Error and Uncertainty Analysis

Error and Uncertainty Analysis - PHYSICS 133 ERROR AND...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
PHYSICS 133 ERROR AND UNCERTAINTY In Physics, like every other experimental science, the numbers we “know” and the ones we measure have always some degree of uncertainty. In reporting the results of an experiment, it is as essential to give the uncertainty, as it is to give the best-measured value. Thus it is necessary to learn both the meaning or definition of uncertainty, and the techniques for estimating this uncertainty. Although there are powerful formal tools for this, simple methods will suffice for us. To large extent, we emphasize a “common sense” approach based on asking ourselves just how much any measured quantity in our experiments could be in error. The experimental error is NOT the difference between your measurement and the accepted “official” value. Error means your experimental estimate of the range of values within which the “true experimental value” of your measurement is likely to lie. This range is determined from what you know, or can figure out experimentally, about your lab instruments and methods. It is conventional to choose the error range as that which would comprise about 68% of the results, if you were to repeat the measurement a very large number of times. In fact, we seldom make the many repeated measurements, so the error is usually an estimate of this range. Note that the error range is defined so as to include most of the likely outcomes, but not all. You might think of the process as a wager: pick the range so that if you bet on the outcome being within your error range, you will be right about 2/3 of the time. If you underestimate the error, you will lose money in your betting; if you overestimate it, no one will take your bet! Error: If we denote quantities that are measured in an experiment by, say, X, Y and Z , then their corresponding errors would be denoted by Δ X , Y and Z . So if L represents the length of a book measured with a meter stick, then you might say the length L = 25.1 ± 0.1 cm, where the central value (usually the most probable value) for the length is 25.1 cm and the error, L is 0.1 cm. Both central value and error of measurements must be quoted in your lab writeups. Note that in this example, the central value is given with just three significant figures. Do not write significant figures ( e.g. L = 25.08533 ± 0.1 cm) beyond the first digit of the error on the quantity. Failure to round off to 25.1 suggests that you assign additional precision to your number, which is misleading. Since the
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/26/2008 for the course PHY 131 taught by Professor Rijssenbeek during the Fall '03 term at SUNY Stony Brook.

Page1 / 4

Error and Uncertainty Analysis - PHYSICS 133 ERROR AND...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online