311 experiment conducted to understand the effects of percen

3.11 experiment conducted to understand the effects of percentage moisture and percentage clay on the compactability of sand, a qual ity characteristic, the following results were obtained. Calculate the effect of each factor and their interaction. Also, verify if the effects are significant. Moisture 6% 3% 1% 48, 44 56, 50 Clay 3% 42, 46 52, 49

Solution

General Linear Model: Response versus Clay Factor, Moisture Factor

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Clay Factor 1 10.125 10.1250 1.05 0.363
Moisture Factor 1 91.125 91.1250 9.47 0.037
Clay Factor*Moisture Factor 1 0.125 0.1250 0.01 0.915
Error 4 38.500 9.6250
Total 7 139.875

Since the p-value for the interaction effect between clay factor and Moisture factor is 0.915>0.05,so accept at 5% level of significance that there is no interaction present between clay factor and Moisture factor.

So,we can marginally test for the effects of clay factor and Moisture factor.

Since the p-value for the clay factor is 0.363>0.05,so accept at 5% level of significance that the clay has no significant effect on the response.

Since the p-value for the Moisture factor is 0.037<0.05,so reject H₀ at 5% level of significance and can conclude that the Moisture has significant effect on the response.