Magnets and pain Refer to the chapter-opening Case Study (page 205). The researchers decided to analyze the patients’ final pain ratings. It also makes

sense to examine the difference between patients’ initial pain ratings and their final pain ratings in both groups. Here are the data:

(a) Construct a comparative dotplot of the data. Describe what you see.

(b) Calculate the mean (average) change in pain rating for each group. Find the difference in the average changes for the two groups (Active – Inactive).

(c) Describe how you could use index cards to randomly reassign the subjects to the treatment groups.

(d) Suppose we used your method in (c) to redo the random assignment 50 times. The Fathom dotplot displays the difference (Active – Inactive) for the average change in pain rating for each of these random assignments. What conclusion would you draw about the effect of magnets on pain relief? Explain.

It can be observed from the given histogram that at -25% and -15%, monthly return is very rare. There is almost no percentage of monthly returns that is close to them. So, the monthly return -25% and -15% are the outlier. It can be observed that the tail is at the left and the maximum value lies around the center which refers to the skewed distribution towards the left.

Calculate the mean of the active data.

$\begin{array}{rcl}\text{Mean}& =& \frac{\text{sumofobservation}}{\text{numberofobservation}}\\ & =& \frac{10+6+\dots +1}{28}\\ & =& 5.18\end{array}$

Calculate the mean of the inactive data

$\begin{array}{rcl}\text{Mean}& =& \frac{\text{sumofobservation}}{\text{numberofobservation}}\\ & =& \frac{4+3+\dots +1}{22}\\ & =& 1.095\end{array}$

The average change in the two groups that are active and inactive can be obtained by taking the difference between the averages of each group.

$\begin{array}{rcl}\text{Average}& =& 5.18-1.095\\ & =& 4.085\end{array}$

As a result, the average change in the two groups is equal to 4.085.

The total number of patients is equal to $22+28=50$

Consider 50 index cards consisting of 22 blue cards and 28 green cards. The following steps can be done in order to randomly assign the treatment groups to the patients.

1. Randomly shuffle the cards and randomly pick the cards from them.
2. Assign treatment to the first 28 cards while no treatments to the remaining cards.

The given Fathom dotplot represents the difference between the active and inactive groups formed due to random assignment of treatments based on the index number.

It can be observed that the differences are mostly close to 0 and it varies mostly between the range -1 to 1. This means that the effect of magnets on pain relief would be either negligible or close to negligible.