# Inferential statistics

The statistic is the scientific study obtained , orders and analyzes the data together in this way to obtain explanations or predictions about phenomena being studied. They are methods, procedures and formulas that allow the person to collect information. In the field of statistics we find the inferential type that is the branch in charge of making a series of deductions from a sample.

## What is inferential statistics?

The inferential statistics is whose function is to perform a series of inferences in the properties , the findings and trends from a sample set to interpret, make comparisons and different types of projections .

• Definition
• Characteristics of inferential statistics
• History
• Applications of inferential statistics
• Types
• Method
• Basic concepts
• How it differs from descriptive statistics
• Importance of inferential statistics
• Examples

## Definition

Inferential statistics is a part of statistics that seeks the appropriate methods and procedures to be able to make inferences in a population using a part of it as a base, which is known as a sample. They are a series of tests of estimation and hypothesis , parametric and of proportions .

It is a process that uses a series of mechanisms that allow establishing and finding deductions also using point estimation tests, hypothesis tests , parametric and non- parametric . It is a science used to analyze populations and trends to know the actions and reactions to specific conditions.

## Characteristics of inferential statistics

The main characteristics that can be observed in inferential statistics are the following:

• They help express the information that has been collected through data.
• It can be known by the name of analytical statistics .
• It is a branch of statistics .
• It uses information that has been collected through studies applied to the samples .
• Use different hypotheses to get the results.
• It performs analyzes on small samples within the population under study.
• Actively participates in scientific studies and marketing analysis .

## History

The beginning of the history of inferential statistics dates from the late nineteenth century but its historical antecedents are very old and go back to Egypt where they used to keep a record of their activities and harvests. Already in the seventeenth century, collective studies began to appear to be able to make inferences to the population and in the same way, different types of probability calculations began to emerge.

## Applications of inferential statistics

Inferential statistics can be used in a number of sciences, for example in the natural sciences where it is used to describe complex thermodynamic models, in the field of quantum physics , in fluid mechanics and in the kinetic theory of gases. In the social sciences it can be used to learn information on studies of birth and mortality, economic models and to study the relationships between human beings.

In medicine , this type of statistics allows establishing a series of guidelines to observe the evolution of diseases and patients, it is also useful to be able to know the mortality rates of serious diseases and the degree of effectiveness in a given drug. Within the politics of a place, it is used to be able to carry out future plans and programs and in the production field it is used to be able to adequately control quality, sales, profits, expenses and inventories.

## Types

The types of inferential statistics are as follows:

#### Parametric statistics

This type of statistics uses statistical data and resolution criteria that are based on known distributions. Its main objective is to be able to make an estimate of the data parameters that a population has carried out on a statistical sample.

#### Nonparametric statistics

Non-parametric statistics do not fit any distribution so they can be applied even if the validity conditions are not the best. This type of test is more valid as it can use a much wider range of situations.

## Method

The method that must be followed to be able to perform an inferential statistics is the following:

#### Pose a problem

This will be the first step and it is a fundamental part of all types of statistical study since it is the problem that marks the need to be able to determine and find the most appropriate solutions for the situation that arises. For its elaboration, it must start with a clear and precise objective as well as study and analyze the means that are available to be able to achieve the objectives .

#### Building a model

The elaboration of the model will generally require a previous study based on theories that help to solve the problem approach and the objectives that have been previously established.

#### Sample extraction

In this step, it is first necessary to carry out a population study which can be carried out using an experimental design in order to be able to collect valid information about the sample taken from the population.

#### Estimate the parameters

It is a very important part because through this step you can check if the observation made to the sample corresponds to what is being stated in the theory of the study.

#### Conclution

This is the last step and it is where all the results that have come out thanks to the study that have been carried out using the different techniques are collected . In this step, the best decisions will be determined to be able to solve the problem that has been raised.

## Basic concepts

Among the basic concepts that are used in inferential statistics, the following are mentioned:

• Summation : used to determine the sum of different terms.
• Frequency distribution : it is used when the data obtained are numerous and for this reason it is better to organize them in groups.
• Histogram of frequencies : these are the frequencies that are located on the graph and where the intervals are plotted.
• Measures of central tendency : is when some of the data collected is repeated more frequently than others and is in the central part of the graph.
• Population : it is the totality of the possible measurements that can be observed in a certain problem.
• Sample : is the set of observations that have been taken or observed in a certain population.

## How it differs from descriptive statistics

The main difference that can be found in these two types of statistics is in the nature of the data. Descriptive statistics is used both within a population and in the sample , while inferential statistics only works with the samples which it uses to draw conclusions. On the other hand, descriptive statistics summarize the long lists of data in order to obtain in this way a series of general characteristics in a group while inferential statistics analyzes and studies all the population data but using only one sample .

## Importance of inferential statistics

Inferential statistics is important for daily life as it is one of the best mechanisms to find solutions to finances , investments and they are also a basic and important point in studies of a scientific nature . It can help to recognize the risk of financial investments and to obtain vital data to support scientific studies .

## Examples

Some examples of inferential statistics are as follows:

• Polls for voting trends that are applied to collect relevant data and thus be able to determine which candidate is the favorite and who occupies the second and third place.
• Marketing analysis to analyze market niches through statistical tools such as surveys.
• In the area of medical epidemiology to be able to determine the concrete data of the affectation of a certain disease on a certain population.