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# Rm 9

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### Rm 9

1. 1. Research Methodology Lecture 9 Farha Hassan
2. 2. Analysis of Variance (ANOVA) <ul><li>Used to compare the means of two or more populations </li></ul><ul><li>It was developed by R. A. Fisher </li></ul>
3. 3. One Way Anova PROBLEM 1 The following is the sales revenue of three salesmen taken on five occasions. Test at 5% level whether there is any difference between the performances of three salesmen. Observations A B C 1 5 3 10 2 6 5 13 3 8 2 7 4 1 10 13 5 5 0 17
4. 4. Reproduce the table with Column Total SS (Treatment) Observations A B C 1 5 3 10 2 6 5 13 3 8 2 7 4 1 10 13 5 5 0 17 TOTAL 25 20 60
5. 5. Reproduce the table with sum of squares SS (Total) Observations A Y a 2 B Y b 2 C Y c 2 1 5 25 3 9 10 100 2 6 36 5 25 13 169 3 8 64 2 4 7 49 4 1 1 10 100 13 169 5 5 25 0 0 17 289 TOTAL 25 151 20 138 60 776
6. 6. Find the Correction Factor Y 2 /N (A + B + C ) 2 / N SS (Total) = Y a 2 + Y b 2 + Y c 2 _ Y 2 / N SS (Treatment) = A/ CN + B/ CN + C/ CN - Y 2 / N SS (Error) = SS (Total) - SS (Treatment)
7. 7. ANOVA TABLE Sources of Variances S S D F Mean Computed F Tabulated F C-1 N-C N-1
8. 8. PROBLEM 2 A company has deputed A, B, C and D to four different training programmes. Check whether there is any significant difference between the training programmes of A, B, C, and D at 5% level of significance. Employees A B C D 1 80 70 65 90 2 90 60 50 89 3 96 55 58 85 4 85 85 55 95 5 70 90 40 80