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::The variance of whole combined observations is
::<math>s^2=\frac{\sum_{i=1}^n (x_i-\bar{x})^2}{n-1}</math>
::The numarator is ''sum of square''
::<math>\sum_{i=1}^n (x_i-\bar{x})^2</math>
::<math>= \sum_{i=1}^n x_i^2 - 2\bar{x} \sum_{i=1}^n x_i + \bar{x}^2 \sum_{i=1}^n 1</math>
-->
→Basic concept of statistical tests
{{Epi StatFloating_Menu}} ==Basic concept of statistical tests==*First remind that**Statistical test is to test
==Comparing Proportions==
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*'''Paired Student's t test'''
::''<math>H_0</math> is '''mean of paired differences''' in the population is '''zero'''.''
::<math>
\begin{align}
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*'''Wilcoxon rank sum test'''<br>='''Mann-Whitney test'''
::''<math>H_0</math> is distribution '''medians or means of outcomes ranks''' in both the two population'''s''' are the same''
:#To rank whole combined observations of two groups
:#To separate back the ranks into two groups
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*'''Wilcoxon signed rank test'''
::''<math>H_0</math> is '''median of paired differences''' in the population is zero''
:#To calculate differences between pairs and discard 0 differences
:#To rank the absolute values of differences (ignoring 0)
::<math>n</math> is sample size (whole combined number of observations)
::<math>k</math> is number of groups
<!--
::The variance of whole combined observations is
::<math>s^2=\frac{\sum_{i=1}^n (x_i-\bar{x})^2}{n-1}</math>
::The numarator is ''sum of square''
::<math>\sum_{i=1}^n (x_i-\bar{x})^2</math>
::<math>= \sum_{i=1}^n x_i^2 - 2\bar{x} \sum_{i=1}^n x_i + \bar{x}^2 \sum_{i=1}^n 1</math>
-->
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*'''Kruskall-Wallis test'''
::''<math>H_0</math> is distribution '''medians or means of outcomes ranks''' in the all population'''s''' are the same''
:#To rank whole combined observations of all groups
:#To separate back the ranks into original groups
*<nowiki>*</nowiki>''needs try to transform data into parametric (e.g., logarithmic), or other considerations''
|}
==Comparing Survival time==
{|class="wikitable"
|-
!style="width:50%"|Life table
!style="width:50%"|Kaplan-Meyer
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*'''Log rank test<br>= Mantel-Cox <math>\chi^2</math> test'''
::<math>H_0</math> is event (survival) rates in each interval are all the same in two groups
::<math>Log\ rank\ statistics = \frac{}{}</math>
|}
