In the following situation we want to compare the mean responses in several popu

Question

In the following situation we want to compare the mean responses in several populations. A double-blind randomized experiment assigned healthy undergraduate students to drink one of four beverages after fasting overnight: water, water with 75 mg of caffeine, water with 75 g of glucose, and water with 75 mg of caffeine and 75 g of glucose. Subjects performed a number of cognitive tasks, including the California Computerized Assessment Package, a computerized reaction time program measuring sustained attention, reaction time, and visual scanning speed. Here are the resulting reaction times (SEM is the standard error of the mean). Identify the population. all students healthy undergraduates who drink one of four beverages healthy undergraduates who fast overnight all undergraduates Identify the response variable. California Computerized Assessment Package score which beverage the participant drank reaction time Give k, the n_ and N. k = n_1 = n_2 = n_3 = n_4 = N = Give the degrees of freedom of the ANOVA F teat. numerator df = denominator df =

Explanation / Answer

a. Popultion : Healthy undergradutes who fast overnight.

b. The response variable : Reaction time ; As the data is collected on reaction time measuring sustained attention and the visualised scanning speed. But the data that is provided is for reaction times ; hence the reposne varaible is reaction time.

c. k = 4 : Number of groups or number of beverages : 4 (water; water and caffeine; water and glucose; water, caffeine, and glucose

n1=16

n2=16

n3=16

n4=16

N= n1+n2+n3+n4 = 64

Degrees of freedom for total =N-1 =63

Degrees of freedom for Between groups = k-1 = 4-1=3

Degrees of freedom for error(or within) = Degrees of freedom for total - Degrees for Between groups =63-3=60

Degrees of freedom for ANOVA test

Numerator df = Degrees of freedom for Between groups =3

Denomirator df = Degrees of freedom for error(within groups) = 60

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