In an experiment on the effect of caffeine on time to complete a manual task. Pa

ID: 3206484 • Letter: I

Question

In an experiment on the effect of caffeine on time to complete a manual task. Paolo has three treatments-0 mg. 150 mg. and 300 mg of caffeine. He assigns an equal number of 13 participants to each of his 3 conditions (39 total people). He calculate his sigma X_tot^2 = 95, (sigma X_tot) = 50, and sigma((sigma S in column)^2/n in column) = 70. Complete the following source table: What should his statistical decision be? What should he conclude about the effect of caffeine on tune to complete the task? What post hoc test would you do to determine which levels are different from one another?

Explanation / Answer

Question 4

Part a

Here, we have to complete the ANOVA table by using the formulas given as below:

We have N = 13+13+13 = 39

SStotal = (X^2) – [(X)^2/N] = 95 – (502/39) = 30.89744

SSwithin = (X^2) – [(X)^2/n] = 95 – 70 = 25

SSbetween = SStotal – SSwithin = 30.89744 – 25 = 5.897436

Total degrees of freedom = N – 1 = 39 – 1 = 38

Degrees of freedom for between groups = total number of groups – 1 = 3 – 1 = 2

Degrees of freedom for within groups = total df – between df = 38 – 2 = 36

MS between = SS between / df between = 5.897436 / 2 = 2.948718

MS within = SS within / df within = 25 / 36 = 0.694444

F = MS between / MS within = 2.948718 / 0.694444 = 4.246157

Completed ANOVA table is given as below:

Source

MSS

Between groups

5.897436

2.948718

4.246154

0.0220961

Within groups

0.69444444

Total

30.89744

Part b

The P-value is given as 0.022 which is less than alpha value of 0.05, so he should reject the null hypothesis at 5% of significance.

Part c

He should conclude that there is sufficient evidence that the average effects of caffeine on time to complete the task due to three treatments are different.

Part d

We would do the Tukey’s post hoc test for multiple comparisons to determine which levels are different from one another.