Homework SourseA study was conducted to determine the effects of two factor
A study was conducted to determine the effects of two factors on the latherability of soap. The two factors were type of water (tap or distilled) and glycerol (present or absent). The outcome measured was the amount of foam produced (in milliliters). The experiment was repeated three times for each combination of the factors. The results are as follows.
No Glycerol
Glycerol
Distilled Water
165 181 168
170 197 190
Tap Water
155 142 139
139 160 160
Analyze the data using a=.05.
Mintab may be used, include output
| No Glycerol | Glycerol | |
| Distilled Water | 165 181 168 | 170 197 190 |
| Tap Water | 155 142 139 | 139 160 160 |
Solution
Ho:there is no effect of two factors i.e. water (tap or distilled) and glycerol (present or absent) on the latherability of soap. H1:there is a effect of two factors i.e. water (tap or distilled) and glycerol (present or absent) on the latherability of soap. SST: total sum of squares, SSA:sum of squares of factor water (tap or distilled) , SSB:sum of squares of factor glycerol (present or absent), SSAB:sum of squares of two factors water (tap or distilled) and glycerol (present or absent) i.e., interaction effect & SSE:sum of squares of error, then SST=326050-[(1966)2/(2*2*12)]=326050-80524.0833=245525.9167, SSA=[((1071)2+(895)2)/24]-80524.0833=81169.3334-80524.0833=645.3334. SSB=[((950)2+(1016)2)/24]-80524.0833=80614.8333-80524.0833=90.75, SSAB=[((514)2+(436)2+(557)2+(459)2)/12]-80524.0833-645.3334-90.75=8.3333, & SSE=SST-SSAB-SSA-SSB=245525.9167-8.3333-645.3334-90.75=244781.5003. The table value of F(1,40) is 4.08 & F(1,60) is 4.
The ANOVA table of two factors i.e. water (tap or distilled) and glycerol (present or absent) on the latherability of soap.
Here Fcal<Ftab at 0.05, so we accept null hypothesis.
Therefore, there is no effect of two factors i.e. water (tap or distilled) and glycerol (present or absent) on the latherability of soap.
| Source of variation | sum of squares | degrees of freedom | mean sum of squares | F test |
| Water(A) | 645.3334 | 2-1=1 | 645.3334/1=645.3334 | 645.3334/5563.2159=0.1160 |
| Glycerol(B) | 90.75 | 2-1=1 | 90.75/1=90.75 | 90.75/5563.2159=0.0163 |
| AB | 8.3333 | (2-1)(2-1)=1 | 8.3333/1=8.3333 | 8.3333/5563.2159=0.0015 |
| Error | 244781.5003 | 2*2*(12-1)=44 | 244781.5003/44=5563.2159 | |
| Total | 245525.9167 | (2*2*12)-1=47 |
