Statistical inference is the process of drawing conclusions or generalizations from the data of interest. Contrary to descriptive statistics, the practice of statistical inference aims to extrapolate from the observed data patterns and explain how the population at large is affected. Generally, a sample of the total population is analyzed and through statistical inference, the larger picture is realized.
Statistical inference allows the theoretical world and the real world to become connected. The theoretical world consists of the statistical and scientific models being used; the different distributions the samples are taken from; the measures being estimated; and the conclusions being conceived from a statistical view point. On the other hand, the real world parallels the populations being evaluated, from which the samples originate. Statistical inference is the medium through which these two worlds can unite so that observable phenomena can be explained.
Often, statistical inference involves the approximation of parameters because the absolute value is unknown. Especially if the distribution being used is in question, an estimation of the unknown distribution is required. In addition to estimating unknown parameters, statistical inference also tries to set confidence or creditable intervals, assume the model type being used, conclude on the hypotheses and classify data points.
Statistical inferences can be extended beyond the information presented in the data set under investigation. However, it is important that researchers are cautious when constructing these types of generalizations, ensuring that they can be justified and thus, not result in false conclusions. This would be problematic considering that the overall objective of statistical inference is to formulate conclusions and understand the true behaviour of different populations.