Question

The famous Hungarian mathematician Alfréd Rényi once declared: “A mathematician is a device for turning coffee into theorems.” A researcher wants to test whether drinking coffee affects scores graduate students achieve in a test of mathematical ability performed an hour later. Thirty volunteers are available for the study.

a) What are the explanatory and response variables in this study?

b) Design a completely randomised experiment for this study, in which each volunteer completes the test ONCE ONLY. Comment on elements of control, randomisation and replication in your design. Your answer should include a schematic diagram or flow chart.

c) Say what comparisons you would make at the end of the experiment.

Answer 1

(a)

In this case the explanatory variable, also called as the control variable, is whether the participant has drunk coffee before the exam or not.

The reponse variable is the score achieved by the participant in the mathematics test.

(b)

In order for the experiment to be completely randomised, we do the following procedure.

The thirty volunteers are randomly divided into two groups of 15 each.

One of the group is made to drink coffee, one hour prior to the exam.

The other group does not get any coffee to drink before the exam.

In this experimental design, the allotment of the candidates to the two groups is completely random, and the element of control - coffee, is given to one group and not to the other.

(c)

At the end of the experiment, the data for the test scores of both the groups is collected and analyzed statistically.

A one tailed t-test is performed, to test the hypothesis that the mean score of candidates who drank coffee is higher than the mean score of the those who didn't drink coffee.

Choosing a significance level of 0.05, we compute the test statistic and a corresponding p-value.

If p < 0.05, we reject the null hypothesis in favor of the alternate, otherwise we retain the null hypothesis.