In this ppt i have solved a problem on Two Way ANOVA. Watch the video of the ppt https://www.youtube.com/watch?v=9nEt-GGV4ks&t=485s Subscribe to Vision Academy https://www.youtube.com/channel/UCjzpit_cXjdnzER_165mIiw

2. Month
Salesmen
A B C D
May 50 40 48 39
June 46 48 50 45
July 39 44 40 39

3. Month
Salesmen
A B C D
May 50 40 48 39
June 46 48 50 45
July 39 44 40 39

7. Month
Salesmen
Total
A B C D
May 50 40 48 39 177
June 46 48 50 45 189
July 39 44 40 39 162
Total 135 132 138 123 528

8. Month
Salesmen
Total A² B² C² D² Total
A B C D
May 50 40 48 39 177 2500 1600 2304 1521 7925
June 46 48 50 45 189 2116 2304 2500 2025 8945
July 39 44 40 39 162 1521 1936 1600 1521 6578
Total 135 132 138 123 528 6137 5840 6404 5067 23448
Step VI:Total Sum of Square (TSS) = RSS-CF
= 23448-23232 = 216

9. Month
Salesmen
Total A² B² C² D² Total
A B C D
May 50 40 48 39 177 2500 1600 2304 1521 7925
June 46 48 50 45 189 2116 2304 2500 2025 8945
July 39 44 40 39 162 1521 1936 1600 1521 6578
Total 135 132 138 123 528 6137 5840 6404 5067 23448

10. Month
Salesmen
Total A² B² C² D² Total
A B C D
May 50 40 48 39 177 2500 1600 2304 1521 7925
June 46 48 50 45 189 2116 2304 2500 2025 8945
July 39 44 40 39 162 1521 1936 1600 1521 6578
Total 135 132 138 123 528 6137 5840 6404 5067 23448

11. TSS = 216
SSM = 95.5
SSS = 42
= TSS-SSM-SSS
= 216 – 95.5 - 42
SSE= 78.5

12. Source of
Variation
Degrees of
Freedom (df)
Sum of
Squares (SS)
Mean Sum of
Squares (MSS)
Variance
Ratio F
Between the
months (V1)
3−1=2 SSM = 95.5 MSSM= SSM/p-1
=95.5/3-1 = 47.75
F=MSSM/MSSE
=47.75/13.083
=3.65
Between the
Salesmen
(V1)
4-1=3 SSS = 42 MSSS= SSS/q-1
=42/4-1 = 14
F=MSSS/MSSE
=14/13.083
=1.07
Error (V2) (3-1)(4-1)=6 SSE = 78.5 MSSE = SSE/(p-1)(q-1)
=78.5/6=13.083
Total 3x4-1=11 TSS = 216
TSS = 216
SSM = 95.5
SSS = 42
SSE = 78.5
Month
Salesmen
A B C D
May 50 40 48 39
June 46 48 50 45
July 39 44 40 39

13. Between the months
Calculated F = 3.65
Tabulated F at 5% level of significance with (2, 6) degree of freedom is 5.14.
Since Calculated F(CV)< F(TV), so we may accept Hₒ and conclude that sales
made during months May, June and July do not differ significantly.
Between the Salesmen
Calculated F = 1.07
Tabulated F at 5% level of significance with (3, 6) degree of freedom is 4.76.
Since Calculated F(CV)< F(TV), so we may accept Hₒ and conclude that sales
made by the A, B, C, and D salesmen do not differ significantly.

14. Prasad, J. (2017). “Unit-7 Introduction to Analysis of Variance.
IGNOU

15. Thank You