Frequentist inference is one of a number of possible techniques of formulating generally applicable schemes for making statistical inference: that implies of drawing conclusions from sample data by the emphasis on the frequency or proportion of the data. An alternative name is frequentist statistics. This is the inference framework in which the well-established methodologies of statistical hypothesis testing and confidence intervals are based. Other than frequentistic inference, the main alternative approach to statistical inference is Bayesian inference, while another is fiducial inference.
While "Bayesian inference" is sometimes held to include the approach to inference leading to optimal decisions, a more restricted view is taken here for simplicity.
Read more about Frequentist Inference: Basis
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“Rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.”
—Nelson Goodman (b. 1906)