## Inference and its process

The etymological origin of the term inference, we must proceed to move to Latin. There we will find how that is the result of the sum of three clearly identifiable parts: the prefix *in* -, which can be translated as “towards”; the verb *ferre* , which can be established as a synonym for “carry,” and finally the suffix – *ia* , which is equivalent to “action or quality.”

Starting from **hypotheses** or **arguments** , it is possible to infer a **conclusion** (which may be true or false). For example: *“I still have not received the official confirmation from the company, what I tell you is just an inference from me”* , *“Every time the team plays, Mariana is missing work: my inference is that tomorrow we will be alone in the office ”* , *“ We cannot be guided by inferences, but we have to wait for the events to be confirmed before making a decision ”* .

**The 3 types of inference**

**1- Deduction**

Deduction is the process of deriving a conclusion from the axioms and facts given. That is, draw a conclusion based on available knowledge and observations.

The conclusion can be drawn by applying the *modus ponens* rule . This inference rule states that if it is known that both P and P → Q are true, it can be concluded that Q must also be true. Inference by deduction is also known as logical inference.

**Example**

Axiom: All mammals have mammary glands. Fact / premise: Whales are mammals. Conclusion: Whales have mammary glands.

**2- Induction**

On the other hand, induction implies deriving a general rule (also called axiom) from particular or specific observations.

This type of reasoning is the opposite of the deductive. Basically, it means extracting conclusions or inferences from various data, going from the specific to the general. Scientists use inductive reasoning to form hypotheses and theories.

**Example**

Data:

- Juan sleeps less than six hours and wakes up tired.
- Lucia sleeps less than six hours and wakes up tired.
- Maria sleeps less than six hours and wakes up tired.
- Carlos sleeps less than six hours and wakes up tired.

Inference: If a person sleeps less than six hours, he wakes up tired.

**3- Abduction**

This type of inference starts from an incomplete set of observations, resulting in the most likely explanation possible.

It is based on making and testing hypotheses using the best available information. It often involves making an assumption after observing a phenomenon for which there is no clear explanation.

**Example**

An example of this are medical diagnoses based on test results. Another example is the jurors’ decisions in the trials, based on the evidence presented to them.

### The inference process

To reach the previous conclusion, the person who would have answered this question has had to follow a process in which he must first read the text, then understand its content, reflect on the subject, remember previous knowledge and finally give his answer.

From here it can be said that the inference can be used in three different phases. There would be a first before receiving the information, in which simply by the context certain predictions or hypotheses could be formulated on the subject. Subsequently, while receiving the information it is already possible to formulate inferences or reformulate them if it is believed that they are wrong. And finally, once all the information has been received, it will be possible to differentiate between the explicit data received and the ideas that are inferred from it.

### Inferential statistics

In the field of mathematics and statistics, the term inference is also used to refer to the deductions we can make from observing a thing. More specifically, statistics can be divided into two main branches: descriptive and inferential. While the former basically deals with collecting, organizing and classifying data, inferential statistics studies the predictions that can be made from those data.

The predictions of this part of the statistics are made on sample groups that represent the total population, being very important to maintain a high degree of reliability and confidence in the methods used to study the data.

That is, inferential statistics would be the set of techniques that allow conclusions to be reached that exceed the limits of the knowledge obtained from the original data.

An example of this type of inference is the electoral surveys, where predictions of general results are made based on the data obtained from a small sample of the population.