Two-Factor ANOVA A student was interested in whether or not drinking coffee just prior to taking an exam

Two-Factor ANOVA

A student was interested in whether or not drinking coffee just prior to taking an exam might help "boost" their productivity in some way and raise their grade. The student managed to convince their honours thesis supervisor to conduct an experiment to address this question. The honours supervisor had a gut feeling that the student should test both coffee drinkers and non-coffee drinkers.

60 students from an undergraduate calculus class volunteered to participate in the experiment. 30 of them identified themselves as "coffee drinkers" and 30 reported that they don’t normally drink any coffee. Each student was randomly assigned to one of three experimental groups: one group consumed a large Tim Horton’s coffee 30 min prior to the start of the calculus mid-term exam. A second group consumed a medium coffee and a third group consumed a cup of apple juice. The experimenter collected the grade (out of 100) for each student on the calculus midterm.

Perform a two-factor ANOVA on these data. Report the results of the tests on the main effects and the interaction effect. Include a table showing the means of each group. Also include graphical display of the data. Based on the results of the ANOVA, conduct whatever follow-up tests (if any) that would be required for you to acquire an understanding of the results of the experiment. Justify your choices of follow-up tests and also discuss your method(s) for controlling for Type-I error (if any). Finally write a short (e.g. 1 paragraph) description of the results of the experiment.

	Large coffee	Medium coffee	Juice
	77	84	73
	64	75	66
	69	79	61
	72	77	67
	76	76	68
Coffee drinkers	72	78	59
	75	83	74
	63	85	72
	65	88	62
	69	81	63
	70	80	67
	65	72	78
	53	77	76
	63	80	88
	74	65	75
Non-coffee	68	67	76
drinkers	66 58	70 81	86 79
	61	75	84
	72	72	68
	67	61	81
	59	76	75