StatTools : Probability : Introduction and Explanation

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Introduction Errors Type I and II Changing Developments References
Probability and Reality Mean Standard Deviation and Standard Error
The scientific approach that characterises the western civilisation is based on reproducible empirical observations. The idea is that repeatedly observed relationships or differences are more likely to reflect reality. Another way of saying this is that, a proposition cannot be accepted unless it is supported by repeated observations.

The problem with repeated observations is that the results, often similar, are not always the same. Experience compels us to abandon the binary idea that something is either true or false. Rather we increasingly see true or false merely as extremes while most of reality is a continuum in between.

Similarly, when we consider a scale (e.g. how tall is a man), we can only state an approximation, a range that most would fit in.

The uncertainty of reality therefore needs to be approached in a consistent and logical way. Probability is a measurement of how likely things are to occur and is one of the ways to represent uncertainty. Statistics is the set of tools to handle probability.