A pharmaceutical company conducts a study to evaluate the relationship between l

Question

A pharmaceutical company conducts a study to evaluate the relationship between length of time taking drug X and size of tumor. They enlist 2400 patients with the same type of benign tumor who have been on drug X for varying lengths of time (measured in days). They find that the longer the patient is on the drug, the smaller the patient’s tumor size (measured in volume). In fact, they report the results as r(2398) = .21, with significance of p < .0001. What is your initial perception of this information? What are other ways, beyond looking at the p-value alone, you could use to try to interpret what this outcome of r(2398) = .21 tells us about the relationship between length of time taking drug X and the size of the tumor? Support your responses.

Explanation / Answer

As the reported p value is less than 0.0001 , which is less than 0.05 , this means that the results are statisitcailly significant and are not by chance . This means that the longer the patient is on the drug, the smaller the patient’s tumor size and this has been proven statistically using the hypothesis test.

H0 : There is no relationship between the length of the does and the tumor size

H1 : There is significant relationship ,  the longer the patient is on the drug, the smaller the patient’s tumor size

If the p value is less than 0.05 , then we reject the null hypothesis in favor of alternate hypothesis .

Also , as we can see the correlation coefficient is

r=0.21 , which means that the correlation between the 2 variables is very low . However , this does not necessarily mean there is a cause and effect relationship. This means that model can only explain the linear relationship betwen the variables , however the non rlationship between the variables is not captured.However , as the relationship is positive theis means that as ine variable increases , the other variable also increases.

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