#2 Consider the following for all questions: The company you work for, Avid, has
ID: 3292036 • Letter: #
Question
#2
Consider the following for all questions: The company you work for, Avid, has developed a drug that they believe can help improve memory. They believe that the drug might be used to treat diseases that affect memory, including Alzheimer’s Disease and dementia. In order to test this, they have collected data for a sample of 12 people. Participants in the study completed memory tests at the beginning of the study, 6 months into the study, and at the end of the study. They were also assessed for change in cognitive functioning over the course of the study. The dataset includes the following information:
Diagnosis: This variable represents the participant’s diagnosis at the time of the study. 1 = Alzheimer’s Disease, 2 = Dementia, 3 = control (no disorder).
Medication: The variable represents whether participants were on the experimental memory drug that may improve memory. 1 = Did not take memory drug, 2 = Took memory drug
Memory_1: This variable represents the score on the memory test taken at the beginning of the study. Possible values range from 1 – 10, with higher numbers representing better memory.
Memory_2: This variable represents the score on the memory test taken 6 months into the study. Possible values range from 1 – 10, with higher numbers representing better memory.
Memory_3: This variable represents the score on the memory test taken at the end of the study. Possible values range from 1 – 10, with higher numbers representing better memory.
Cognitive_Change: This variable represents the overall change in cognitive function from the beginning to the end of the study. Scores range from 1 – 5, with higher numbers indicating more improvement.
You have been asked to help complete the data analysis and create a report to help your bosses interpret the success of the drug. The data from the study is provided below:
Is there a positive relationship between memory scores at the start of the study (Memory_1) and memory scores at the end of the study (Memory_3)?
Calculate the appropriate test to address this question BY HAND either using a word processing document or handwritten on paper, then enter your final answer rounded to two decimal places (if applicable) below.
Based on your work determine if it is appropriate to calculate the coefficient of determination for this scenario. If it is appropriate, calculate this value BY HAND using the data provided on the table,and your work from Question #2, and/or additional hand calculations. Report that value as part of a formal conclusion based on your work in both this item and Question #2 below.
If it is not appropriate, report a formal conclusion based just on Question #2 below and write "not appropriate" in your work.
Explanation / Answer
It is suspected that drug might be helpful in improving memory score. Compute the Pearson correlation coeffcient for the variables Memory 1 (x) and Memory 3(y).
r=sigma (x-xbar)(y-ybar)/sqrt[{sigma (x-xbar)^2}{sigma (y-ybar)^2}]
=62.67/sqrt(72.67*66.92)
=0.899
The sign of r is positive and close to 1, which indicates a strong positive relationship between the variables.
Follow the steps to conduct a test to determine if there is positive relationshuip at the start of the study (Memory 1) and at the end of the study (Memory 3).
State the hypotheses: Let rho denote the population linear correlation coefficient for the variables Memory1 and Memory 2. Then the null and alternative hypotheses are:
H0:p=0 versus H1:p>0 (note > sign is used to see positive relationship).
Decide on significance level: alpha=0.05.
Compute the value of test statistic.
t=r/sqrt {(1-r2)/(n-2)}, where, r is the correlation coeffciient and n is the number of paired samples.
From previous calculations, r=0.899, n=12
t=0.899/sqrt{(1-0.899^2)/(12-2)}
=6.49
p value for n-2=12-2=10 degrees of freedom is: 0.00007.
Rejection rule: Reject null hypothesis if p value is less than 0.05. Here, p value is less than 0.05, therefore, reject null hypothesis.
Conclude: There is sufficient sample evidence to conclude that there exists positive relationship between the variables memory1 and memory2. In other words drug might be useful in improving memory score.
Since, there is evidence of positive relationship between the variables, therefore, coeffciient of determination is appropriate. The coefficient of determination, R^2 is 0.899^2=0.8082.
This explains that around 80.82% variation in memory2 is accounted for variation in memory1.
x (x-xbar) y (y-ybar) (x-xbar)(y-ybar) (x-xbar)^2 (y-ybar)^2 3 -1.667 2 -3.417 5.6961 2.7789 11.6759 5 0.333 5 -0.417 -0.1389 0.1109 0.1739 4 -0.667 6 0.583 -0.3889 0.4449 0.3399 3 -1.667 5 -0.417 0.6951 2.7789 0.1739 1 -3.667 2 -3.417 12.5301 13.4469 11.6759 3 -1.667 3 -2.417 4.0291 2.7789 5.8419 2 -2.667 4 -1.417 3.7791 7.1129 2.0079 4 -0.667 5 -0.417 0.2781 0.4449 0.1739 9 4.333 9 3.583 15.5251 18.7749 12.8379 8 3.333 7 1.583 5.2761 11.1089 2.5059 8 3.333 9 3.583 11.9421 11.1089 12.8379 6 1.333 8 2.583 3.4431 1.7769 6.6719 xbar=4.667 ybar=5.417 total:62.67 total:72.67 total:66.92Related Questions
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