By R. H. Leaver, T. R. Thomas (auth.)
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Extra info for Analysis and Presentation of Experimental Results
In practice values oft are computed corresponding to certain set areas of the tails, that is, to set probabilities that the value oft will lie outside the quoted limits. Sets of these values have been calculated for a range of values of v (appendix A). 9. 5, there is less than one chance in ten that both samples came from the same population; if It I = 8, the chance is less than one in a thousand. 1 per cent level. It is important to bear in mind that these are arbitrary criteria. They have more in common with the standard of proof required by juries than with that required by mathematicians.
The most common variation is to change the limits of integration; thus is 1 - P(t) 35 NORMAL DISTRIBUTION some tables integrate from 0 to t while others integrate from -t to t. ° p(t)cit =roo Jo p(t)dt = 1/2 so 1; p(t) cit = e. 11) Jo A slightly more difficult problem is set by some writers' use of the e"or function. This is defmed as 2 erf (t/(2) 112 ) =(7t)1/2 f t/(2) 112 0 exp ( -s2 ) ds It is related to P(t) by 2P(t) = erf (t/(2) 112 ) + 1 As statisticians rarely use it anyway it hardly seems worth the trouble.
Figure 3. 6. 4 with origin referred to the mean. 6 then p. ip(x)dx = f_:'oo x2p(x)- 2p. 2 J_:'oo p(x) dx = ll2 - 2P. 2 + P. 11) 24 ANALYSIS AND PRESENTATION OF EXPERIMENTAL RESULTS Returning to our analogue, this equation is the equivalent of the parallel-axis theorem for moments of inertia; where a 2 is analogous to the moment of inertia about the centre of gravity and IJ. 9, equivalent to the moment of inertia about the origin. If x is measured from the mean, and 1J. 12) Clearly, the variance is a measure of the spread or dispersion of the variate about the mean of the distribution.
Analysis and Presentation of Experimental Results by R. H. Leaver, T. R. Thomas (auth.)