notes4 - MTH4106 Notes 4 What is Statistics about?...

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MTH4106 Introduction to Statistics Notes 4 Spring 2012 What is Statistics about? We collect data, then analyse the data, and then interpret the results, to find out about real-world phenomena. There is aways variability in the data: we need to extract meaningful patterns. Because of the variability, our conclusions cannot be certain. We need to quantify the uncertainty, so that we can make definite decisions and judge how likely it is that we are right. Here are some areas of application, with some typical problems. Agriculture Which varieties of wheat make the best bread? Manufacturing Can we make a cheaper detergent that is just as effective as the current one? Health Does an aspirin a day protect against stroke? If so, are there any side-effects? Education What is the best way to teach young children mental arith- metic? Biology How does biodiversity affect the enviroment? Social science Do people live in better houses than they did 20 years ago? Economics How is the credit crunch affecting food prices? Market research What sort of advertising campaign is most effective? Environmental studies Are people who live near mobile-phone masts more likely to get cancer? Meteorology Is global warming a reality? Psychology Are shyness and loneliness related? Before starting any of these investigations, we need to stop and ask: What do we want to investigate? What should we measure? How should we measure it? 1
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Three methods of collecting data 1) Take a sample from a population . First we have to define the population. (It is just a set, and there is no need for its elements to be people.) How do we choose the sample? At random, or for convenience, or to make it representative? Do we ask questions (in which case, how do we word the questionnaire?), or
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notes4 - MTH4106 Notes 4 What is Statistics about?...

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