差分

{{Floating_Menu}} ==Basic concept of statistical tests==*First remind that**Statistical test is to test ==Comparing Proportions==

!colspanstyle="2width:80px"|comparisons!style="width:200px250px"|Independent samples<br>(Unpaired in case of two)!style="width:200px250px"|Dependent samples<br>(Paired in case of two)

!rowspan="4" style="width:80px"|Propotions! style="width:40px"|2proportions

!rowspan="3"|&ge; 3 or moreproportions

==Comparing Means==

!colspanrowspan="2" rowspanstyle="2width:80px"|comparisons

!style="width:200px250px"|Independent samples<br>(Unpaired in case of two)!style="width:200px250px"|Dependent samples<br>(Paired in case of two)!style="width:200px250px"|Independent samples<br>(Unpaired in case of two)!style="width:200px250px"|Dependent samples<br>(Paired in case of two)|- style="vertical-align:top"!rowspan="2" style="width:80px"|Means!style="width:40px3"|2means |''Enough large sample''

 |rowspan="3" style="vertical-align:top"|*'''Paired Student's t test'''::''<math>H_0</math> is '''mean of paired differences''' in the population is '''zero'''.''::<math>\begin{align}paired\ t & = \frac{\bar{d}}{SE_d} \\& = \frac{\bar{d}}{\frac{s}{\sqrt{n}}} \\\end{align}</math>::where <math>\bar{d}</math> is the mean of differences of paired observations |rowspan="3" style="vertical-align:top"|*'''Wilcoxon rank sum test'''<br>='''Mann-Whitney test'''::''<math>H_0</math> is '''medians or means of ranks''' in the two population'''s''' are the same'':#To rank whole combined observations of two groups:#To separate back the ranks into two groups:#To look up ''critical range'' relevant to both numbers of observations and whether '''the sum of ranks''' in '''the group of smaller number of observation''' (=statistics) is outside the range or not::if outside the range, p-value is smaller than designated |rowspan="3" style="vertical-align:top"|*'''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):#To make the sum of ranks of '''positive difference''' and the sum of ranks of '''negative differences''' ('signed rank'):#To look up '''critical value''' relevant to numbers of pairs with non-0 differences and whether '''the smaller sum of rank''' (=statistics) is smaller than the critical value::if smaller than the critical value, p-value is smaller than designated |-|''Small sample size <30 in a group''

 |-|''Large discrepancy in SDs between groups''*'''Bootstrap'''*'''Non-parametric'''*'''Fisher-Behrens'''*'''Welch''' |-!&ge; 3 means|style="vertical-align:top"|*'''Paired Student's t testOne-way ANOVA'''

paired\ t F & = \frac{\sum_{j=1}^k \sum_{j=1}^{n_j} (x_{ij}-\bar{dx_j})^2 }{SE_dk-1 } \\& = \div \frac{\barsum_{dj=1}}{^k (\fracbar{sx_j}{-\sqrtbar{nx})^2 }{ n-k } \\

::where <math>\bar{d}n</math> is the mean of differences sample size (whole combined number of paired observations)|::<math>k</math> is number of groups*'''Wilcoxon rank sum test'''**AKA '''Mann<!--Whitney test'''|::The variance of whole combined observations is *'''Wilcoxon signed rank test'''::<math>s^2=\frac{\sum_{i=1}^n (x_i-\bar{x})^2}{n-1}</math>**here ::The numarator is 'signed' means sum of square'take into account signs of differences of paired data'|::<math>\sum_{i=1}^n (x_i-\bar{x})^2</math>!3 or more::<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>|-->*'''ANOVA'''|style="vertical-align:top"|*'''Linear-regression model'''

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::''<math>H_0</math> is '''medians or means of 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:#To make sum of ranks in each group::<math>H = \frac{n-1}{n} \sum_{i=1}^k \frac{n_i(\bar{R}-E_R)}{s^2}</math>::<math>H</math> is Kruskal-Wallis statistics::<math>n_i</math> is number of observations in group <math>i</math>::<math>\bar{R}</math> is the mean of rank sum in group <math>i</math>::<math>E_R</math> is expected value of the rankings::<math>s^2</math> is the variance of rank::To look up ''critical values'' relevant to '''sum of ranks''' in '''the group of smaller number of observation'''|style="vertical-align:top"|*<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|-|colspan="2"|*'''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>