Beispiele zu 2x2 exakten Tests (Fisher, Boschloo, CSM, exakte z-Tests) inkl. post-hoc Poweranalyse

In diesem Video zeige ich 3 Beispiele für exakte Tests bei 2x2-Kontingenztafeln inkl. einer post-hoc Poweranalyse und der näherungsweisen Berechnung des benötigten Stichprobenumfangs; mit kritischen Anmerkungen zur Poweranalyse.

R-Statistics: https://www.r-project.org
R-package "Exact": https://www.rdocumentation.org/packag...
R-package "Exact2x2": https://www.rdocumentation.org/packag...

R-Skript: Beipsiel 1 - Ziehen ohne Zurücklegen
data = matrix(c(2,1,1,16), nrow=2)
rownames(data) = c("gezogen", "nicht_gezogen")
colnames(data) = c("rot", "schwarz")
addmargins(data)
#
library(Exact)
chisq.test(data)
fisher.test(data, alternative="two.sided")
exact.test(data, "two.sided", method="boschloo")
exact.test(data, "two.sided", method="z-pooled")
exact.test(data, "two.sided", method="z-unpooled")
exact.test(data, "two.sided", method="CSM")
#
library(pwr)
pwr.chisq.test(w=sqrt(3.391/20), df=1, N=20, sig.level=0.05, power=NULL)
power.exact.test(p1=2/3, p2=1/17, n1=3, n2=17, "two.sided", alpha=.05, method="Fisher")
power.exact.test(p1=2/3, p2=1/17, n1=3, n2=17, "two.sided", alpha=.05, method="Boschloo")
power.exact.test(p1=2/3, p2=1/17, n1=3, n2=17, "two.sided", alpha=.05, method="z-pooled")
power.exact.test(p1=2/3, p2=1/17, n1=3, n2=17, "two.sided", alpha=.05, method="z-unpooled")
power.exact.test(p1=2/3, p2=1/17, n1=3, n2=17, "two.sided", alpha=.05, method="CSM")
#
library(exact2x2)
p0 = .66667
p1 = .05882
ss2x2(p0, p1, sig.level=0.05, power=.80, "two.sided")
###

R-Skript: Beipsiel 2 - Gartenkresse
data = matrix(c(12, 7, 3, 8), nrow=2)
rownames = c("feucht", "normal")
colnames = c("gekeimt", "nicht_gekeimt")
addmargins(data)
#
library(Exact)
chisq.test(data)
fisher.test(data, alternative="greater")
exact.test(data, "greater", method="boschloo")
exact.test(data, "greater", method="z-pooled")
exact.test(data, "greater", method="z-unpooled")
exact.test(data, "greater", method="CSM")
#
library(pwr)
pwr.chisq.test(w=sqrt(2.2967/30), df=1, N=30, sig.level=0.1, power=NULL)
power.exact.test(p1=12/15, p2=7/15, n1=15, n2=15, "greater", alpha=.05, method="Fisher")
power.exact.test(p1=12/15, p2=7/15, n1=15, n2=15, "greater", alpha=.05, method="Boschloo")
power.exact.test(p1=12/15, p2=7/15, n1=15, n2=15, "greater", alpha=.05, method="z-pooled")
power.exact.test(p1=12/15, p2=7/15, n1=15, n2=15, "greater", alpha=.05, method="z-unpooled")
power.exact.test(p1=12/15, p2=7/15, n1=15, n2=15, "greater", alpha=.05, method="CSM")
###

R-Skript: Beipsiel 3 - Lasterleben
data = matrix(c(15,30,23,18), nrow=2)
rownames = c("Rauch_ja", "Rauch_nein")
colnames = c("Alk_ja", "Alk_nein")
addmargins(data)
#
library(Exact)
chisq.test(data)
fisher.test(data, "two.sided")
exact.test(data, "two.sided", model="multinomial", method="boschloo")
exact.test(data, "two.sided", model="multinomial", method="z-pooled")
exact.test(data, "two.sided", model="multinomial", method="z-unpooled")
#
library(pwr)
pwr.chisq.test(w=sqrt(3.6321/86), df=1, N=86, sig.level=0.05, power=NULL)
power.exact.test(p1=15/38, p2=30/48, n1=38, n2=48, "two.sided", alpha=.05, method="Fisher")
power.exact.test(p1=15/38, p2=30/48, n1=38, n2=48, "two.sided", alpha=.05, method="Boschloo")
power.exact.test(p1=15/38, p2=30/48, n1=38, n2=48, "two.sided", alpha=.05, method="z-pooled")
power.exact.test(p1=15/38, p2=30/48, n1=38, n2=48, "two.sided", alpha=.05, method="z-unpooled")
###

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