Question

The oleoresin of trees is obtained by cutting a tapping gash in the bark and removing the resin that collects there. Acid treatments can also improve collection. In this experiment, four randomly selected trees (Dipterocarpus kerrii) will be tapped seven times each (so that there will be a total of 28 observations in the resulting dataset). Each of the tappings will be randomly assigned to be treated with a different strength of sulfuric acid (0, 2.5, 5, 10, 15, 25, and 50% strength), and the resin collected from each tapping is the response (in grams). We would like to determine the effect of acid treatments on resin output. The data was analyzed as a Randomized Complete Block Design.

a. We know that ??? = 35407.26, ??(?????) = 28439.46, and the test statistic for testing the acid treatment effect is ? = 0.71. Give the ANOVA table.

b. Calculate and interpret the relative efficiency.

Answer 1

a)

ANOVA
	SS	df	MS	F
Treatment	8379.72	6	1396.62	0.71
Block	85318.38	3	28439.46	14.46
Residual	35407.26	18	1967.07
Total	129105.36	27

a:No. of treatments = 7

b: No.of blocks = 4

df Treatment = a-1 =6

df Block = b-1 = 3

df Residual = (a-1)(b-1) = 18

df Total = ab-1 = 27

MS Residual = SS Residual/df Residual

SS Block = df Block * MS Block

F Block = MS Block/MS Residual

MS Treatment = MS Residual * F Treatment

SS Treatment = MS Treatment * df Treatment

SS Total = SS(Treatment+Block+Residuals)

b) Relative efficiency (RE) = (((b-1)*MS Block)+(b(a-1)MS Residual))/((ab-1)*MS Residual)

= (((4-1)*85318.38)+(4*6*35407.26))/((4*7-1)*35407.26)

= 1.157