44
Stata Technical Bulletin
STB-58
Examples
Typing sskdlg in the Command window calls the dialog box. Without checking the options or changing the default values,
the following output is displayed on pressing the OK button:
--- Begin -----------------------------------------------
Results for kappa=O, pl=0.1, p2=0.1,
d=0.1 [95% Conf. Interval]:
* Sample size = 384
---End-------------------------------------------------
Changing the input parameters and checking all options will produce the following display
--- Begin -----------------------------------------------
Results for kappa=0.1, pl=0.2, p2=0.2,
d=0.2 [95% Conf. Interval]:
* Sample size = 114
* Value of Q = 1.182
Given the values specified above, the
maximum sample size is 126 for a
kappa of .289
If the sample size is fixed at 50,
given the kappa, pl, p2 and CI stated
above, d = .215.
---End-------------------------------------------------
The above set of statements are worth commenting on from a practical view point. The first indicates that if the researcher states
that a) both raters are expected to find a prevalence of 20% of the event of interest, b) the null-hypothesis for к is 0.1, and c)
he or she is ready to tolerate a rather lenient absolute precision of 0.2, given a 95% confidence interval, this reliability study
will need at least a sample size of 114 subjects.
The second statement conveys that if the researcher is not prepared to make any assumption about the value of к , i.e., to
assert a null hypothesis for the parameter, the most stringent situation (given all the other parameters he or she has specified)
would occur when к = 0.289 for which a sample size of 126 would be needed.
The last output says that, given the other specified values, if resources or logistics allow for just 50 subjects in a reliability
study, the absolute precision would be 0.215. This, in turn, is only slightly worse than the value specified in the first place (0.2),
which means that the researcher may decide to go ahead with his or her “half sized” study since not much precision would have
been lost.
As has been hinted so far, there are many situations that arise from irregular or incompatible specifications. In those
circumstances, sskdlg precludes any unwarranted output. For instance, the output below follows a possible mishap (value of d
relative to «), displaying in red the message
The specified value of d (0.8) is incompatible
with the kappa you selected (0.5), since
both confidence limits (-.3 and 1.3)
exceed the possible boundary values for kappa
(-.11 and 1, respectively), given the
specified marginals (pl = 0.1 and p2 = 0.1).
Sample size will not be calculated.
Turning to some graphical outputs, Figure 2 shows a “Graph S” for the parameters specified above. Note that this graph has
been constrained to kappa values between 0 and 0.7. Sample size starts at 96, peaks at 126 where «max = 0.289, and decreases
to 78 at к = 0.7. Also note that “k_max” has been checked and a vertical line positioned at «max.