Question

A farmer wants to determine the effect of 5 different concentrations of lime on the pH of the soil on a farm. 15 soil samples are used in the experiment, 5 from each of 3 different locations. The 5 soil samples from each location are then randomly assigned to the 5 concentrations of lime and 1 week after the lime is applied the pH of the soil is measured.

(a) What type of design was utilized?

(b) Given that SST= 1.429, SS(lime) = 1.142 and SSE = 0.117, complete the ANOVA table and perform a appropriate testing ? Use α = 0.01.

Answer 1

(a) Here we use Randomized block design (RBD). There are 5 treatments (i.e. 5 different concentrations of lime) and 3 blocks (i.e. 3 different locations).

(b)

Sources	SS	DF	MS=SS/DF	Cal. F	p-value
Treatment	1.142	5-1=4	1.142/4=0.2855	0.2855/0.014625=19.5214	P(F>19.5214|F~F4,8)=0.0003 R-code: round(1-pf(19.5214,4,8),4)
Block	1.429-1.142-0.117=0.170	3-1=2	0.170/2=0.085	0.085/0.014625=5.8120	P(F>5.8120|F~F2,8)=0.0276 R-code: round(1-pf(5.8120,2,8),4)
Error	0.117	4*2=8	0.117/8=0.014625
Total	1.429	15-1=14

Since p-value corresponding block factor>0.01, there is insignificant effect due to location at 1% level of significance. However p-value corresponding Treatment factor<0.01, so there is significant effect due to 5 different concentrations of lime at 1% level of significance.