Question

In an experiment to test the effect of antibiotics, fifteen pigeons are first trained to recognize which symbol marks the correct cup containing food. The measure of their training is the percentage of pecks made to the correct cup (PCT_CCUP). The pigeons are then randomly assigned to one of three groups, and their initial value (Time 0) of PCT_CCUP is recorded. Then the pigeons are given an injection. Group 1 receives a saline injection, Group 2 receives antibiotic ‘C’, and Group 3 receives antibiotic ‘P’. PCT_CCUP is measured 24 hours later, and again 48 hours later. The experiment is designed to test whether the antibiotics cause the pigeons to forget their training, and whether the effect of the antibiotic is different at 24 and 48 hours post-injection.

a. Identify the experimental design.

b. The table below shows the relevant sums of squares. Fill in the degrees of freedom, and explain the degrees of freedom for the error term

Source DF Type III SS

time __ 1195.600000

inject __ 149.733333

time*inject __ 134.666667

pigeon(inject) __ 2970.800000

Experimental error __ 92.400000

Answer 1

(a): The experimental design is Two Way ANOVA how to know becuase there two categorical variable(time and inject) and one continous variable( Percentage of Pecks).

(b):  

The are 2 levels in time that is 24 and 48 hours.

There 3 levels in inject that is saline injection, antibiotic C, and antibiotic P.

a is number of levels in time and b is number of level in inject.

n is total observation.

a=2, b=3 and n=15

Source	DF
time	(a-1) = 2-1=1
inject	(b-1)=3-1 = 2
time*inject	(a-1)(b-1) = (2-1)(3-1) = 1*2 = 2
Error	(n-ab) = 15-2*3 = 15-6 = 9

The error is 9 and an important part of the model it value which used to see how much variation in population means.