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...