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# Frequentist Inference

In the study of statistics, frequentist inference represents one of the main schools of thought in discussing the frequency and/or proportion of data from which conclusions are drawn. Statistical practices, such as the concepts of hypothesis testing and the construction of confidence intervals, are based from this theory of thought.

Frequentist inference is based from the idea that probability is a limiting frequency1. The framework for frequentist inference is that probabilities are based from experiments with an infinite number of sequences and thus, a probability can be formulated once trials for an experiment have been run numerous times. Essentially, the probability measure which is generated explains the likelihood of similar occurrences taking place if that experiment was replicated again and again.

For instance, when probability statements are made such as ones involving confidence intervals, say a 95% confidence interval, this details the likelihood of whether a repeated event lies within this 95% range. Under the frequentist approach, probabilities are not attributed to unknown parameters. Instead, parameters are set as fixed, non-random qualities1.

Furthermore, the frequentist inference approach is continuously contested against the Bayesian School of practice. Several differences separate these two theories. For one, the way probability is defined differs because with the Bayesian theory probability can be associated for what is known about a parameter using the probability distribution2. Secondly, Bayesian statistics can be applied to unknown parameters.

The main feature of frequentist inference is its basis on the hypothetical repetition of data from a sample. This allows researchers to make generalizations from samples and inferences which can be applied to the population at large. Hypothesis testing, point estimates and confidence interval estimates concerning a fixed, but unknown population parameter can be focused upon under this train of thought2.

References:

1. Wagenmakers, E-J., Lee, M., Lodewyckx, T., and Iverson, G. (2014). Preprint of the Book Chapter: "Bayesian Versus Frequentist Inference". Retrieved from: http://www.socsci.uci.edu/~mdlee/WagenmakersEtAl2008.pdf

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