Question

If we have learned to solve problems by one method, we often have difficulty bringing new insight to similar problems. However, electrical stimulation of the brain appears to help subjects come up with fresh insight. In a recent experiment \({ }^{17}\) conducted at the University of Sydney in Australia, 40 participants were trained to solve problems in a certain way and then asked to solve an unfamiliar problem that required fresh insight. Half of the participants were randomly assigned to receive non-invasive electrical stimulation of the brain while the other half (control group) received sham stimulation as a placebo. The participants did not know which group they were in. In the control group, \(20 \%\) of the participants successfully solved the problem while \(60 \%\) of the participants who received brain stimulation solved the problem. (a) Is this an experiment or an observational study? Explain. (b) From the description, does it appear that the study is double-blind, single-blind, or not blind? (c) What are the variables? Indicate whether each is categorical or quantitative. (d) Make a two-way table of the data. (e) What percent of the people who correctly solved the problem had the electrical stimulation? (f) Give values for \(\hat{p}_{E},\) the proportion of people in the electrical stimulation group to solve the problem, and \(\hat{p}_{S},\) the proportion of people in the sham stimulation group to solve the problem. What is the difference in proportions \(\hat{p}_{E}-\hat{p}_{S} ?\) (g) Does electrical stimulation of the brain appear to help insight?

Short answer

(a) This is an experiment because treatments were applied. (b) This is a double-blind study. (c) Variables are 'Type of Stimulation' (categorical) and 'Problem Solving Success' (categorical). (d) A two-way table can be drawn from the description. (e) 75% of the people who correctly solved the problem had electrical stimulation. (f) \(\hat{p}_{E}=0.6, \hat{p}_{S}=0.2\), and the difference is 0.4 or 40%. (g) Electrical stimulation appears to help with insight.

Step-by-step solution

Experiment or Observational Study

This scenario can be classified as an experiment because participants were randomly assigned to receive different types of brain stimulation, therefore a treatment was deliberately applied.

Blindness of the Study

It appears that the study is double-blind. This is because neither the participants (subjects) nor the experiment conductors (investigators) knew which type of electrical stimulation each participant received, whether actual or sham.

Identifying Variables

The two variables are 'Type of Stimulation' and 'Problem Solving Success'. The 'Type of Stimulation' (with two levels: electrical stimulation, sham) is the independent variable and is categorical. The 'Problem Solving Success' (with two outcomes: success, not successful) is the dependent variable and also categorical.

Generating a Two-Way Table

One way to structure this table is by placing 'Type of Stimulation' in rows and 'Problem Solving Success' in columns. The cell entries should be the number of outcomes observed for the intersecting row and column categories. For instance, for participants who received electrical stimulation and solved the problem, the number is \(60\%\) of 20, or 12 people. The table structure ensures that the sum of all entries equals the total number of participants, which is 40.

Calculate the Percentage of Successful Problem Solvers

The number of people (in both groups) who correctly solved the problem is the sum of the 'successful' cell entries from both rows, which is 12 for electrical stimulation and 4 for sham stimulation, total of 16 people. Since the question asks for the percentage who had electrical stimulation, calculate \(\frac{12}{16}*100 = 75\%\).

Calculate the Proportions and Their Difference

The proportion of people in the electrical stimulation group to solve the problem, \(\hat{p}_{E}\), is \(\frac{12}{20}=0.6\) or 60%. The proportion of people in the sham stimulation group to solve the problem, \(\hat{p}_{S}\), is \(\frac{4}{20}=0.2\) or 20%. The difference in the proportions, \(\hat{p}_{E}-\hat{p}_{S}\), is \(0.6 - 0.2 = 0.4\) or 40%.

Determine the Effect of Electrical Stimulation

Based on the calculated proportions and their difference, it appears that electrical stimulation of the brain may help with insight, since a greater proportion (60%) of participants in the electrical stimulus group successfully solved the problem compared to the sham group (20%). However, without a proper significance test, we cannot definitively state that the electrical stimulation are causative to successful problem solving.