By David C. Baird
A complement to all introductory physics classes that have a robust lab component.
The ever-increasing use of the pc as a device for information research and acquisition has no longer eradicated the necessity for a grounding, sound experimentation layout, Baird keeps to stress the basics of experimentation with additional attention for the facility of recent technology.
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Additional info for Experimentation : an introduction to measurement theory and experiment design
11, get an impression of how the means of the groups are clustered around the mean (119) of the population. This clustering shows us the degree of improvement in precision obtained by taking the mean of 10 cr (= 12) 2 cr. (= crf2) limits 10", (= crf4) limits\ I , \ / 2- x e- I 4 'o"lg. 12 X X 6 x X x x I I 8 10 12 x I 14 I 16 18 Distribution of sample standard deviations. values, instead of one single reading. 7). 8. These limits of ±4 are plotted about the mean on Fig. 11. Note how this value has the same kind of relationship to the distribution of means as (J' had for the distribution curve of single values, and how it therefore serves as a measure of the improvement in precision which 45 THE NATURE OF MEASUREMENT has resulted from the duplication of readings to form a sample.
Here the repetition of counts, over equal time intervals, of randomly occurring events follows a skew distribution known as the Poisson distribution. If the number of counts in each interval is small the distribution is markedly skew, but the curve approximates the normal distribution more closely as the number of counts increases. The statistics of this distribution play a very important role in nuclear physics but it is not discussed here further because its application is limited to counting experiments.
On these curves are marked the lu s limits, showing the range within which the observer stands a 68 per cent chance of having his sample standard deviation fall . The situation looks correspondingly worse for the 2u. limit~ . and it can be seen that for n = 10, 95 per cent of the possible s values lie within limits of ±u/ 2, and for n = 3, 95 per cent lie within a range which is large enough to cover 0 up to 2u. 10 s Sample standard deviation distributions for small samples. known. 8) to give the actual numerical value for (J' s .
Experimentation : an introduction to measurement theory and experiment design by David C. Baird
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