**Inferential statistics aim to describe a population from a sample and thus to perform «**

*inference*».## Introduction

Inferential statistics are used to describe a population from a ^{ 1 } sample and thus to make “inferences” . There are many statistical tools to choose from according to the objectives of the study, the type of data, distribution laws…

By definition, “* an inference is an operation by which one passes from one truth to another, judged as such according to its link with the first”*. In other words, inferential statistics, unlike descriptive statistics, aim to derive a general behavior according to the individual or according to another series of data..

## 1. Calculate sample size

First step, calculate the **sample size** to collect to ensure a good representation of the population.

## 2. Collect data

The **data collection** must be done according to a predetermined protocol adapt to the context and objective of the study.

## 3. Calculate the characteristics

The different coefficients related to **descriptive statistics** : pmiddle arameter, variance and extended. This gives an idea of the data collected and indications on the prospects of the study.

## 4. Identify the law of data distribution

Whatever the purpose of the study, the law of data distribution is an essential element that will guide the choice of statistical tools. It is necessary that :

- Set up a
**distribution graph** - Interpret the result a priori
- Set up a
**fit test** - Deduce the distribution law

## 5. Analyze data according to your goal

### Estimate a proportion, a standard deviation or an average of a population

From a sample of a population, we want to estimate its mean, standard deviation or proportion. For example, in the sample, we find 10% of default. We want to know what is the proportion of the entire population. For this, we use an estimation by **confidence interval**.

### Compare groups of data of identical variables

We want to compare different populations of the same variable. This is particularly the case when one wants to know if the results of an action bear fruit. Data is compared before / after improvements. Then we identify if the two populations are significantly different or not. & Nbsp; For this, use the **hypothesis testing**.

### Studying correlations and / or predicting behaviors between groups of data of different variables

It is desired to compare data to understand cause-and-effect relationships. One thus seeks to study the influence of one or more variables on one or more others and to set up a model which makes it possible to predict the behavior of this one. Different tools are used depending on the type of data :

Variable expliquée Y |
|||
---|---|---|---|

Quantitative continue et discrète | Qualitative nominale et ordinale |
||

Variable explicative X | Quantitative continue ou discrète | Exemple : X : Diamètre d'un arbre Y : Hauteur d'un arbre | Exemple : X : Taille Y : Couleur des cheveux |

Qualitative | Exemple : X : Traitement pharmacologique Y : Taux de globules blancs | Exemple : X : Port de la ceinture de sécurité Y : Gravité des blessures |

## 6. Perform the study

For the continuation, it is enough to follow the process of course of the chosen tool.

## 7. Calculate the significance and conclude

Regardless of the statistical tool used and the type of study, the role of the statistician is to ensure that the result obtained is significantly viable. In other words,

Is the result obtained real or only due to chance?

For this, we use a **Hypothesis test**.

## Source

1 – C. P. Dancey, J. reidy (2007) – Statistiques sans maths pour psychologues

J. P. Oriol (2007) – Formation à la statistique par la pratique d’enquêtes par questionnaires et simulation

A. Baccini (2010) – Statistique descriptive élémentaire

T. Lorino (2005) – Probabilités et statistique

S. Robin (2007) – Régression linéaire simple