Question

A study compared the effectiveness of several antidepressants by examining the experiments in which they had passed the FDA requirements. Each of those experiments compared the active drug with a placebo, an inert pill given to some of the subjects. In each experiment, some patients treated with the placebo had improved, a phenomenon called the placebo effect. Patients' depression levels were evaluated on the Hamilton Depression Rating Scale, where larger numbers indicate greater improvement. (The Hamilton scale is a widely accepted standard that was used in each of the independently run studies.) The following scatterplot compares mean improvement levels for the antidepressants and placebos for several experiments. Is it appropriate to calculate the correlation? Explain

Answer 1

Yes, it is appropriate to calculate the correlation between the mean improvement levels for the antidepressants and placebos. This allows us to assess the relationship between the effectiveness of the antidepressants and the placebo effect.

Step-by-step explanation:

Yes, it is appropriate to calculate the correlation between the mean improvement levels for the antidepressants and placebos. The correlation is a statistical measure that assesses the strength and direction of the relationship between two variables.

In this case, the variables are the mean improvement levels for the antidepressants and placebos across several experiments. By calculating the correlation, we can determine whether there is a relationship between the effectiveness of the antidepressants and the placebo effect.

To calculate the correlation, we need to use a statistical measure such as Pearson's correlation coefficient. This coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.

Using the data from the scatterplot, we can calculate the correlation coefficient to assess the relationship between the mean improvement levels for the antidepressants and placebos.

For example, if the correlation coefficient is close to -1, it would suggest that as the mean improvement levels for the antidepressants increase, the mean improvement levels for the placebos decrease.

On the other hand, if the correlation coefficient is close to 1, it would suggest that as the mean improvement levels for the antidepressants increase, the mean improvement levels for the placebos also increase.

A correlation coefficient close to 0 would suggest that there is no relationship between the mean improvement levels for the antidepressants and placebos.