Question

) The National Institute of Health (NIH) is conducting clinical trials of two antiviral drugs used to treat patients with acute respiratory distress syndrome (ARDS). Each subject in a group of 400 volunteer patients diagnosed with severe ARDS was randomly assigned to a treatment plan which consisted of either Drug A, Drug B, or a placebo. A breakdown of the number of subjects who recovered (vs did not recover) for each of the three treatment plans is shown in the two-way table below. Treatment Plan Drug A Drug B Placebo Recovered 58 82 51 Did not recover 75 52 82

a) Manually compute the expected counts for the top row of cells (Recovered) in the table. Show your work.

b) Manually compute the contribution of the upper left cell (Recovered / Drug A) to the chisquared statistic. Show your work. (continued)

c) At a 5% significance level, is there a statistically significant relationship between the treatment plan applied and patient outcome? Show the expected counts and explain why it is appropriate to analyze the data with a chi-square test. Include the test statistic value and p-value in your answer and state your conclusion in the context of the study’s objective. (Note: Manually enter your data into StatKey OR upload the data file from ARDS Clinical Trial Dataset B, which can be found on Blackboard under today’s date.)

d) Assume there is significant evidence of a relationship. Show the individual cell contributions to the chi-squared statistic and use them to explain what the data tells us about the nature of the relationship between the treatment plan used and patient outcome.

Answer 1

A)

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	DRUG A	DRUG B	PLACEBO				Total
RECOVERED	133*191/400=63.508	134*191/400=63.985	133*191/400=63.508				191
NOT RECOVERD	133*209/400=69.493	134*209/400=70.015	133*209/400=69.493				209

C)

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   15.336                          
                              
Level of Significance =   0.05                          
Number of Rows =   2                          
Number of Columns =   3                          
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 3- 1 ) =   2                          
                              
p-Value =   0.0005   [Excel function: =CHISQ.DIST.RT(χ²,df) ]                      
Decision:    p-value < α , Reject Ho                          

There is relationship between the recoverd and not recovedre.

Critical Value =   5.991   [ Excel function: =CHISQ.INV.RT(α,DF) ]                      

D)

	(fo-fe)^2/fe
RECOVERED	0.478	5.072	2.463
NOT RECOVERD	0.436	4.635	2.251

Thanks in advance!

revert back for doubt

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