Probability Theory and Statistical Inference

In the online encyclopedia, Wikipedia, probability theory is defined as "the branch of mathematics concerned with analysis of random phenomena" (Probability Theory, 2007). The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance. Due to the nature of probability estimates, the conclusions cannot be considered 100% accurate, therefore a margin of error is assigned. When a guess on the weather for tomorrow is made by using intuition and nothing else, a person might say they are seventy-five percent sure that it will rain tomorrow. This implies that there is a twenty-five percent chance that it would not rain. In mathematical probability the outcome must satisfy certain properties or axioms (DeGroot & Schervish, 2002). These include that the probability must be greater than or equal to zero, and the probability that one of possible outcomes will happen is 100%.

Statistical inference is the use of statistics to make inferences concerning some unknown aspect of a population. According to author Melecio Deauna it uses formal techniques in order to make these conclusions based on samples, a collection of some elements in a population (2005). Therefore, a conclusion can be made that if the sample satisfactorily represents the population, the information that has been gathered is a good estimate or ballpark figure of the population parameter, the technique that was used to generate the data (DeGroot & Schervish, 2002).

It is apparent that both probability theory and statistical inference deal with unknowns. Probability theory concentrates on random events, whereas statistical inference creates conclusions based upon samples of data. Neither are infallible and both are assigned a margin for error.