6
Rear Aisle Location Sales: 4.6, 6.0, 4.0, 2.8, 2.2, 2.8
Ho: There is no significant difference in the mean sales of the three aisles
Ha: There is a significant difference in the mean sales of the three aisles
One factor ANOVA

Mean             n    Std. Dev

6.07            6      1.648    Front

2.07            6      0.653    Middle

3.73            6      1.418    Rear

3.96          18       2.089    Total

ANOVA table

Source             SS          df         MS              F   p-value

Treatment        48.444            2    24.2222          14.10    .0004

Error            25.760          15      1.7173

Total            74.204          17
The ANOVA results showed a p- value of 0.00036. Since 0.00036 < 0.05, we Ho was rejected in favor of Ha.
It was concluded that there was a significant difference in the mean sales of the three aisles.
From the pair-wise table, it was found that all p- values are < α. This means all the aisles have significantly different mean
sales.

DQ #2 When would you use ANOVA in your education, your personal life, or some issue in politics? Create an ANOVA
table that consists of 3 or 4 treatments on your issue (suggestion: create the table in Word, then copy and paste into
the DQ).

ANOVA techniques can be similarly used in the field of education to see if the mean scores of three sections of doctoral
level students taught by three different professors are significantly different. A typical ANOVA table for this research
question would look like:
Students        Professor A          Professor B           Professor C
1                9                     8.5                8.6
2                7                     8                  8.6
3                7.5                   9                  8
4                7                     7                  7.8
5                7.7                   7.3                7.5

The ANOVA output for the above problem would be as shown below:
One factor ANOVA

Mean           n    Std. Dev
7.64         5      0.820     Professor A
7.96         5      0.826     Professor B
8.10         5      0.490     Professor C
7.90       15       0.704     Total

ANOVA table
Source          SS         df       MS                    F         p-value
Treatment       0.556          2     0.2780             0.52             .6059
Error           6.384        12      0.5320
Total           6.940        14

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