Question

A researcher investigated the effect of caffeine on performance on a test of attention. Twenty people were given regular black coffee, twenty people were given espresso, twenty people were given soda, and twenty people were given an energy drink. Afterwards, they were all given tests of attention. What is the 〖df〗within? What is the 〖df〗between? What is the critical value of F for the 0.05 significance level (using Figure 12.6. F-table for use with ANOVA)?

〖df〗within = number of participants in the study (known as Ntotal) minus the number of groups (known as k) = 76

〖df〗_between = number of groups, or levels of the independent variable (known as k) – 1 = 3

The critical value of F for the 0.05 significance level is 2.73.

Answer 1

Solution:

We are given that: A researcher investigated the effect of caffeine on performance on a test of attention.

Twenty people were given regular black coffee,

Twenty people were given espresso,

Twenty people were given soda, and

Twenty people were given an energy drink.

That is there are 4 groups or we can say there are 4 treatments.

thus k = number of treatments = 4

Each group has 20 people, so total people in the study = 20 X 4 = 80 people.

That is: N = 80

We have to find df within and df between .

df within = N - k

df within = 80 - 4

df within = 76

and

df between = k - 1

df between = 4 - 1

df between = 3

Significance level =

We have to look in F table for df numerator = 3 and df denominator = 76 at 0.05 significance level.

We can see , F critical value for df numerator = 3 and df denominator = 76 at 0.05 significance level is

F critical value = 2.73