A Bout The System

**kallieb** · 10-31-2007, 08:08 PM

Originally Posted by Mr JP Fugley

If there are 4 options and you only have to deal with 0.1% then your adjustment is only 0.025% on average for each of them. Whilst that may represent a reasonably large number of people, depending on the base, it is statistically insignificant, which is more important. Certainly better than reporting 100.1%.

The proper way to do it would be to both round up and round down, resulting in a figure of 100%.

There is debate about that, as I recall from my Stats class. One principle so drilled into my memory was (to quote as I'm too tired to remember all the nuances):

Precision and Rounding Be sure in your percentage tables (and, indeed, in any analysis) to claim no more precision than your data warrant. Retain only significant digits--that is, digits that are reliable and in which you have confidence. In practice this usually means you should round percentages off to either whole numbers or one decimal place. This guideline has exceptions, but not many when working with social scientific data. Percentages with more than one decimal place usually make false claims to precision. Calculators and computers usually give many decimal places (often as many as eight), but most of those digits are not significant.
As a general rule in statistics, keep as many digits as you can while applying formulas and calculating in order to minimize rounding errors during computation. Then round off your final number to no more than one more decimal place than you started with. If you begin with whole numbers (as in tallies of cases), round your final numbers (e.g., percentages) to one decimal place or perhaps even whole numbers. Since this is only a general rule, it has exceptions. As always, therefore, think about what you are doing and decide how many digits you have confidence in.
Ridiculous extra digits (generally those beyond one decimal place) normally should be rounded to the nearest number. Some examples: Round 21.32 to 21.3 and round 15.66 to 15.7. What about rounding a number ending in 5 like 48.65 or 17.35? A common practice is to round 5s off to the nearest even number. Thus, for example, 48.65 is rounded to 48.6, while 17.35 is rounded to 17.4. This "even rule" for rounding insures that in the long run about half of numbers ending in 5 are rounded up and about half are rounded down.

Since the authors of the study considered it significant enough to retain the extra digits (for reasons they didn't post, but we must presume) their end result of 100.1% was purposeful, and according to Statistical references, quite appropriate.

My goodness my brains are rusty in this regard. This discussion is refreshing.

**Mr JP Fugley** · 10-31-2007, 08:18 PM

Thing is tho' they only went to 1 decimal, which is what caused the 100.1%, because of the rounding up. Had they thought that accuracy was important then they ony had to go to another decimal place, maybe 2 to get it to 100%.

Since they went to only 1 decimal, for a large group, that suggests that the figures were more intended as illustrative than statistically accurate. Meaning, to my mind, that doing a small bit of rounding down, in addition to the rounding up, to get it to 100% would have been a better idea.