One's nose was constantly being rubbed into numerical issues, which reminded us not to overlook them.īy the way, if issues like this interest you, consider applying to StataCorp for employment. Why don't you fix that? In the old Fortran days in which I grew up, one would never expect a^3 to equal a*a*a.
This is ironic because when numerical issues arise that do not have a similarly easy solution, users are disappointed. In this case, a^3 is exactly equal to a*a*a. It is because we do this that things work as you expect. People do not realize the extreme caution we go to on what might seem the minor issues. That Stata calculates a^b by repeated multiplication for -64<=b<=-1 and 1<=b<=64 is not something we have ever mentioned. The answer is that exp() and ln() are approximations to the true functions, and in fact, so is * an approximation for the underlying idea of multiplication. In particular, it watches for b as an integer, 10, and you may be asking yourself in what sense exp(b*ln(a)) is an approximation. Stata does watch for special values of b in calculating a^b. Whether one should watch integers for such special values is an interesting question. Integers have exact numerical representations even in digital computers, so computers can watch for integers and take special actions. One solution to this problem, if a solution is necessary, would be to introduce a new function, say, invpower(a,b), that returns a^(1/b). Watching for 1/3 and doing something special is problematic. The problem is not only that 1/3 has no exact decimal representation, but it has no exact binary representation, either. You might be tempted to say Stata (or other software) should just get this right and return -2. 2power repeated Power analysis for repeated-measures analysis of variance Same as above, but for sample sizes of 20, 24, 28, and 32 power repeated 25 27 22, varerror(42) corr(.3) n(20(4)32) Same as above, but show results in a graph of sample size versus power power repeated 25 27 22, varerror(42) corr(. Nick’s supposition was correct, in this particular case, and for most values of a and b, Stata calculates a^b as exp(b*ln(a)). He didn’t say where he was going, but I answered his question. Title intro Introduction to power and sample-size analysis DescriptionRemarks and examplesReferencesAlso see Description Power and sample-size (PSS) analysis is essential for designing a statistical study. He was focusing on examples such as (-8)^(1/3), where Stata produces a missing value rather than -2, and he wanted to know if our calculation of that was exp((1/3)*ln(-8)). He said he was writing something for the Stata Journal and wanted the details on how we calculated a^b. I got an email from Nicholas Cox (an Editor of the Stata Journal) yesterday. Excuse me, but I’m going to toot Stata’s horn.
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