Use One-Way ANOVA to analyze the data set, data, given for this homework. Use 5%
ID: 3073343 • Letter: U
Question
Use One-Way ANOVA to analyze the data set, data, given for this homework.
Use 5% level of significance.
1) Do the Levene test in order to compare the variance of the sales level at four different in-store locations.
2) If there are no significant differences between the variance of sales, then conduct the one-way ANOVA hypothesis test to compare the average sales level at four different in-store locations.
3) If you have seen evidence of difference among the average sales levels at these four different in-store locations, then identify which in-store locations have significantly different average sales than other in-store locations, by using the Tukey procedure.
In-aisle Front Kiosk Expert 32.22 31.47 30.1932.13 31.86 32.29 32 30.33 30.9130.29 30.25 30.25 30.55 30 30.06 30.78 29.96 30.79 30.95 31.13 31 30.5 30 29.96 27.74Explanation / Answer
1.
Test for Equal Variances: C1 versus C2
95% Bonferroni confidence intervals for standard deviations
C2 N Lower StDev Upper
Expert 6 0.097978 0.17646 0.58637
Front 7 0.270391 0.46824 1.33961
In-aisle 5 0.545876 1.03403 4.28994
Kiosk 8 0.213675 0.35848 0.91998
Levene's Test (Any Continuous Distribution)
Test statistic = 0.68, p-value = 0.575
Since p-value=0.575>0.05, hence we conclude that there are no significant differences between the variance of sales.
2.
One-way ANOVA: C1 versus C2
Source DF SS MS F P
C2 3 21.606 7.202 23.83 0.000
Error 22 6.648 0.302
Total 25 28.254
Since p-value=0.000<0.05 hence we conclude that there is an evidence of difference among the average sales levels at these four different in-store locations.
3.
Grouping Information Using Tukey Method
C2 N Mean Grouping
Front 7 32.1386 A
Kiosk 8 30.7575 B
Expert 6 30.2783 B C
In-aisle 5 29.5820 C
Means that do not share a letter are significantly different.
Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of C2
Individual confidence level = 98.91%
C2 = Expert subtracted from:
C2 Lower Center Upper -------+---------+---------+---------+--
Front 1.0104 1.8602 2.7101 (---*----)
In-aisle -1.6213 -0.6963 0.2287 (----*---)
Kiosk -0.3458 0.4792 1.3041 (---*----)
-------+---------+---------+---------+--
-2.0 0.0 2.0 4.0
C2 = Front subtracted from:
C2 Lower Center Upper -------+---------+---------+---------+--
In-aisle -3.4510 -2.5566 -1.6621 (---*----)
Kiosk -2.1717 -1.3811 -0.5905 (---*---)
-------+---------+---------+---------+--
-2.0 0.0 2.0 4.0
C2 = In-aisle subtracted from:
C2 Lower Center Upper -------+---------+---------+---------+--
Kiosk 0.3047 1.1755 2.0463 (---*---)
-------+---------+---------+---------+--
-2.0 0.0 2.0 4.0
The pairs (Expert, Front), (In-aisle, Front), (Kiosk, Front) and (In-aisle, Kiosk) are significantly different since their confidence intervals do not contain zero.
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