A generic drug is being tested to test its efficacy (effectiveness) at reducing blood pressure in patients with hypertension (a.k.a. high blood pressure). In a randomized, double-blind experiment with 200 patients, 100 are given the name-brand drug (control group) and 100 are given a generic version of the drug (treatment group). In the control group, the average reduction in blood pressure is 15.2 mmHG with a standard deviation of 11.5 mmHG. In the treatment group, there is an average reduction of 14.6 mmHG and a standard deviation of 12.5 mmHG. Neither group has any outliers. A researcher claims that this study shows the generic drug is not as effective as the name-brand drug. What would be the reply of a statistician? A] The point estimate for the generic drug is lower than that of the name-brand drug, which means the generic drug is less effective. The researcher is correct. B] The standard deviations are quite large within each group relative to the size of the difference in point estimates. It is unclear if there is a real difference in the effectiveness of the two drugs or if the difference is just due to chance. C] While there is some uncertainty in the point estimates, the sample sizes for each group are large, indicating that the difference must be real. D] Because the difference in sample means is under 1 mmHG, we can safely conclude the drugs are equally effective.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A generic drug is being tested to test its efficacy (effectiveness) at reducing blood pressure in patients with hypertension (a.k.a. high blood pressure). In a randomized, double-blind experiment with 200 patients, 100 are given the name-brand drug (control group) and 100 are given a generic version of the drug (treatment group). In the control group, the average reduction in blood pressure is 15.2 mmHG with a standard deviation of 11.5 mmHG. In the treatment group, there is an average reduction of 14.6 mmHG and a standard deviation of 12.5 mmHG. Neither group has any outliers. A researcher claims that this study shows the generic drug is not as effective as the name-brand drug. What would be the reply of a statistician?
A] The point estimate for the generic drug is lower than that of the name-brand drug, which means the generic drug is less effective. The researcher is correct.
B] The standard deviations are quite large within each group relative to the size of the difference in point estimates. It is unclear if there is a real difference in the effectiveness of the two drugs or if the difference is just due to chance.
C] While there is some uncertainty in the point estimates, the sample sizes for each group are large, indicating that the difference must be real.
D] Because the difference in sample means is under 1 mmHG, we can safely conclude the drugs are equally effective.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
