Before going into the details of parametric and non-parametric tests, let's look at how a statistical test works. The Ellistat Data Analysis module allows you to carry out these tests.

A statistical test works as follows:

- We consider a null hypothesis in which there is no difference between the samples.
- The probability of falling into the same configuration as that obtained with the samples observed under the null hypothesis is calculated. This probability is known as the "alpha risk" or "p-value".
- If alpha risk < 5%, it is considered too unlikely to obtain such a configuration under the null hypothesis. We therefore reject the null hypothesis and consider that the difference between the samples is significant. For this reason, all the results of the statistical tests proposed by Ellistat will be associated with an alpha risk value with the following scale:

- If alpha risk < 0.01, the difference will be considered highly significant<.
- If alpha risk < 0.05, the difference is considered significant
- If the alpha risk is less than 0.1, the difference is considered to be borderline (it cannot be said that there is a significant difference, but the hypothesis is interesting).
- If alpha risk > 0.1, the difference will be considered insignificant

## Example

## Throw n°1

On the face of it, it would be rather risky to bet that the coin is piped, as it could just as easily have happened with a standard coin.

In this case, the null hypothesis is: the coin is not tipped, so it has one chance in two of coming up heads or tails. The probability of an unpiped coin coming up heads is 50%.

As a result, the probability of getting tails after the first toss of an unpiped coin is 50%, so the alpha risk of the test is :

## Throw n°2

Does this mean that the game has been rigged?

So the question arises: at what alpha risk can we say that the coin has been tipped?

As a general rule, in industry, the alpha risk limit is set at 5%.

In other words :

- If the alpha risk is less than 5%, the null hypothesis is rejected and the coin is considered to be tipped.
- If the alpha risk is > 5%, it cannot be said that the coin is tipped. However, this does not mean that the coin is not piped, as this depends on the number of throws made.

## Example continued

^{th}Toss: coin lands on tails: alpha risk = 12.5%

^{th}Toss: coin lands on tails: alpha risk = 6.75%

^{th}Toss: coin lands on tails: alpha risk = 3.375%

^{th}We can therefore say that the coin is tipped with a risk of less than 5%.

## Parametric vs. non-parametric tests

When making population comparisons or comparing a population with a theoretical value, there are two main types of test: parametric tests and non-parametric tests.

## Parametric tests

## Non-parametric tests

## Here are the modules you can use to calculate these indicators:

### Data Analysis

Statistics in 1 click. Use the power of statistics to find out what's behind your production data from the SPC, APC or IQC modules. Thanks to its machine learning algorithms, the Data Analysis module can be used to understand the origin of machine drift or to differentiate suppliers statistically.