diff --git a/source/statistics/index.rst b/source/statistics/index.rst index 75988cb..ee3e426 100644 --- a/source/statistics/index.rst +++ b/source/statistics/index.rst @@ -2,10 +2,9 @@ Statistics ========================= .. toctree:: - :maxdepth: 2 :numbered: + :maxdepth: 2 - introduction + metrics -dlkdd -sd +Statistics notes. diff --git a/source/statistics/introduction.rst b/source/statistics/metrics.rst similarity index 93% rename from source/statistics/introduction.rst rename to source/statistics/metrics.rst index f1f7691..b178e51 100644 --- a/source/statistics/introduction.rst +++ b/source/statistics/metrics.rst @@ -1,14 +1,11 @@ -Introduction -================== - Metrics ----------------- +================== * **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. Variance -^^^^^^^^^^^^^^ +------------------ 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) Covariance -^^^^^^^^^^^^^^ +------------------ Covariance is a way to quantify the relationship between two random variables :math:`X` and :math:`Y` (`source `_). 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} Standard deviation -^^^^^^^^^^^^^^^^^^^^^ +----------------------- 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 (SEM) quantifies the error that is potentially made when computing the mean. @@ -72,7 +69,3 @@ Output example: ----- Experiment 3 ----- Means SD: 1.27 SEM 1.26 - - -Degree of freedom --------------------