Solutions to Selected Exercises 181- What is the difference between equivalence testing and noninferiority?
In equivalence testing, we require that the difference be no greater than a specifi ed
δ and no less than − δ. In noninferiority testing, there is no restriction on how much
larger the treatment mean is compared to the control mean, but the treatment mean
minus the control mean cannot be less than − δ , where δ is now called the nonin-
feriority margin. - Describe the difference between a one - tailed and a two - tailed test and describe
situations where one is more appropriate than the other.
Sometimes, the alternative is only interesting in one direction. For example, in
clinical trials, we are usually only interested in showing that the treatment is supe-
rior to the control. This would mean that we want the average treatment effect to
be statistical signifi cantly higher than the control. If the average treatment effect
is less than the average control treatment effect, it is just as bad as if there were
no difference. - What are meta - analyses? Why might they be needed?
Meta - analyses are analyses that combine information from several studies on the
same or similar endpoints. The purpose is to use the information to draw stronger
conclusions about the endpoint than was possible from any individual study. The
can be necessary when several small studies show trends that are not statistically
signifi cant but are all or most in the same direction. The meta - analysis may be able
to provide research results that are signifi cant rather than just a trend. - Based on the data in Table 6.1 , do you think it is plausible that the true mean
difference in temperature between New York and Washington would be 3 ° F?
Would the power of the test be higher, lower, or the same if the true mean
difference were 5 ° F? Does the power depend on the true mean difference? If
so, why?
Yes: The observed difference is 3 ° or more higher in Washington versus New York
in January, March, April, July, August, September, October, and November, and is
2 ° higher in the other 4 months (February, May, June, and December).
Assuming the variance of the difference does not change the power of the test
would be higher if the true mean difference were 5 ° instead of 3 °. This is because
the greater the separation of the center of the distribution, the less the distributions
overlap.
Chapter 7- Defi ne the following terms:
(a) Association
(b) The correlation coeffi cient
(c) Simple linear regression
(d) Multiple linear regression
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