|
    
|
 |
Precision
- Role of Confidence Level
The confidence
level is an index of certainty. For example (With N=93 per group) we might
report that the treatment improves the response rate by 20 percentage
points, with a 95% confidence interval of plus/minus some 13 points (7
to 33). This means that in 95% of all possible studies, the confidence
interval computed in this manner will include the true effect. The confidence
level is typically set in the range of 99% to 80%.
The 95% confidence
interval will be wider than the 90% interval, which in turn will be wider
than the 80% interval. For example, compare Figure 4, which shows the
expected value of the 80% confidence interval, with Figure 3 which is
based on the 95% confidence interval. With a sample of 100 cases per group
the 80% confidence interval is plus/minus some 9 points (11 to 29) while
the 95% confidence interval is plus/minus some 13 points (7 to 34).
The researcher
may elect to report the confidence interval for more than one level of
confidence, for example "The treatment improves the cure rate by
10 points (80% confidence interval 11 to 29, and 95% confidence interval
7 to 34. It has also been suggested that the researcher use a graph to
report the full continuum of confidence intervals by as a function of
confidence levels. (See Poole, 1987a,b,c; Walker, 1986a,b)
Precision
- Role of Tails
The researcher
may elect to compute two-tailed or one-tailed bounds for the confidence
"interval". A two-tailed confidence interval extends from some
finite value below the observed effect to another finite value above the
observed effect. A one-tailed confidence "interval" extends
from minus infinity to some value above the observed effect, or from some
value below the observed effect to plus infinity (the logic of the procedure
may impose a limit other than infinity, such as 0 and 1 for proportions).
A one-tailed confidence interval might be used if were concerned only
with effects in one direction. For example, we might report that a drug
increases the remission rate by 20 points with a 95% lower limit of 15
points (the upper limit is of no interest).
For any given
sample size, dispersion and confidence level, a one-tailed confidence
"interval" is "narrower" than a two tailed interval
in the sense that the distance from the observed effect to the computed
boundary is smaller for the one-tailed interval (the one-tailed case is
not really an interval, since it has only one boundary). As was the case
with power analysis, however, the decision to work with a one-tailed procedure
rather than a two-tailed procedure should be made on substantive grounds,
rather than as a means for yielding a more precise estimate of the effect
size.
Previous | Next
|
