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@ -2,10 +2,9 @@ Statistics
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=========================
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.. toctree::
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:maxdepth: 2
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:numbered:
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:maxdepth: 2
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introduction
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metrics
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dlkdd
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sd
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Statistics notes.
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@ -1,14 +1,11 @@
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Introduction
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==================
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Metrics
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----------------
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==================
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* **Expected value/Espérance**: Noted :math:`\mathbb{E}[X]`, is a **theorical value**. For example, when playing coin
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flipping, the expected value for getting heads or tails is 0.5.
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Variance
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^^^^^^^^^^^^^^
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------------------
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Variance can be seen as the expected squared deviation from the expected value of a random variable :math:`X`.
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@ -16,7 +13,7 @@ Variance can be seen as the expected squared deviation from the expected value o
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\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)
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Covariance
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^^^^^^^^^^^^^^
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------------------
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Covariance is a way to quantify the relationship between two random variables :math:`X` and
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:math:`Y` (`source <https://www.youtube.com/watch?v=qtaqvPAeEJY>`_). Covariance **DOES NOT**
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@ -33,7 +30,7 @@ Null
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\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}
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Standard deviation
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^^^^^^^^^^^^^^^^^^^^^
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-----------------------
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Standard deviation provides a way to interprete the variance using the unit of :math:`X`.
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@ -42,7 +39,7 @@ Standard deviation provides a way to interprete the variance using the unit of :
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Standard Error of the Mean
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^^^^^^^^^^^^^^^^^^^^^^^^^^^
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-----------------------------
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Standard Error of the Mean (SEM) quantifies the error that is potentially made when computing the mean.
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@ -72,7 +69,3 @@ Output example:
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----- Experiment 3 -----
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Means SD: 1.27
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SEM 1.26
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Degree of freedom
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-------------------
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