ABSTRACT
One of our major objectives when carrying out a statistical analysis of data is to obtain a statement of characteristics that are relevant to the total population, or at least to the target population (see Chapter 2), and the parameters or characteristics that we seek are, for example, the population mean and the population standard deviation. More concisely, at times these may be called the true mean, etc., this term thus implying that it is the value which would be obtained from analysing the whole body of data concerning the phenomenon under study. The values that in practice are obtained, however, are usually based on only part of the body of data, this being the result either of a deliberate choice or because no more data are available, i.e. these values are based on only a sample of the conditions. Thus what is usually obtained is not the true or population mean but the sample mean; the same applies to the standard deviation too. Before proceeding to any assessment of the differences between different series of data, or to any further conclusions based on the mean and the standard deviation, it is therefore essential that some thought be given to the relationship between these sample statistics and the true parameters.
