EXHIBIT 2 The N Crowd An MD/Ph.D at a major research institution is studying a n

Question

EXHIBIT 2 The N Crowd An MD/Ph.D at a major research institution is studying a new cannabis-based pain medication. The patients who volunteer for the study are randomly divided into two groups. Group 1 is given a placebo (Treatment 1). After one hour, group members rate the effectiveness of the pain relief on a scale of 1 to 100. Group 2 is given the new drug (Treatment 2), then group members rate the pain relief effec tiveness in a similar way. Initially, only 25 volunteers were available for each group. By the end of the month, however, there were 25,000 volunteers in each group, making this the largest clinical trial in recent memory. Amazingly, there is only a one-point difference between the ratings of the placebo group and the ratings of the active treatment group at each stage. Formally, the following choice has to be made: Ho: Treatment 2 is no different than Treatment 1 HA: Treatment 2 is different than Treatment 1 ·

Explanation / Answer

differences between any sample means will be significant if the sample is large enough,

we see that if n = 25000 , p-value = 0 << 0.05 ,whereas n = 50 ,p-value =0.8604 > > 0.05

we find effect size

d = |X1bar - X2bar|/sqrt(s1^2 + s^2)/2)=1/sqrt(20^2 +20^2)/2) = 1/20 = 0.05

which is low .

hence

we can not reliably infer practically significance from statistically significance.

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