# 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.