diff --git a/source/conf.py b/source/conf.py index ff3415f..e03cb71 100644 --- a/source/conf.py +++ b/source/conf.py @@ -6,7 +6,7 @@ # -- Project information ----------------------------------------------------- # https://www.sphinx-doc.org/en/master/usage/configuration.html#project-information -project = 'ScienceNotes' +project = 'Science Notes' copyright = '2023, Loïc Guégan' author = 'Loïc Guégan' release = '0.1' diff --git a/source/index.rst b/source/index.rst index 5bf2380..7f85282 100644 --- a/source/index.rst +++ b/source/index.rst @@ -8,9 +8,13 @@ Welcome to ScienceNotes's documentation! .. toctree:: :maxdepth: 2 - :caption: Contents: + :numbered: + :caption: Statistics - statistics/index + statistics/notations + statistics/metrics + statistics/bessel_correction + statistics/bayes_theorem Indices and tables diff --git a/source/statistics/index.rst b/source/statistics/index.rst deleted file mode 100644 index fd0977a..0000000 --- a/source/statistics/index.rst +++ /dev/null @@ -1,13 +0,0 @@ -Statistics -========================= - -.. toctree:: - :numbered: - :maxdepth: 2 - - notations - metrics - bessel_correction - bayes_theorem - -Statistics notes. diff --git a/source/statistics/metrics.rst b/source/statistics/metrics.rst index 7cdf2e1..8469c18 100644 --- a/source/statistics/metrics.rst +++ b/source/statistics/metrics.rst @@ -12,7 +12,7 @@ occurring we have: .. math:: \mathbb{E}[X]=x_1p_1+x_2p_2+\cdots+x_np_n -When working with a sample, the following is an unbiased estimator of the expected value (`source `_): +When working with a sample, the following is an unbiased estimator of the expected value (`source `__): .. math:: \overline{x}=\frac{\sum_{i=1}^n x_i}{n} @@ -36,7 +36,7 @@ Covariance ------------------ Covariance is a way to quantify the relationship between two random variables :math:`X` and -:math:`Y` (`source `_). Covariance **DOES NOT** +:math:`Y` (`source `__). Covariance **DOES NOT** quantify how strong this correlation is! If covariance is: Positive @@ -72,6 +72,10 @@ Standard Error of the Mean (SEM) quantifies the error that is potentially made w .. math:: \mathrm{SEM}=\sigma_X^{-}=\sqrt{\frac{\mathbb{V}[X]}{n}}=\frac{\sigma}{\sqrt{n}} +When working with a sample of :math:`n` individuals, an estimator of the SEM is: + +.. math:: + s_{\overline{x}}=\frac{s}{\sqrt{n}} Here is how to interpret it. If :math:`n=1`, the error is at most :math:`\sqrt{\mathbb{V}[X]}=\sigma_X` which is the standard deviation or :math:`X`. @@ -96,11 +100,6 @@ Output example: ----- Experiment 3 ----- Means SD: 1.27 SEM 1.26 - -When working with a sample of :math:`n` individuals, an estimator of the SEM is: - -.. math:: - s_{\overline{x}}=\frac{s}{\sqrt{n}} Degree of Freedom --------------------