Re: Significant figures - a Modest Proposal

[Leigh Palmer <palmer@SFU.CA>]

> When the students use a hand-held timer to time an object, the timer
> provides a reading down to the hundreths of a second.  The resolution of
> the measurement is about 0.01 s.
>
> However, the measurement is not accurate to 0.01 s.  Due to reaction time,
> the measurement cannot be repeated exactly the same from case to case.
> For example, when timing a ball that is dropped from about a meter, most
> students obtain a spread in their timings of about 0.1 s.
>
> In other words, the precision is on the order of 0.1 s and the resolution
> is on the order of 0.01 s.

I would have said that the measurement's accuracy is of order 0.1 s.
The value of the uncertainty in the measurement would be determined
only after repeated measurement except in unusual circumstances (e.g.
a single event, a quantized quantity). The precision reported in the
data should still be 0.01 s (and there should be no "plus or minus").

> There may be other contributions to poor accuracy, e.g., bias in reaction
> time, parallax, poorly calibrated timer, etc.; here I am only discussing
> the distinction between resolution and precision.  BTW, because precision
> refers to the repeatability of a measurement, poor precision can be
> addressed somewhat by multiple readings, whereas poor resolution cannot.

I don't believe precision relates to repeatability.

> I'm not an expert on error analysis so I may be mistaken about this.  If
> so, I'd appreciate if someone would set me straight before I mislead all
> of my students.

I'm not an expert either, but I think the example above is incorrect.
I can't even consult a standard reference, I'm afraid, but I would
probably do so before teaching this to a group of students.

I would also spend some time talking about the terms "error" and
"uncertainty". In this case I do know what the experts say, and I am
in disagreement with some of them (as they are with one another).

Leigh