by
lmh » Tue Jan 09, 2018 12:08 pm
not really an empower user here (been a few years since I last saw it) but some general observations:
(1) If you want your calculator to give you the same results as empower, you have to start with the same numbers. If empower is doing its job properly, it will keep maximum precision through the whole process and round at the final number it presents to you. Does it also round the areas that it reports? Because if you start your calculator-calculations with rounded areas, but it started with the true area, then of course your value will have lost precision.
(2) Not relevant in this case, but for general information: numerical calculation isn't totally trivial. There are very good ways to destroy precision completely. Your calculator will certainly work to plenty of decimal places - it will have one or two spare that it doesn't display. Excel has 15 by default, I think. Empower will have loads too. But say you subtract the average of 6 replicate injections (1000.1234) from one of the individual measurements (1000.0234) the answer is now -0.1000. Note that you have just lost 4 decimal places of precision by looking at the small difference between two large numbers. Do this a couple of times in a calculation and suddenly those 15 significant figures have dwindled to 5 or less.
(3) Validation: You cannot prove that a calculation is correct by running it on test-values, although this is a good thing to do, to screen for obvious errors. Proof in arithmetic, like any branch of maths, is by being right, rather than producing the right answer X times and therefore, by extrapolation, always.
(4) Rounding in other packages: there are multiple conventions for rounding. Excel and Access use reputable ways to round, but behave differently. Excel uses arithmetic rounding (0.5 is upward), vba and Access use banker's rounding (0.5 moves in different directions depending on whether the integer part is odd or even). Rounding, again, isn't totally trivial, but if your final decision based on an analysis depends on which way you carry out your rounding, you have rounded far too far, and there is something seriously wrong with the methodology!