% of Ash Mortar Cubes Compressive Strength after 28days (MPa) Total Mean

0 32 32.7 32.5 97.2 32.420 21.7 16.3 19.4 57.4 19.1340 10.5 12.4 12 34.9 11.6360 7.7 9.3 8.5 25.5 8.580 3.2 3.4 3.5 10.1 3.37100 0 0 0 0 0

Ʃ= 225.1 Ʃ= 75.03

Analysis Of Variance (ANOVA)

Data :

Equations :

1.) Sum of SquaresA.) SS total = (Ʃ(xi)2) + (Ʃx)2/N

= (322 + 32.72 + 32.52 + 21.72 + 16.32 + 19.42 + 10.52 + 12.42 + 122 + 7.72 + 9.32 + 8.52 + 3.22 + 3.42 + 3.52) - (225.12/15)

B.) SS treatment = ( (1/n) x ((Ʃxi)2 per percentage) )- (Ʃx)2/N= 97.22 + 57.42 + 34.92 + 25.52 + 10.12 - (225.12/15)

C.) SS error = (SS total) - (SS treatment)= 1544.57 - 1526.9

2.) Degree of FreedomD.) df total = N - 1

= 15 - 1 = 14E.) df treatment = a - 1

= 6 - 1 = 5F.) df error = N - a

= 15 - 6 = 93.) Mean Square

G.) MS treatment = SS treatment / df treatment= 1526.9/5 = 305.26

H.) MS error = SS error / df error= 18.28/9 = 2.03

4.) Observed F value, Fo:I.) Fo = MS treatment / MS error

=1544.57

=1526.9

= 18.28

= 305.26/2.03 = 150.37J.) Fcritical = 3.482 (from table)

Decision :

Fo > Fcritical, reject null hypothesis and alternative hypothesis is accepted.

Official Values of F critical for the 0.05 significance level:Dftreatment/

dferror 1 2 3 4 5 6 7 8 9 10

1 161.44600 199.49900 215.70700 224.58300 230.16000 233.98800 236.76700 238.88400 240.54300 241.88200

2 18.51280 19.00000 19.16420 19.24670 19.29630 19.32950 19.35310 19.37090 19.38470 19.39590

3 10.12800 9.55208 9.27662 9.11717 9.01343 8.94067 8.88673 8.84523 8.81232 8.78549

4 7.70865 6.94428 6.59139 6.38823 6.25607 6.16313 6.09421 6.04103 5.99880 5.96435

5 6.60788 5.78615 5.40945 5.19216 5.05034 4.95029 4.87586 4.81833 4.77246 4.73506

6 5.98737 5.14325 4.75706 4.53369 4.38737 4.28386 4.20667 4.14681 4.09901 4.05996

7 5.59146 4.73742 4.34683 4.12031 3.97152 3.86598 3.78705 3.72572 3.67667 3.63653

8 5.31764 4.45897 4.06618 3.83785 3.68750 3.58058 3.50046 3.43810 3.38812 3.34717

9 5.11736 4.25649 3.86254 3.63309 3.48166 3.37376 3.29274 3.22959 3.17890 3.13727

10 4.96459 4.10282 3.70827 3.47805 3.32584 3.21718 3.13547 3.07166 3.02038 2.97824