# StatEL : Test of distribution normality

Several normality tests are available. Choose the most convenient test, according to nature of your data. Normality distribution of your data may affect validity of statistic test you will have to practice.

# 1 - Shapiro - Wilks' W test :

## 1.1 - Principles of Shapiro-Wilks' W test :

This normality test is convenient for low effectives (<50). Its principle is based on comparaison of 2 values T1 and T2 which each estimate variance of the sample under hypothesis of normal distribution.

Data are ranked and coefficient an(i) is specified in a statistic table.

W value is compared to critical values from the Shapiro - Wilks' table.

## 1.2 - How to use Shapiro-Wilks' W test with StatEL :

StatEL just requires that you select the cells range related to data whose you want to test normality distribution. To proceed the selection, you just have to clic on the first cell of your data with the mouse and to stretch until the last cell of your data.

If you did wrong, you just have to try again, new selection will erase references of previous selection.

Results display on a new sheet of your Excel file :

A "Whiskers plot" is automatically drawn to illustrate results :

# 2 - Khi² test for normality :

## 2.1 - Principles of Khi² test :

This test is made for analysis of important effectives (>50). Total effective is divided in K different classes and we compare observed effectives on each class with theoretical effectives, calculated under normality hypothesis.

Calculated Khi² is then compared to the limit value from the Khi² table.

Nota bene : classes are gathered when theoretical effectives are lower than 5 (condition to use the test). If, in spite of gathering, theoretical effectives are still lower than 5, test is not valid which is notified by a red message in the conclusions of results sheet.

## 2.2 - How to use Khi² test for normality :

As for the Shapiro - Wilks' W test (cf. above), StatEL just requires that you select the cells range related to data whose you want to test normality distribution. To proceed the selection, you just have to clic on the first cell of your data with the mouse and to stretch until the last cell of your data.

If you did wrong, you just have to try again, new selection will erase references of previous selection.

Results display on a new sheet of your Excel file :

A "Whiskers plot" and 2 graphs about data distribution are automatically drawn to illustrate results :

# 3 - Kolmogorov - Smirnov test :

## 3.1 - Principles of Kolmogorov - Smirnov test :

The Kolmogorov - Smirnof test is used to compare an observed distribution with a theoretical normal distribution. Thus, we calculate the gaps between observed value of the repartition function and the theoretical value under hypothesis of normality. We reject hypothesis of normality if at least one of the gaps is higher than the limit value supplied by the Kolmogorov - Smirnov table.

## 3.2 - How to use Kolmogorov - Smirnov test :

As for the Shapiro - Wilks' W test and Khi² test for normality (cf. above), StatEL just requires that you select the cells range related to data whose you want to test normality distribution. To proceed the selection, you just have to clic on the first cell of your data with the mouse and to stretch until the last cell of your data.

If you did wrong, you just have to try again, new selection will erase references of previous selection.

Then you have to specify characteristics (mean and standard-deviation) of the theoretical normal distribution.

Results display on a new sheet of your Excel file :

A "Whiskers plot" and a graph about data distribution are automatically drawn to illustrate results :

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