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

sense to examine the difference between patients鈥 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 鈥 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 鈥 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.

Short Answer

Expert verified

Part (a)

Part (b) Mean Active: 1.095; Mean Inactive: 4.085; Mean: 4.085

Part (c)

  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.

Part (d) There is no significant effect that can be concluded due to magnets on pain relief.

Step by step solution

01

Part (a) Step 1. Observe the Histogram

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.

02

Part (b) Step 1. Compute the mean of the active data

Calculate the mean of the active data.

Mean=sumofobservationnumberofobservation=10+6++128=5.18

03

Part (b) Step 2. Compute the mean of the inactive data

Calculate the mean of the inactive data

Mean=sumofobservationnumberofobservation=4+3++122=1.095

04

Part (b) Step 3. Compute the mean difference between active and inactive.

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.

Average=5.181.095=4.085

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

05

Part (c) Step 1. Explanation to use index cards

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.
06

Part (d) Step 1. Conclusion about the effect of the magnet on pain relief. 

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.

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