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