# Inferential statistics

Inferential statistics is a branch of statistics that uses statistical tools to make predictions or generalizations about a population based on limited observations made from data collected from a sample of the population. This is useful because in most cases, it is very difficult, or prohibitively expensive to collect data about an entire population.

The use of confidence intervals and hypothesis testing are two key aspects of inferential statistics.

## Confidence intervals

A confidence interval is a range of values within which the true parameter (such as the population mean) lies with a known (chosen) degree of certainty, called the confidence level. Confidence intervals are a useful tool for estimating parameters, since they take sampling error (error that arises from the fact that a sample by definition cannot capture an entire population) into account.

## Hypothesis testing

Hypothesis testing is a method of statistical inference that tests the results of a survey or experiment to see whether or not the obtained results are valid. The goal is to determine whether or not to accept or reject a given statistical hypothesis based on whether or not collected sample data is consistent with the hypothesis.

## Descriptive and inferential statistics

The study of statistics exists as a way to help us analyze and better understand variability in the world around us. Descriptive statistics is arguably the simplest form of statistics. It provides us with tools for organizing and summarizing variability in collections of data. There is no uncertainty in descriptive statistics, as it is not based on the assumption that a set of data represents a larger population. It only describes these sets of observed data in terms of attributes such as distribution (frequency), central tendency (averages), and variability (spread).

In contrast, inferential statistics uses observed data to make conclusions, generalizations, or predictions about a population. This involves the use of probability theory, which takes into account sampling error due to the sample size always being smaller than the population it is intended to represent. Thus, the validity of the conclusions drawn in inferential statistics is subject to factors such as sample size and the random sampling methods used. These are factors that do not need to be taken into consideration when using descriptive statistics.

Both descriptive and inferential statistics are widely used, often together, depending on the intent of the study. Generally, descriptive statistics is useful for observing patterns in data, while inferential statistics examines the sample data to make predictions about the relationships between variables in the data and how they may relate to the larger population.