Researchers carry out an experiment testing a new surgery aimed at reducing recovery time of knee injuries. Five individuals received the new treatment, and five individuals received the old treatment. Their recovery time, in days, is given in the following table.
Time New 8, 10, 7, 9, 12
Old 10, 14, 8, 8, 13
(b) Based on the boxplots, does it seem like there is any benefit to using the new treatment instead of the old treatment? Answer by commenting on the centers and spreads within each treatment group. (Hint: less recovery time is “good”.)
(c) Suppose a recovery time of 9 or fewer days is considered to be “fast”, and a recovery
time of 10 or more days is considered to be “slow”. Convert the above data into a
contingency table for the variables Treatment Type and Recovery Speed.
(d) Describe how the lurking variable Severity of knee injury could complicate the simple
conclusion that the new treatment is better because it tends to result in reduced
recovery time (potentially resulting in Simpson’s paradox).
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