By David Roxbee Cox, E. J. Snell
This ebook could be of curiosity to senior undergraduate and postgraduate scholars of utilized statistics.
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Extra info for Applied statistics: principles and examples
In some cases the value of m may be unclear, although of course in extreme cases it may not be necessary to specify m with any precision. Thus possibility (iii) of those listed above is the one where allowance for adjustment of the analysis in the light of the data may be crucial. g. parametric tests under rather different detailed assumptions and nonparametric tests of different kinds, and then to choose the test giving the most significant result. This is a poor approach, dishonest if what is done is concealed; if it were to be adopted, however, some adjustment for selection would again be essential.
1) where g is a known function and p is a vector of unknown parameters. In some applications the distribution of Yt may be determined by the mean, as for example in Poisson, binomial and exponential distributions. In other applications it may be possible to express Yt (i = 1, ... 3) where the et are independent and identically distributed random variables of zero mean. In these cases, modelling of the systematic and random components of the variables can be considered separately. Note, however, that if the shape of the distribution of Yt changed notably with the explanatory variable, such separation of systematic and random components of the system might not be feasible.
Checking on the adequacy of the model is important not only in the definitive stage of the analysis, but more particularly in the preliminary phase when we are aiming to develop an appropriate model. There are broadly five ways of examining the adequacy of a model, although some of these ways are quite closely related. They are: (i) the calculation of discrepancies between observed values of key responses and values fitted from the model. These discrepancies, usually called residuals, can be calculated so that if the model is adequate, the residuals should be very nearly completely random.