Читать книгу Experimental Design and Statistical Analysis for Pharmacology and the Biomedical Sciences - Paul J. Mitchell - Страница 31

Whenever we perform an experiment, we obtain measurements according to our observations, and as described in earlier chapters our aim is to collect data in a precise and accurate manner. Statistics may be defined as the science of collecting, summarising, presenting, and interpreting such data. A collection of data on their own is not information, but a valid summary and description of that data set derive information by putting the data into context. Statistics therefore involves summarising a collection of data in a clear and understandable way such that our reader or audience may see clearly the similarity or differences between the groups in our experiment.

One very important issue we need to accept in statistics is that in almost all cases, we only work with samples taken from whole populations of subjects. Consequently, we are almost always faced with the situation in which we estimate population parameters from the samples we have obtained.

For example, suppose we wanted to determine the height of students at your university or institution. We would not be able to determine the height of every single student, so we would choose a ‘representative sample’ of students, measure their height, and then estimate the average height from these values.

 A statistical population, therefore, is the set of all possible values (our observations/measurements) that could possibly be measured.

 A sample is the subset of the population for which we have a limited number of observations drawn at random from the population that will be used to describe the parent population (see Figure 4.1).

Figure 4.1 A data sample is a random set of values drawn from the parent population.

By necessity this process involves the tacit assumption that the sample group is truly representative of the parent population. Furthermore, if we take a large number of samples from the population and divide those randomly into subgroups of equal size, then each subgroup should truly represent the parent population. Furthermore, if the last statement is true, then each subgroup should be equal to each other. In reality, of course, there will be some differences not only between the subgroups but also to the parent population, and it is determining the importance of those differences where we rely on statistical analysis.