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Loic Guegan 2023-10-14 19:21:10 +02:00
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7
source/statistics/index.rst
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@ -2,10 +2,9 @@ Statistics
========================= =========================
.. toctree:: .. toctree::
:maxdepth: 2
:numbered: :numbered:
:maxdepth: 2
introduction metrics
dlkdd Statistics notes.
sd

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source/statistics/introduction.rst → source/statistics/metrics.rst
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@ -1,14 +1,11 @@
Introduction
==================
Metrics Metrics
---------------- ==================
* **Expected value/Espérance**: Noted :math:`\mathbb{E}[X]`, is a **theorical value**. For example, when playing coin * **Expected value/Espérance**: Noted :math:`\mathbb{E}[X]`, is a **theorical value**. For example, when playing coin
flipping, the expected value for getting heads or tails is 0.5. flipping, the expected value for getting heads or tails is 0.5.
Variance Variance
^^^^^^^^^^^^^^ ------------------
Variance can be seen as the expected squared deviation from the expected value of a random variable :math:`X`. Variance can be seen as the expected squared deviation from the expected value of a random variable :math:`X`.
@ -16,7 +13,7 @@ Variance can be seen as the expected squared deviation from the expected value o
\mathbb{V}[X]=\mathbb{E}[X-\mathbb{E}[X]]^2=\frac{\sum_{i=1}^n (x_i - \mathbb{E}[X])^2}{n}=\mathrm{Cov}(X,X) \mathbb{V}[X]=\mathbb{E}[X-\mathbb{E}[X]]^2=\frac{\sum_{i=1}^n (x_i - \mathbb{E}[X])^2}{n}=\mathrm{Cov}(X,X)
Covariance Covariance
^^^^^^^^^^^^^^ ------------------
Covariance is a way to quantify the relationship between two random variables :math:`X` and Covariance is a way to quantify the relationship between two random variables :math:`X` and
:math:`Y` (`source <https://www.youtube.com/watch?v=qtaqvPAeEJY>`_). Covariance **DOES NOT** :math:`Y` (`source <https://www.youtube.com/watch?v=qtaqvPAeEJY>`_). Covariance **DOES NOT**
@ -33,7 +30,7 @@ Null
\mathrm{Cov}(X,Y)=\mathbb{E}[(X-\mathbb{E}[X])(Y-\mathbb{E}[Y])]=\frac{\sum_{i=1}^n (x_i - \mathbb{E}[X])(y_i - \mathbb{E}[Y])}{n} \mathrm{Cov}(X,Y)=\mathbb{E}[(X-\mathbb{E}[X])(Y-\mathbb{E}[Y])]=\frac{\sum_{i=1}^n (x_i - \mathbb{E}[X])(y_i - \mathbb{E}[Y])}{n}
Standard deviation Standard deviation
^^^^^^^^^^^^^^^^^^^^^ -----------------------
Standard deviation provides a way to interprete the variance using the unit of :math:`X`. Standard deviation provides a way to interprete the variance using the unit of :math:`X`.
@ -42,7 +39,7 @@ Standard deviation provides a way to interprete the variance using the unit of :
Standard Error of the Mean Standard Error of the Mean
^^^^^^^^^^^^^^^^^^^^^^^^^^^ -----------------------------
Standard Error of the Mean (SEM) quantifies the error that is potentially made when computing the mean. Standard Error of the Mean (SEM) quantifies the error that is potentially made when computing the mean.
@ -72,7 +69,3 @@ Output example:
----- Experiment 3 ----- ----- Experiment 3 -----
Means SD: 1.27 Means SD: 1.27
SEM 1.26 SEM 1.26
Degree of freedom
-------------------