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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Module--
Title produced by softwareChi-Squared Test, McNemar Test, and Fisher Exact Test
Date of computationWed, 13 Nov 2013 15:53:59 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/13/t1384376046yt5x640902968u7.htm/, Retrieved Tue, 10 Feb 2026 13:19:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=225020, Retrieved Tue, 10 Feb 2026 13:19:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact381

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Chi-Squared and McNemar Tests] [] [2010-11-16 14:44:39] [b98453cac15ba1066b407e146608df68]
- RMP     [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [ws] [2013-11-13 20:53:59] [4c736a442787d42e94a9d9bc48424aaa] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
'A'	'A'	'D'	'A'	'B'	'B'
'A'	'C'	'A'	'B'	'A'	'C'
'D'	'B'	'A'	'A'	'D'	'A'
'D'	'C'	'C'	'D'	'D'	'B'
'B'	'A'	'C'	'A'	'A'	'A'
'B'	'D'	'D'	'C'	'A'	'B'
'A'	'D'	'A'	'A'	'B'	'A'
'B'	'B'	'C'	'A'	'B'	'C'
'B'	'B'	'C'	'A'	'B'	'D'
'A'	'A'	'C'	'D'	'B'	'B'
'A'	'D'	'A'	'C'	'A'	'D'
'B'	'B'	'A'	'A'	'A'	'D'
'A'	'B'	'A'	'A'	'D'	'A'
'A'	'A'	'A'	'B'	'A'	'A'
'C'	'A'	'A'	'A'	'A'	'D'
'C'	'C'	'C'	'A'	'B'	'A'
'B'	'C'	'C'	'C'	'B'	'A'
'A'	'A'	'A'	'A'	'A'	'C'
'A'	'A'	'A'	'B'	'B'	'D'
'C'	'C'	'A'	'A'	'A'	'B'
'C'	'C'	'A'	'B'	'A'	'D'
'D'	'D'	'A'	'A'	'D'	'A'
'A'	'A'	'A'	'A'	'B'	'B'
'A'	'A'	'A'	'B'	'D'	'A'
'A'	'C'	'A'	'D'	'A'	'C'
'A'	'C'	'A'	'A'	'D'	'D'
'B'	'B'	'A'	'C'	'A'	'C'
'C'	'A'	'C'	'A'	'B'	'A'
'C'	'C'	'A'	'A'	'B'	'A'
'B'	'C'	'C'	'C'	'D'	'B'
'D'	'D'	'C'	'A'	'A'	'D'
'D'	'C'	'D'	'D'	'C'	'A'
'A'	'D'	'C'	'C'	'A'	'D'
'B'	'A'	'A'	'A'	'B'	'C'
'B'	'D'	'C'	'A'	'B'	'B'
'C'	'C'	'D'	'D'	'A'	'D'
'D'	'D'	'D'	'D'	'D'	'A'
'B'	'C'	'C'	'A'	'B'	'B'
'D'	'D'	'A'	'C'	'A'	'D'
'B'	'C'	'A'	'C'	'C'	'D'
'A'	'C'	'A'	'C'	'B'	'D'
'B'	'C'	'C'	'A'	'A'	'A'
'A'	'C'	'A'	'A'	'A'	'D'
'B'	'C'	'C'	'C'	'D'	'A'
'A'	'D'	'C'	'C'	'D'	'C'
'A'	'B'	'D'	'A'	'D'	'B'
'A'	'A'	'C'	'A'	'B'	'D'
'C'	'B'	'C'	'B'	'B'	'C'
'B'	'A'	'A'	'B'	'A'	'A'
'A'	'C'	'C'	'A'	'C'	'C'
'C'	'A'	'A'	'A'	'A'	'D'
'C'	'D'	'C'	'C'	'B'	'A'
'C'	'C'	'D'	'A'	'D'	'A'
'B'	'A'	'A'	'A'	'D'	'A'
'C'	'C'	'D'	'D'	'D'	'C'
'A'	'C'	'C'	'D'	'B'	'B'
'A'	'B'	'A'	'A'	'A'	'B'
'D'	'B'	'A'	'A'	'B'	'D'
'A'	'B'	'C'	'B'	'D'	'D'
'B'	'B'	'A'	'C'	'D'	'A'
'D'	'D'	'D'	'D'	'D'	'A'
'A'	'B'	'A'	'A'	'C'	'B'
'B'	'B'	'A'	'A'	'D'	'B'
'D'	'B'	'C'	'B'	'B'	'A'
'B'	'D'	'A'	'A'	'B'	'B'
'B'	'A'	'A'	'A'	'D'	'C'
'B'	'B'	'A'	'A'	'D'	'A'
'D'	'D'	'A'	'B'	'D'	'B'
'A'	'A'	'D'	'A'	'B'	'B'
'B'	'A'	'A'	'A'	'B'	'A'
'A'	'B'	'D'	'D'	'B'	'B'
'D'	'A'	'C'	'B'	'A'	'A'
'B'	'A'	'A'	'A'	'B'	'B'
'A'	'A'	'A'	'A'	'B'	'D'
'B'	'D'	'A'	'A'	'C'	'C'
'A'	'D'	'A'	'D'	'D'	'A'
'A'	'A'	'A'	'A'	'A'	'B'
'B'	'D'	'A'	'B'	'C'	'A'
'D'	'D'	'D'	'A'	'B'	'B'
'A'	'D'	'A'	'A'	'C'	'D'
'C'	'B'	'A'	'A'	'B'	'C'
'A'	'A'	'A'	'A'	'A'	'D'
'B'	'A'	'A'	'A'	'B'	'D'
'A'	'C'	'C'	'A'	'A'	'B'
'C'	'B'	'C'	'B'	'B'	'B'
'C'	'D'	'A'	'C'	'B'	'B'
'A'	'A'	'C'	'D'	'B'	'B'
'C'	'B'	'A'	'A'	'B'	'B'
'D'	'C'	'A'	'A'	'C'	'A'
'C'	'C'	'C'	'A'	'D'	'A'
'D'	'B'	'D'	'D'	'A'	'B'
'B'	'C'	'A'	'A'	'C'	'A'
'B'	'A'	'A'	'A'	'B'	'B'
'C'	'D'	'C'	'A'	'B'	'A'
'D'	'D'	'D'	'A'	'C'	'D'
'A'	'B'	'A'	'C'	'A'	'C'
'A'	'B'	'A'	'A'	'D'	'A'
'B'	'D'	'A'	'D'	'B'	'C'
'A'	'B'	'A'	'A'	'A'	'C'
'C'	'B'	'C'	'C'	'B'	'D'
'A'	'B'	'A'	'A'	'A'	'D'
'A'	'B'	'A'	'B'	'D'	'A'
'B'	'A'	'A'	'A'	'A'	'B'
'C'	'D'	'C'	'B'	'D'	'C'
'C'	'A'	'A'	'B'	'B'	'A'
'A'	'C'	'D'	'A'	'D'	'A'
'A'	'B'	'A'	'A'	'A'	'C'
'A'	'A'	'A'	'A'	'B'	'A'
'B'	'B'	'A'	'B'	'D'	'A'
'A'	'A'	'D'	'D'	'D'	'A'
'D'	'B'	'A'	'A'	'B'	'A'
'D'	'C'	'A'	'A'	'D'	'A'
'C'	'A'	'A'	'B'	'C'	'C'
'C'	'C'	'D'	'B'	'B'	'A'
'A'	'B'	'D'	'C'	'A'	'B'
'A'	'C'	'A'	'A'	'A'	'D'
'C'	'A'	'C'	'A'	'B'	'A'
'B'	'A'	'C'	'D'	'B'	'B'
'C'	'B'	'D'	'B'	'B'	'D'
'A'	'B'	'A'	'A'	'B'	'A'
'C'	'A'	'D'	'B'	'D'	'A'
'D'	'D'	'A'	'A'	'B'	'A'
'A'	'A'	'D'	'A'	'B'	'C'
'A'	'A'	'A'	'A'	'B'	'D'
'C'	'D'	'C'	'A'	'B'	'C'
'D'	'C'	'A'	'A'	'C'	'C'
'A'	'C'	'C'	'C'	'A'	'D'
'A'	'A'	'A'	'B'	'A'	'D'
'C'	'B'	'C'	'D'	'A'	'C'
'B'	'C'	'D'	'B'	'B'	'B'
'C'	'C'	'A'	'C'	'C'	'C'
'D'	'C'	'D'	'B'	'D'	'A'
'A'	'A'	'A'	'D'	'B'	'D'
'D'	'D'	'D'	'B'	'B'	'A'
'A'	'A'	'C'	'A'	'B'	'B'
'C'	'D'	'C'	'A'	'A'	'A'
'D'	'D'	'D'	'D'	'D'	'A'
'B'	'B'	'C'	'B'	'B'	'A'
'D'	'B'	'D'	'C'	'D'	'A'
'B'	'B'	'D'	'D'	'B'	'C'
'D'	'B'	'D'	'D'	'C'	'B'
'C'	'B'	'A'	'D'	'B'	'D'
'D'	'B'	'C'	'D'	'A'	'A'
'D'	'B'	'A'	'A'	'B'	'B'
'D'	'D'	'A'	'B'	'B'	'B'
'A'	'D'	'D'	'D'	'A'	'C'
'C'	'D'	'A'	'A'	'A'	'B'
'B'	'B'	'D'	'A'	'D'	'B'
'C'	'D'	'A'	'A'	'D'	'C'
'B'	'C'	'D'	'D'	'D'	'A'
'A'	'A'	'D'	'D'	'A'	'B'
'A'	'A'	'C'	'A'	'C'	'A'
'B'	'A'	'A'	'D'	'A'	'D'
'B'	'A'	'A'	'D'	'D'	'B'
'B'	'B'	'C'	'D'	'D'	'A'
'C'	'D'	'D'	'D'	'C'	'A'
'B'	'C'	'A'	'A'	'C'	'A'
'C'	'A'	'D'	'D'	'B'	'A'
'C'	'B'	'C'	'D'	'A'	'C'
'B'	'C'	'A'	'B'	'C'	'D'
'C'	'B'	'D'	'D'	'D'	'A'
'B'	'B'	'D'	'D'	'C'	'A'

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225020&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225020&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225020&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Tabulation of Results
Connected x Separate
ABCD
A2214117
B1313116
C810109
D19612

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Connected  x  Separate \tabularnewline
  & A & B & C & D \tabularnewline
A & 22 & 14 & 11 & 7 \tabularnewline
B & 13 & 13 & 11 & 6 \tabularnewline
C & 8 & 10 & 10 & 9 \tabularnewline
D & 1 & 9 & 6 & 12 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225020&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Connected  x  Separate[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]A[/C][C]22[/C][C]14[/C][C]11[/C][C]7[/C][/ROW]
[C]B[/C][C]13[/C][C]13[/C][C]11[/C][C]6[/C][/ROW]
[C]C[/C][C]8[/C][C]10[/C][C]10[/C][C]9[/C][/ROW]
[C]D[/C][C]1[/C][C]9[/C][C]6[/C][C]12[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225020&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225020&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Tabulation of Results
Connected x Separate
ABCD
A2214117
B1313116
C810109
D19612






Tabulation of Expected Results
Connected x Separate
ABCD
A14.6715.3312.6711.33
B11.6812.2110.099.02
C10.0510.518.687.77
D7.67.956.575.88

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Connected  x  Separate \tabularnewline
  & A & B & C & D \tabularnewline
A & 14.67 & 15.33 & 12.67 & 11.33 \tabularnewline
B & 11.68 & 12.21 & 10.09 & 9.02 \tabularnewline
C & 10.05 & 10.51 & 8.68 & 7.77 \tabularnewline
D & 7.6 & 7.95 & 6.57 & 5.88 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225020&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Connected  x  Separate[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]A[/C][C]14.67[/C][C]15.33[/C][C]12.67[/C][C]11.33[/C][/ROW]
[C]B[/C][C]11.68[/C][C]12.21[/C][C]10.09[/C][C]9.02[/C][/ROW]
[C]C[/C][C]10.05[/C][C]10.51[/C][C]8.68[/C][C]7.77[/C][/ROW]
[C]D[/C][C]7.6[/C][C]7.95[/C][C]6.57[/C][C]5.88[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225020&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225020&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Tabulation of Expected Results
Connected x Separate
ABCD
A14.6715.3312.6711.33
B11.6812.2110.099.02
C10.0510.518.687.77
D7.67.956.575.88






Statistical Results
Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)
Chi Square Statistic20.1
P value0.01

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test with simulated p-value
	 (based on 2000 replicates) \tabularnewline
Chi Square Statistic & 20.1 \tabularnewline
P value & 0.01 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225020&T=3

[TABLE]
[ROW][C]Statistical Results[/C][/ROW]
[ROW][C]Pearson's Chi-squared test with simulated p-value
	 (based on 2000 replicates)[/C][/ROW]
[ROW][C]Chi Square Statistic[/C][C]20.1[/C][/ROW]
[ROW][C]P value[/C][C]0.01[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225020&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225020&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Statistical Results
Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)
Chi Square Statistic20.1
P value0.01


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = Pearson Chi-Squared ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = Exact Pearson Chi-Squared by Simulation ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
R code (references can be found in the software module):
library(vcd)
cat1 <- as.numeric(par1) #
cat2<- as.numeric(par2) #
simulate.p.value=FALSE
if (par3 == 'Exact Pearson Chi-Squared by Simulation') simulate.p.value=TRUE
x <- t(x)
(z <- array(unlist(x),dim=c(length(x[,1]),length(x[1,]))))
(table1 <- table(z[,cat1],z[,cat2]))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
bitmap(file='pic1.png')
assoc(ftable(z[,cat1],z[,cat2],row.vars=1,dnn=c(V1,V2)),shade=T)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tabulation of Results',ncol(table1)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste(V1,' x ', V2),ncol(table1)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ', 1,TRUE)
for(nc in 1:ncol(table1)){
a<-table.element(a, colnames(table1)[nc], 1, TRUE)
}
a<-table.row.end(a)
for(nr in 1:nrow(table1) ){
a<-table.element(a, rownames(table1)[nr], 1, TRUE)
for(nc in 1:ncol(table1) ){
a<-table.element(a, table1[nr, nc], 1, FALSE)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
(cst<-chisq.test(table1, simulate.p.value=simulate.p.value) )
if (par3 == 'McNemar Chi-Squared') {
(cst <- mcnemar.test(table1))
}
if (par3 != 'McNemar Chi-Squared') {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tabulation of Expected Results',ncol(table1)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste(V1,' x ', V2),ncol(table1)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ', 1,TRUE)
for(nc in 1:ncol(table1)){
a<-table.element(a, colnames(table1)[nc], 1, TRUE)
}
a<-table.row.end(a)
for(nr in 1:nrow(table1) ){
a<-table.element(a, rownames(table1)[nr], 1, TRUE)
for(nc in 1:ncol(table1) ){
a<-table.element(a, round(cst$expected[nr, nc], digits=2), 1, FALSE)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Statistical Results',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, cst$method, 2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Chi Square Statistic', 1, TRUE)
a<-table.element(a, round(cst$statistic, digits=2), 1,FALSE)
a<-table.row.end(a)
if(!simulate.p.value){
a<-table.row.start(a)
a<-table.element(a, 'Degrees of Freedom', 1, TRUE)
a<-table.element(a, cst$parameter, 1,FALSE)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'P value', 1, TRUE)
a<-table.element(a, round(cst$p.value, digits=2), 1,FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')