add statistics draft

math/statistics.md

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+# Statistics
+
+## Definitions
+
+### Range
+
+```php
+ArrayUtils::range($values);
+```
+
+$$
+range = max(values) - min(values)
+$$
+
+### Mean (arithmetic)
+
+```php
+Average::mean($values);
+```
+
+$$
+mean = \frac{1}{n}\sum_{i=1}^{n}a_i
+$$
+
+## Variable types
+
+Variables are characteristics (i.e. height, weight)
+
+### Quantitive
+
+Quantitative variables represent a measer, they are numeric.
+
+#### Discrete
+
+Countable and finite possibilities/results/options.
+
+#### Continuous
+
+Not countable and infinite number of possibilities/results/options.
+
+### Qualitative
+
+Qualitative variables represent categories/levels, they are not numeric.
+
+#### Nominal
+
+Cannot be ordered, they have the same importance/level/value (i.e. hair color). A category can also by yes/no (= two levels).
+
+#### Ordinal
+
+Can be ordered, they have different importance/level/value (i.e. risk severity)
+
+### Transformation
+
+It is possible to transfrom variables:
+
+* Continuous to discrete: by removing steps in between (i.e. age only in years)
+* Quantitive to qualitive: by asigning numeric ranges a quality (i.e. school grades in pass and fail)
+
+## Tests
+
+### Chi-square
+
+#### Goodness of fit test
+
+#### Test of independence
+
+### t-test
+
+#### One sample
+
+#### Two samples
+
+#### Paired samples
+
+### Correlation
+
+#### Pearson correlation
+
+#### Spearman's rank correlation