method is extremely important. The best approaches to sampling from a finite population, as in our asthma example, are to use either a simple random sample or a stratified random sample. Stratification is used when it is known that the response of interest is related to some factor (e.g. age or sex).
Choice of appropriate sampling method is not always obvious, and may involve a mixture of the methods we have described. Always seek advice if you are in doubt, as the cost of advice in relation to the cost of obtaining the sample is very small. Scheaffer et al. (2011) provide a very good introduction to all aspects of survey sampling.
2.13 Statistics and Parameters
Measures that describe a variable of a sample are called statistics. It is from the sample statistics that the parameters of a population are estimated. Thus, the average weight of a sample of new‐born male babies is the statistic that is used to estimate the average weight (parameter) of a population of new‐born male babies. An easy way to remember this is: Statistics is to sample as parameter is to population.
Sometimes populations appear to be rather abstract or hypothetical concepts, in which case their parameters are also hypothetical. We can calculate an ‘average temperature’ from a sample of 10 observations collected from a patient over a day. What exactly is the parameter that this statistic is estimating? It is the hypothetical ‘population’ of all temperature observations that could be made during the observation period.
In estimating a population parameter from a sample statistic, the number of observations in a sample can be critical. Some statistical methods depend upon a minimum number of sampling units, and where this is the case, it should be borne in mind before commencing your study. While it is true that larger samples will invariably result in greater statistical confidence, there is nevertheless a ‘diminishing returns’ effect. In many cases the time, effort and expense involved in collecting very large samples might be better spent in extending the study in other directions. We offer guidance as to what constitutes a suitable sample size for each statistical technique as it arises.
2.14 Descriptive and Inferential Statistics
Descriptive statistics are used to organize, summarize and describe measures of a sample. No predictions or inferences are made regarding population parameters. Inferential (or deductive) statistics, on the other hand, are used to infer or predict population parameters from sample measures. This is done by a process of inductive reasoning based on the mathematical theory of probability. Fortunately, only a very minimal knowledge of the mathematical theory of probability is needed in order to apply the rules of the statistical methods, and the little that is needed will be explained. However, no‐one can predict exactly a population parameter from a sample statistic, but only indicate with a stated degree of confidence within what range it lies. The degree of confidence depends upon the sample selection procedures and the statistical techniques used.
2.15 Parametric and Non‐Parametric Statistics
Statistical methods commonly fall into one of two classes – parametric and non‐parametric. Parametric methods are the oldest, and although most often used by statisticians, may not always be the most appropriate for analysing medical data. Parametric methods make strict assumptions that may not always hold true.
More recently, non‐parametric methods have been devised that are not based upon stringent assumptions. These are frequently more suitable for processing the sort of data we collect. Moreover, they are generally simpler to apply since they avoid the laborious and repetitive calculations involved in some of the parametric methods, although, as we note elsewhere, computers that are used intelligently can help with this. The circumstances under which a particular method should be used will be described as it arises. A summary showing which methods should be applied in particular circumstances is provided in Section 11.8.
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