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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_chi_squared_tests.wasp

Title produced by software

Chi-Squared Test, McNemar Test, and Fisher Exact Test

Date of computation

Mon, 17 Dec 2012 15:42:55 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t13557769968ulykv0sthjxsps.htm/, Retrieved Tue, 10 Feb 2026 21:25:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201198, Retrieved Tue, 10 Feb 2026 21:25:50 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

405

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 14:33:59] [b98453cac15ba1066b407e146608df68]
- R     [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Connected en Sepa...] [2012-12-17 19:02:23] [4187c7efada0bc11e94a41d61d855f64]
-   P     [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Connected en Sepe...] [2012-12-17 19:07:59] [4187c7efada0bc11e94a41d61d855f64]
-   P         [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Connected en Sepa...] [2012-12-17 20:42:55] [f2ee352554ba43a37c941acf183fae36] [Current]
-    D          [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Chi square (weeks-)] [2012-12-21 16:14:10] [74be16979710d4c4e7c6647856088456] 
-    D          [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2012-12-21 16:20:21] [74be16979710d4c4e7c6647856088456] 
- R PD          [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Chi square TXUSED] [2012-12-21 16:52:21] [4187c7efada0bc11e94a41d61d855f64] 

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Dataseries X:

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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'

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201198&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201198&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201198&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Tabulation of Results
Connected x Separate
	A	B	C	D
A	22	14	11	7
B	13	13	11	6
C	8	10	10	9
D	1	9	6	12

\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=201198&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=201198&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201198&T=1

As an alternative you can also use a QR Code:

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

Tabulation of Results
Connected x Separate
	A	B	C	D
A	22	14	11	7
B	13	13	11	6
C	8	10	10	9
D	1	9	6	12

Tabulation of Expected Results
Connected x Separate
	A	B	C	D
A	14.67	15.33	12.67	11.33
B	11.68	12.21	10.09	9.02
C	10.05	10.51	8.68	7.77
D	7.6	7.95	6.57	5.88

\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=201198&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=201198&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201198&T=2

As an alternative you can also use a QR Code:

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

Tabulation of Expected Results
Connected x Separate
	A	B	C	D
A	14.67	15.33	12.67	11.33
B	11.68	12.21	10.09	9.02
C	10.05	10.51	8.68	7.77
D	7.6	7.95	6.57	5.88

Statistical Results
Pearson's Chi-squared test
Chi Square Statistic	20.1
Degrees of Freedom	9
P value	0.02

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Chi Square Statistic & 20.1 \tabularnewline
Degrees of Freedom & 9 \tabularnewline
P value & 0.02 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201198&T=3

[TABLE]
[ROW][C]Statistical Results[/C][/ROW]
[ROW][C]Pearson's Chi-squared test[/C][/ROW]
[ROW][C]Chi Square Statistic[/C][C]20.1[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]9[/C][/ROW]
[ROW][C]P value[/C][C]0.02[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201198&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201198&T=3

As an alternative you can also use a QR Code:

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

Statistical Results
Pearson's Chi-squared test
Chi Square Statistic	20.1
Degrees of Freedom	9
P value	0.02

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = Pearson Chi-Squared ;

Parameters (R input):

par1 = 1 ; par2 = 2 ; par3 = Pearson Chi-Squared ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code