BCA TU Stats - Steps to solve two way ANOVA with example
Today we will be solving the question of two way ANOVA by following the simple steps:
Steps to solve ANOVA problem with example
Lets see a question:
Following data relates to the yield rate of five different types of plots in which 3 different types of fertilizers were used. Test at 5% level of significance whether the difference in the yield is insignificant due to fertilizers or due to the type of land.
Here you can see question is asking for the difference in two things yield and fertilizer. Therefore, this is two-way classified data.Now lets start solving the question.
Create this table:
|
Land |
F1 |
F2 |
F3 |
Ti |
Squares of Ti |
|
I |
20 |
30 |
25 |
=75 |
5625 |
|
II |
18 |
25 |
28 |
=71 |
5041 |
|
III |
16 |
22 |
18 |
=56 |
3136 |
|
IV |
23 |
15 |
22 |
=60 |
3600 |
|
V |
13 |
28 |
17 |
=58 |
3364 |
|
Tj |
90 |
120 |
110 |
T= 320 |
Total =20766 |
| Squares of Tj |
8100 |
14400 |
12100 |
Total= 34600 |
|
First Step: Calculate: Ti sq. (Sum of squares of row) =
20766
Second Step: Calculate: Tj sq. (Sum of squares of col) =
34600
Third Step: Calculate T ( Grand Total of Ti or
Tj)= 320
Fourth Step: Calculate CF = / N (N= no. of rows X no. of cols) = 320/ 15= 6826.66
Fifth: Calculate Summation of squares of all the elements ( 20 sq. + 30 sq. + 25 sq. + ………..+ 17 sq.) = 7202.
Sixth: Calculate the following:
· TSS= Fifth Step Answer- CF = 7202- 6826.66 = 375.33
·
SSR=
(Summation of Ti sq./ col)- CF = 20766/3 - 6826.66 = 95.33
·
SSC
= (Summation of Tj sq. / row) - CF= 34600/5-
6826.66 = 93.33
·
SSE
= TSS-SSR-SSC= 184.67
Seventh Step: ANOVA Table
|
Source of Variance |
DF |
SS |
MS |
|
Row |
Row-1= 4 |
95.33= SSR |
M1=
95.33/4= 23.832 |
|
Col |
Col- 1= 2 |
93.33=SSC |
M2= 93.33/2= 46.665 |
|
Error |
4X2= 8 |
184.66= SSE |
M3= 184.67/8= 23.083 |
|
Total |
Total = 14 |
|
|
|
|
|
|
|
Eight:
Now Calculate two F calculated (Fc):
For Fc1, we will consider M1 and M3. Bigger is numerator and smaller
is denominator.
Fc1= M1/M3 = 1.032
For Fc2, we will consider M2 and M3. Bigger is numerator and smaller
is denominator.
Fc2= M2/ M3 = 2.021
Ninth Step:
Calculate F Tabulated from the F Table:
Since the question has given 5% we will check the alpha 0.05
table.
For Ft1, we will write F0.05(DF of M1, DF of M3)
F0.05(4,8)
Now go to the fourth row and eighth column, the intersection
value is called F Tabulated Value.
Ft1= 3.83
In the Same way for Ft2:
F0.05(2,8) = 4.45
Step ten: Conclusion
Since Fc1 is smaller than Ft1, H0 is accepted.
Since Fc2 is smaller than Ft2, H1 is accepted.
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