# 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