Analysis and Presentation of Experimental Results by R. H. Leaver, T. R. Thomas (auth.)

By R. H. Leaver, T. R. Thomas (auth.)

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1. (a) Normal (Gaussian) frequency distnbution. (b) Normal frequency distribution with origin referred to population mean. 1 we have three variables to handle sirnultaneously;x, 1J. and o. 2) The new variable t is dimensionless, because x, 1J. and o are always in the same units. lb). 3) where p(t) is the probability density and is simply the value of the ordinate of the Gaussian curve corresponding to an abscissa of value t. To obtain a probability we must fmd the area under some portion of the curve.

It is not a convenient parameter and has limited use. 1. 2 The median If the values of the variate are arranged in an array, the median is the middle value, or the arithmetic mean of the two middle values. The median divides the histogram into two equal parts. The values which divide the histogram into four parts are called quartiles, and those dividing the diagram into ten and a hundred parts are called deciles and percentiles respectively. 3 The mean The mean is the most useful parameter describing central tendency, and is simply the average value of the variate, and is denoted by x.

1 per cent level. 11 becomes t = Afae. 12 a~ = (aA)2 ai a:xa a + (aA )2 aib a:xb Both differentials are unity, hence 2 2 2 ae,. 14) It only remains to express the population variance in terms of the sample variances. 15) where v =na + nb - 2 is the number ofdegrees offreedom. The statistic t has its own family of probability distributions, one for every value of v. 2a). 2b) is the probability that the samples will have a value of t outside the limits. 2. (a) Two cu~es of the family oft-distributions.

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