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ページの作成:「==Proportions== {|class="wikitable" |- !colspan="2"|comparisons !style="width:200px"|Independent samples<br>(Unpaired in case of two) !style="width:200px"|Dependent sampl…」
==Proportions==
{|class="wikitable"
|-
!colspan="2"|comparisons
!style="width:200px"|Independent samples<br>(Unpaired in case of two)
!style="width:200px"|Dependent samples<br>(Paired in case of two)
|-
!rowspan="4" style="width:80px"|Propotions
! style="width:40px"|2
|
*'''Z test'''
::<math>
\begin{align}
z & = \frac{p_1-p_2}{SE_{pooled(p_1-p_2)}} \\
& = \frac{p_1-p_2}{\sqrt{\frac{\bar{p}(1-\bar{p})}{n_1}+\frac{\bar{p}(1-\bar{p})}{n_2}}}
\end{align}
</math>
|
|-
!rowspan="3"|3 or more
|''Enough large sample''
*'''<math>\chi^2</math> test'''
::<math>\chi^2 = \sum \frac{(O - E)^2}{E}</math>
::<math>O</math> = observed values<br><math>E</math> = expected values
|rowspan="3" style="vertical-align:top"|
*'''McNemar's <math>\chi^2</math> test'''
::<math>
\begin{align}
& McNemar's\ \chi^2 \\
& = \frac{(n_1-n_2)^2}{n_1+n_2}
\end{align}
</math>
::<math>n_i</math> = number of observations in discordant pair
|-
|''Testing linear association''
*'''<math>\chi^2</math> trend test'''
::<math>
\begin{align}
& \chi^2 trend \\
& = \frac{(\bar{x_1}-\bar{x_2})^2}{s^2(\frac{1}{n_1}+\frac{1}{n_2})} \\
& s = \sqrt{\sum \frac{(x_i-\bar{x_i})^2}{n-1}}
\end{align}
</math>
::<math>x_i</math> = weighted values
::<math>n_i</math> = number of observations
|-
|''≥1 cell expected value <5''
'''Fisher's exact test'''
*very rare in real researches
|}
==Means==
{|class="wikitable"
!colspan="2" rowspan="2"|comparisons
!colspan="2"|Parametric<br>i.e., normally distributed
!colspan="2"|Non-parametric<br>i.e., not normally distributed
|-
!style="width:200px"|Independent samples<br>(Unpaired in case of two)
!style="width:200px"|Dependent samples<br>(Paired in case of two)
!style="width:200px"|Independent samples<br>(Unpaired in case of two)
!style="width:200px"|Dependent samples<br>(Paired in case of two)
|- style="vertical-align:top"
!rowspan="2" style="width:80px"|Means
!style="width:40px"|2
|
''Enough large sample''
*'''Z test'''
::<math>
\begin{align}
z & = \frac{\bar{x_1}-\bar{x_2}}{SE_{(\bar{x_1}-\bar{x_2})}} \\
& = \frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}
\end{align}
</math>
''Small sample size <30 in a group''
*'''Student's t test'''
::<math>
\begin{align}
t & = \frac{\bar{x_1}-\bar{x_2}}{SE_{(\bar{x_1}-\bar{x_2})}} \\
& = \frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{(n_1-1)+(n_2-1)}}\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}
\end{align}
</math>
''Large discrepancy in SDs between groups''
*'''Bootstrap'''
*'''Non-parametric'''
*'''Fisher-Behrens'''
*'''Welch'''
|
*'''Paired Student's t test'''
::<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
|
*'''Wilcoxon rank sum test'''
**AKA '''Mann-Whitney test'''
|
*'''Wilcoxon signed rank test'''
**here 'signed' means 'take into account signs of differences of paired data'
|-
!3 or more
|
*'''ANOVA'''
|
*'''Linear-regression model'''
*Repeated measures ANOVA
|
*'''Kruskall-Wallis test'''
|
<nowiki>*</nowiki>needs try to transform data into parametric (e.g., logarithmic), or other considerations
|}
{|class="wikitable"
|-
!colspan="2"|comparisons
!style="width:200px"|Independent samples<br>(Unpaired in case of two)
!style="width:200px"|Dependent samples<br>(Paired in case of two)
|-
!rowspan="4" style="width:80px"|Propotions
! style="width:40px"|2
|
*'''Z test'''
::<math>
\begin{align}
z & = \frac{p_1-p_2}{SE_{pooled(p_1-p_2)}} \\
& = \frac{p_1-p_2}{\sqrt{\frac{\bar{p}(1-\bar{p})}{n_1}+\frac{\bar{p}(1-\bar{p})}{n_2}}}
\end{align}
</math>
|
|-
!rowspan="3"|3 or more
|''Enough large sample''
*'''<math>\chi^2</math> test'''
::<math>\chi^2 = \sum \frac{(O - E)^2}{E}</math>
::<math>O</math> = observed values<br><math>E</math> = expected values
|rowspan="3" style="vertical-align:top"|
*'''McNemar's <math>\chi^2</math> test'''
::<math>
\begin{align}
& McNemar's\ \chi^2 \\
& = \frac{(n_1-n_2)^2}{n_1+n_2}
\end{align}
</math>
::<math>n_i</math> = number of observations in discordant pair
|-
|''Testing linear association''
*'''<math>\chi^2</math> trend test'''
::<math>
\begin{align}
& \chi^2 trend \\
& = \frac{(\bar{x_1}-\bar{x_2})^2}{s^2(\frac{1}{n_1}+\frac{1}{n_2})} \\
& s = \sqrt{\sum \frac{(x_i-\bar{x_i})^2}{n-1}}
\end{align}
</math>
::<math>x_i</math> = weighted values
::<math>n_i</math> = number of observations
|-
|''≥1 cell expected value <5''
'''Fisher's exact test'''
*very rare in real researches
|}
==Means==
{|class="wikitable"
!colspan="2" rowspan="2"|comparisons
!colspan="2"|Parametric<br>i.e., normally distributed
!colspan="2"|Non-parametric<br>i.e., not normally distributed
|-
!style="width:200px"|Independent samples<br>(Unpaired in case of two)
!style="width:200px"|Dependent samples<br>(Paired in case of two)
!style="width:200px"|Independent samples<br>(Unpaired in case of two)
!style="width:200px"|Dependent samples<br>(Paired in case of two)
|- style="vertical-align:top"
!rowspan="2" style="width:80px"|Means
!style="width:40px"|2
|
''Enough large sample''
*'''Z test'''
::<math>
\begin{align}
z & = \frac{\bar{x_1}-\bar{x_2}}{SE_{(\bar{x_1}-\bar{x_2})}} \\
& = \frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}
\end{align}
</math>
''Small sample size <30 in a group''
*'''Student's t test'''
::<math>
\begin{align}
t & = \frac{\bar{x_1}-\bar{x_2}}{SE_{(\bar{x_1}-\bar{x_2})}} \\
& = \frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{(n_1-1)+(n_2-1)}}\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}
\end{align}
</math>
''Large discrepancy in SDs between groups''
*'''Bootstrap'''
*'''Non-parametric'''
*'''Fisher-Behrens'''
*'''Welch'''
|
*'''Paired Student's t test'''
::<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
|
*'''Wilcoxon rank sum test'''
**AKA '''Mann-Whitney test'''
|
*'''Wilcoxon signed rank test'''
**here 'signed' means 'take into account signs of differences of paired data'
|-
!3 or more
|
*'''ANOVA'''
|
*'''Linear-regression model'''
*Repeated measures ANOVA
|
*'''Kruskall-Wallis test'''
|
<nowiki>*</nowiki>needs try to transform data into parametric (e.g., logarithmic), or other considerations
|}
