diff --git a/source/statistics/bessel_correction.rst b/source/statistics/bessel_correction.rst new file mode 100644 index 0000000..48d1df3 --- /dev/null +++ b/source/statistics/bessel_correction.rst @@ -0,0 +1,4 @@ +Bessel's Correction +----------------------- + +TODO diff --git a/source/statistics/degree_of_freedom.rst b/source/statistics/degree_of_freedom.rst deleted file mode 100644 index 07b872c..0000000 --- a/source/statistics/degree_of_freedom.rst +++ /dev/null @@ -1,4 +0,0 @@ -Degree of Freedom -=================== - -BAM diff --git a/source/statistics/index.rst b/source/statistics/index.rst index c260514..5ea0cae 100644 --- a/source/statistics/index.rst +++ b/source/statistics/index.rst @@ -6,6 +6,6 @@ Statistics :maxdepth: 2 metrics - degree_of_freedom + bessel_correction Statistics notes. diff --git a/source/statistics/metrics.rst b/source/statistics/metrics.rst index d738d36..fee9adf 100644 --- a/source/statistics/metrics.rst +++ b/source/statistics/metrics.rst @@ -70,3 +70,32 @@ Output example: ----- Experiment 3 ----- Means SD: 1.27 SEM 1.26 + +Degree of Freedom +-------------------- + +The degree of freedom is a quantity defined for a given computation. +It corresponds to the number of parameters that are allowed to vary in that computation. +In other words, how many varying values are contributing to the computation. +For example, when computing the mean of a random variable :math:`X={x_1,...,x_n}`, there are :math:`n` parameters +that are allowed to change in the following formula: + +.. math:: + \overline{x}=\frac{\sum_{i=1}^n x_i}{n} + +Thus, the degree of freedom in this computation is :math:`n`. +When computing the standard deviation of :math:`X`, we have: + +.. math:: + \hat{\sigma}_x=\frac{\sum_{i=0}^n (x_i-\overline{x})^2}{n} + +In this case, the degree of freedom is :math:`n-1`. As the mean is already known, only :math:`n-1` +of the :math:`x_i` are allowed to vary. By knowing :math:`n-1` of the :math:`x_i`, we can deduce the last +one as follow: + +.. math:: + \overline{x}=\frac{(\sum_{i=1}^{n-1} x_i) + x_n}{n} \Longrightarrow x_n = n\overline{x} - (\sum_{i=1}^{n-1} x_i) + + + +