Analysis of Variance
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 Squares df Mean Square F Sig.
Between Groups
Within Groups
Total 9.650
S
T 2
11
13 4.825
R 2.180 .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
Total 44947.000
378299.040
423246.040 3
96
99 14982.333
3940.615 3.802 .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
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 Squares df Mean Square F Sig.
Between Groups
Within Groups
Total 9.650
S
T 2
11
13 4.825
R 2.180 .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
Total 44947.000
378299.040
423246.040 3
96
99 14982.333
3940.615 3.802 .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