Comparisons Between Means and Correlations

Question

Two samples of 21 men each are brought into a room and told they are to help another person in the next room learn a simple problem by giving him an electric shock as a punishment for wrong responses. The participant has a dial with 20 levels of shock that he can administer, 20 being the highest level. Another person is with the participant during the observation; he encourages one group to administer higher and higher levels of shock, whereas he does not so encourage members of the other group. The person supposedly receiving the shocks and the “persuader” are really actors, but the people administering the “shocks” do not know this. The point of the study is to test whether people are influenced by pressure from others when given the opportunity to hurt other individuals without fear of disapproval. The results are these: The average shock level administered by participants encouraged to use higher levels was 16.2 (s1 = 3.46) and that administered by the other group was 13.8 (s2 = 3.61). Test whether encouragement to shock has an effect on mean shock level administered. 

Answer 1

Note that we are asked to detect that the mean shock levels in the two groups are different and not which one is bigger. So we use a two-tailed test. Since the significance is not givven, we will use the default value of α = 0.05.

Conduct it as a two-sample t-test. Also, s₂/s₁ = 3.61/3.46 = 1.04, so we should pool and so the test will have 40 degrees of freedom.

s_p = √[((n₁ - 1)s₁² + (n₂ - 1)s₂²) / (n₁ + n₂ - 2)] = √[((21 - 1)3.46² + (21 - 1)3.61²) / (21 + 21 - 2)] = 3.5358

SE = s_p√(1/n₁ + 1/n₂) = 3.5358 / √10 = 1.11812

t = (μ1 - μ2) / SE = (16.2 - 13.8) / 1.11812 = 2.14647

p = 0.03795399

So there is evidence that encouragement affects the shock level.