By R. H. Leaver, T. R. Thomas (auth.)
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Additional info for Analysis and Presentation of Experimental Results
Setting aside this limitation, it is not difficult to imagine readings in this case taking values from far below to well above the true length in a continuous fashion. Alternatively, in an experiment concerned with the number of defective components produced in a shift from a particular machine, the variate will be an integer resulting from counting the components. If the experiment continues over several shifts a sample of a discrete variable will result. As the sample size is increased, we feel intuitively that the additional information will, in the first case, allow a better estimate of the true length to be made and in the second case, give a clearer picture of the distribution of the numbers of defective parts.
No purely statistical criterion can give us absolute 47 ERRORS AND THEIR SIGNIFICANCE certainty, but it can give us a very accurate balance of probabilities; and many men have been justly hanged on flimsier evidence. Let us now apply our test to the example of the last section. Suppose the two sets of measurements contained five and seven observations respectively. 64 with 5 + 7 - 2 = 10 degrees of freedom. 76 at the 2 per cent level. The difference between the two sets of readings is therefore significant at the 5 per cent level but not at the 2 per cent level.
Consider, however, the flow Vofliquid of viscosity 11 through a capillary of radius a and length L under a pressure difference p given by . 7) 41 ERRORS AND THEIR SIGNIFICANCE Suppose we wished to make use of this phenomenon to measure the viscosity of the liquid. 7 and applying the superposition of errors theorem gives us finally In other words, the fractional error in a contributes four times as much to the derived error in 11 as any of the other variables. As the radius of a capillary is in any case very small and very difficult to measure, we might justifiably conclude that this is not a suitable experiment for viscosity determination, although much used for this purpose.
Analysis and Presentation of Experimental Results by R. H. Leaver, T. R. Thomas (auth.)