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Unformatted text preview: Statistics (061541) Introducing inference summary sheet • Inference is the drawing of conclusions from certain basic facts or premisses. In classical statistics, the certain basic facts correspond largely to the sample data that we see, whereas the premisses correspond to the mathematical model that we believe decribes the population (most of which we don’t see), the sample data, and the relationship between the sample and the population. • The inferences that we make are generally not certain - i.e. we draw conclusions that are probably true or probably false, or somewhere in between. One of our aims will be to quantify the validity of the inference. Terminology • A population is the group of people or objects of interest. It is common to call the people or objects units or subjects . • A sample is the subset of the population actually examined. • A simple random sample (SRS) of size n consists of a subset of size n of the population, where each unit has the same chance of being included in the sample (and indeed, every subset of size n has an equal chance of being included). • There are many other kinds of sample. In particular, the stratified random sample takes a SRS from each of several strata. For example, one could take a SRS for men and for women. Quota sampling is a further kind of sampling beloved of opinion pollsters. This kind of sample aims deliberately to make the sample actually representative of the population. • Beware the many pitfalls involved in sampling. Ask yourself the questions (1) is the sample truly random? (2) for surveys, is the wording of questions going to result in bias? (3) for voluntarily completed questionnaires, will nonresponse lead to bias? • Randomisation is essential not only as a guard against bias, but also because the process of statistical inference is the drawing of conclusions about the main population from the sample, and this process depends upon the laws of probability , which describe random behaviour . • A statistic is a number that is calculated from the sample data, usually a summary. For example, the sample mean and SD....
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- Spring '10