A research team at a large university hospital has just completed a pilot study of an innovative new treatment that is intended to be used to treat patients in the later stages of prostate cancer. They had 12 patients, males, ranging in age from 47 to 73. All had been diagnosed as in stage 4 of the disease within 4 weeks of agreeing to participate in the study. Here from lowest to highest, are the number of weeks that the patients lived after treatment began:
3, 5, 6, 6, 8, 8, 9, 9, 9, 10, 11, 45
The meannumber of weeks that a prostate cancer patient lives after receiving a confirmed diagnosis of being in stage 4 is 9.6 (with a standard deviationof 3.2)
The researchers were overjoyed that the mean number of weeks that the patients in this study survived was 10.75 with a standard deviation of 11.02. They are presenting this result to the committee in charge of distributing grant money to researchers in the hospital.
Pretend you are on the committee and write a statement expressing your views on the level of promise that this study shows. Keep in mind what you learned in this module about measures of central tendencyand under what conditions the different types should be used, the meaning of the standard deviation, and any other relevant comments you would have if you were a member of the committee evaluating this study to determine if more money should be granted to these researchers.
The issue you need to keep in mind here is the influence of outliers on the mean. Clearly, most patients are living between 6-9 weeks (7/12 patients fall in that range). The fact that one patient lived 45 weeks is what is pulling the mean up to 10.75 and should definitely not be taken as an …
Explains the effect of an outlier in a statistical decision and in interpreting the meaning of a study.