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# Various statistical tests

A statistical test (or testing a hypothesis) consists of detecting significant differences:
• Between a studied and a target value (Comparison test of a theoretical value or a conformity test).
• Between two populations (Comparison test of a population or homogeneity test)
• Concerning the linking of two variables (correlation or association test)
• With respect to data compatibility in relation to a distribution law (adequacy test)
From a data sampling, the statistical test will calculate the probability of obtaining a certain sampling configuration by assuming that the data is:
• Compliant with the target in the case of a comparison test for a theoretical value
• Homogeneous in the case of a population comparison test
• Perfectly associated in the case of a correlation test
• Compliant with a distribution law in the case of an adequacy test.
This hypothesis is called a null hypothesis because it assumes that there is no difference between the data.
Here are the statistical tests that are mainly used:
Case studiesParametric tests
(hypothesise from a distribution law)
Non-parametric tests
(Does not make a hypothesis from a distribution)
Comparison with a theoretical value
Equality of a frequency to a valueTest 1 P
Average equal to a valueTheoretical test z
Theoretical test t
Run test
Sign test
Population comparison
Comparison of two paired populationsPaired t testPaired Wilcoxon test
Sign test
Comparison of the placement of 2 populationsz test
t test
B to C
Mann Whitney test
Comparison of the placement of k populationsANOVAKrustal-Wallis test
Comparison of two frequenciesTest 2P
Correlations
Correlation of 2 variablesR ² and student coefficientSpearman Coeft
Kendal Coeft
Correlation of k variables with a YMulti-linear regression

## Population comparison :

These tests allow for the comparison of several populations containing quantitative measurements among themselves. For example, batches produced by two different machines, the grades for different classes, etc...
Example 1: Does the red machine produce at a higher mean than the blue machine?
Example 2: You have take a sample of the grades in different maths classes. Are the grades of the different classes homogeneous on average and by variant?

### Frequency test

The frequency tests make it possible to compare the proportion of appearances of a phenomenon among several batches. For example, comparison of the proportion of defects between one production configuration and another.
Example 3: You received two batches from two different suppliers. With the data that you have available, can you tell if supplier A is significantly better than supplier B?
Example 4: According to the following results, is there a machining configuration that will significantly reduce the incidence of burs?
P = 0,02P = 0,04P = 0,06
Without burs252235
With burs621
Borderline430

### Comparison test of a theoretical value:

The comparison tests of a theoretical value enable the comparison of a population with a theoretical value.
Example 5: After measuring the following neutrino speed, can we say that they move at a speed significantly higher than the speed of light which is 299,000 km/s?
Example 6: Let us assume that there are 50% women in the population. In a company with 952 people, 440 are women and 512 are men. Is this a significant difference?

### Correlation test:

Correlation tests make it possible to verify if two quantitative variables seem linked.
Example 7: You measured the strength of a spring at a breaking point compared to the pressure at which it was produced. Does the pressure have an influence on the resistance of the spring?

### Multiple linear regression test:

Also called large table analysis...This analysis enables you to find the influential factors on your Y when you have a large table of data containing Y's as functions of X on each line.
Example 8: You want to maximize result A in regards to different parameters that you have highlighted. What are the significant factors and how can the result A be maximized:

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