Analysis of Variance

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APPLIED STATISTICS
TUTORIAL 3: ANALYSIS OF VARIANCE (ANOVA)

1.When ¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬more than two population means are compared, one uses the analysis of variance technique.

2.The distribution used for analysis of variance is F test.

3.Analysis of variance is used to ______________________________. A. compare nominal data.
B. compare population proportion.
C. simultaneously compare several population means.

4. In ANOVA, F statistic is used to test a null hypothesis such as: A.
B.
C.
5. If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate? A. Too many degrees of freedom

B. No difference between the population means
C. A difference between at least one pair of population means 6.Experiments on accuracy of three types of measuring devices have been implemented. The results were analyzed using SPSS and generate as a following OUTPUT 1: OUTPUT 1
Sum of SquaresdfMean SquareFSig.
Between Groups
Within Groups
Total9.650
S
T2
11
134.825
R2.180.159
Based on the OUTPUT 1, determine the values R, S and T.
ANSWER:

7.Based on the OUTPUT 2, what is your conclusion on the rental rates between the four cities at ? OUTPUT 2
ANOVA

Rental per month for two-bedded apartments
Sum of Square
df
Mean Square
F
Sig.
Between Groups
Within Groups
Total44947.000
378299.040
423246.0403
96
9914982.333
3940.6153.802.013

ANSWERS:

We conclude that the rental rates is differ for different cities.

8.The research department at Evergreen Supermarket wants to know the average of customer served by cashier at counter A, B, C and D at certain hours. The manager observed each of the four counters for a number of certain hours. The following TABLE 1 gives the number of customers served by the four counters during each of the observed hours.

TABLE 1
Counter
ABCD
14
16
21
19
139
11
9
8
12
86
9
16
8
11
1319
14
16
21
15

i)List the dependent variable and independent variable.
ANSWERS:
dependent variable: the number of customer served by cashier independent variable: counter A, B, C and D

ii)Write the suitable hypothesis statement for the study
ANSWERS:
H0: A = B = C = DvsH1: NOT all means are equal

iii)At the 5% significance level, test your hypothesis. Given sum squares of error, SSE = 158.2. ANSWERS:

CV = F0.05,3,18 = 3.1599
F > CV so reject H0.
NOT all mean number of customers is equal served by the four counters during each of the observed hours.

9.This study are extended to check the pairwise comparisons between means. Based on the following OUTPUT 3, give your conclusion towards the productivity of cashier at counter A and counter B at  = 6%.

OUTPUT 3

ANSWERS:

H0: A = BvsH1: A  B
p-value = 0.006<  = 0.06
so reject H0.
At 0.06 significance level, the productivity of cashier at counter A and counter B is different. 10.A study was made to see whether the differences in the flame bulbs (in hours) with different brands. Given the different bulbs are expected to affect the flame bulbs, it was also considered in the study to reduce experimental error. The results are given in TABLE 2 below: TABLE 2

Power of bulb
(watt)Bulb BrandTotal
XYZ
50
100
15036.6
32.3
32.138.5
38.4
36.335.5
30.1
29.5110.6
100.8
97.9
Total101.0113.295.1309.3
Given
i)Identify the dependent variable, treatment factors and blocking factors for the study. ANSWER:
Dependent variable: the flame bulbs
Treatment factors: the bulb brand
Blocking factors: power of bulb

ii)Complete the following ANOVA table:
ANSWER:
SOURCEdfSum of SquaresMean of SquaresF
Bulb Brand256.806728.4033...
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