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Adjustment tests identify the law our data follows.

## Introduction

Adjustment tests are statistical tests to determine that it is the most appropriate law for data. This allows us subsequently to :

• Predetermine the behavior of the studied system.
• Choose the best test to compare samples.

## Choose the fit test

There are a multitude of adjustment tests, from the simplest to the most complex. The table below proposes a classification of these tests according to the objective and the type of data. :

 Test the normality Test at a different law Anderson Darling Test de Lilliefors Shapiro Wilk Normal probability plot Kolmogorov Smirnov : n1 and n2 > 30 and similar χ2 : the best for small samples The normality of the data being an important condition in most statistical tools (hypothesis tests, control cards …), we advise to check this condition with several tests, making sure that all the tests validate or invalidate this condition.

## Other solutions

In the case where we have non-normal data but we want to use tests or tools requiring normality, we have 2 choices :

• Try to understand why our data is not normal. Was there a specific event ? have we collect the data correctly ?
• Second solution but not recommended, we can transform the variables. For this, there are different techniques (transformed Johnson …) but we will use the Box-Cox transform :

The goal of this transformation is to take our data and apply the following formula :  λ is a parameter that must be varied in steps of 0,1 to – 10 à 10. This parameter will be varied until we find our transformed data closest to the normal distribution. Once validated, we will apply the same formula with our comparison limits.

By ensuring that this technique worked, a normality test is performed with the transformed data.

## Source

F. Bergeret, S. Mercier (2011) – Maîtrise statistique des procédés – Principes et cas industriels

A. Grous (2013) – Eléments d’analyse de la fiabilité et du contrôle qualité