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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

Tue, 04 Nov 2014 14:29:09 +0000

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/2014/Nov/04/t1415111358xx27g6d1b7z2a9s.htm/, Retrieved Thu, 12 Feb 2026 15:05:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=251290, Retrieved Thu, 12 Feb 2026 15:05:48 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

421

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-02 12:08:26] [d253a55552bf9917a397def3be261e30]
- R PD  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-02 13:24:24] [d253a55552bf9917a397def3be261e30]
-   PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-04 13:45:57] [d253a55552bf9917a397def3be261e30]
-   PD        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-04 14:29:09] [940a3d9bc049bdd1effc6e8b1116301d] [Current]
-   PD          [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-04 14:33:29] [d253a55552bf9917a397def3be261e30] 
-    D            [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-04 14:36:42] [d253a55552bf9917a397def3be261e30] 
-    D              [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-04 14:42:15] [d253a55552bf9917a397def3be261e30] 
-   PD                [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-05 13:43:52] [d253a55552bf9917a397def3be261e30] 
-   PD              [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-05 13:42:05] [d253a55552bf9917a397def3be261e30] 
-   PD            [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-05 13:33:14] [d253a55552bf9917a397def3be261e30] 
-   PD          [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-11-05 13:30:21] [d253a55552bf9917a397def3be261e30] 

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'B' "'B'" "'A'" "'A'"
'A' "'C'" "'A'" "'C'"
'D' "'A'" "'D'" "'B'"
'D' "'B'" "'D'" "'C'"
'A' "'A'" "'B'" "'A'"
'A' "'B'" "'B'" "'D'"
'B' "'A'" "'A'" "'D'"
'B' "'C'" "'B'" "'B'"
'B' "'D'" "'B'" "'B'"
'B' "'B'" "'A'" "'A'"
'A' "'D'" "'A'" "'D'"
'A' "'D'" "'B'" "'B'"
'D' "'A'" "'A'" "'B'"
'A' "'A'" "'A'" "'A'"
'A' "'D'" "'C'" "'A'"
'B' "'A'" "'C'" "'C'"
'B' "'A'" "'B'" "'C'"
'A' "'C'" "'A'" "'A'"
'B' "'D'" "'A'" "'A'"
'A' "'B'" "'C'" "'C'"
'A' "'D'" "'C'" "'C'"
'D' "'A'" "'D'" "'D'"
'B' "'B'" "'A'" "'A'"
'D' "'A'" "'A'" "'A'"
'A' "'C'" "'A'" "'C'"
'D' "'D'" "'A'" "'C'"
'A' "'C'" "'B'" "'B'"
'B' "'A'" "'C'" "'A'"
'B' "'A'" "'C'" "'C'"
'D' "'B'" "'B'" "'C'"
'A' "'D'" "'D'" "'D'"
'C' "'A'" "'D'" "'C'"
'A' "'D'" "'A'" "'D'"
'B' "'C'" "'B'" "'A'"
'B' "'B'" "'B'" "'D'"
'A' "'D'" "'C'" "'C'"
'D' "'A'" "'D'" "'D'"
'B' "'B'" "'B'" "'C'"
'A' "'D'" "'D'" "'D'"
'C' "'D'" "'B'" "'C'"
'B' "'D'" "'A'" "'C'"
'A' "'A'" "'B'" "'C'"
'A' "'D'" "'A'" "'C'"
'D' "'A'" "'B'" "'C'"
'D' "'C'" "'A'" "'D'"
'D' "'B'" "'A'" "'B'"
'B' "'D'" "'A'" "'A'"
'B' "'C'" "'C'" "'B'"
'A' "'A'" "'B'" "'A'"
'C' "'C'" "'A'" "'C'"
'A' "'D'" "'C'" "'A'"
'B' "'A'" "'C'" "'D'"
'D' "'A'" "'C'" "'C'"
'D' "'A'" "'B'" "'A'"
'D' "'C'" "'C'" "'C'"
'B' "'B'" "'A'" "'C'"
'A' "'B'" "'A'" "'B'"
'B' "'D'" "'D'" "'B'"
'D' "'D'" "'A'" "'B'"
'D' "'A'" "'B'" "'B'"
'D' "'A'" "'D'" "'D'"
'C' "'B'" "'A'" "'B'"
'D' "'B'" "'B'" "'B'"
'B' "'A'" "'D'" "'B'"
'B' "'B'" "'B'" "'D'"
'D' "'C'" "'B'" "'A'"
'D' "'A'" "'B'" "'B'"
'D' "'B'" "'D'" "'D'"
'B' "'B'" "'A'" "'A'"
'B' "'A'" "'B'" "'A'"
'B' "'B'" "'A'" "'B'"
'A' "'A'" "'D'" "'A'"
'B' "'B'" "'B'" "'A'"
'B' "'D'" "'A'" "'A'"
'C' "'C'" "'B'" "'D'"
'D' "'A'" "'A'" "'D'"
'A' "'B'" "'A'" "'A'"
'C' "'A'" "'B'" "'D'"
'B' "'B'" "'D'" "'D'"
'C' "'D'" "'A'" "'D'"
'B' "'C'" "'C'" "'B'"
'A' "'D'" "'A'" "'A'"
'B' "'D'" "'B'" "'A'"
'A' "'B'" "'A'" "'C'"
'B' "'B'" "'C'" "'B'"
'B' "'B'" "'C'" "'D'"
'B' "'B'" "'A'" "'A'"
'B' "'B'" "'C'" "'B'"
'C' "'A'" "'D'" "'C'"
'D' "'A'" "'C'" "'C'"
'A' "'B'" "'D'" "'B'"
'C' "'A'" "'B'" "'C'"
'B' "'B'" "'B'" "'A'"
'B' "'A'" "'C'" "'D'"
'C' "'D'" "'D'" "'D'"
'A' "'C'" "'A'" "'B'"
'D' "'A'" "'A'" "'B'"
'B' "'C'" "'B'" "'D'"
'A' "'C'" "'A'" "'B'"
'B' "'D'" "'C'" "'B'"
'A' "'D'" "'A'" "'B'"
'D' "'A'" "'A'" "'B'"
'A' "'B'" "'B'" "'A'"
'D' "'C'" "'C'" "'D'"
'B' "'A'" "'C'" "'A'"
'D' "'A'" "'A'" "'C'"
'A' "'C'" "'A'" "'B'"
'B' "'A'" "'A'" "'A'"
'D' "'A'" "'B'" "'B'"
'D' "'A'" "'A'" "'A'"
'B' "'A'" "'D'" "'B'"
'D' "'A'" "'D'" "'C'"
'C' "'C'" "'C'" "'A'"
'B' "'A'" "'C'" "'C'"
'A' "'B'" "'A'" "'B'"
'A' "'D'" "'A'" "'C'"
'B' "'A'" "'C'" "'A'"
'B' "'B'" "'B'" "'A'"
'B' "'D'" "'C'" "'B'"
'B' "'A'" "'A'" "'B'"
'D' "'A'" "'C'" "'A'"
'B' "'A'" "'D'" "'D'"
'B' "'C'" "'A'" "'A'"
'B' "'D'" "'A'" "'A'"
'B' "'C'" "'C'" "'D'"
'C' "'C'" "'D'" "'C'"
'A' "'D'" "'A'" "'C'"
'A' "'D'" "'A'" "'A'"
'A' "'C'" "'C'" "'B'"
'B' "'B'" "'B'" "'C'"
'C' "'C'" "'C'" "'C'"
'D' "'A'" "'D'" "'C'"
'B' "'D'" "'A'" "'A'"
'B' "'A'" "'D'" "'D'"
'B' "'B'" "'A'" "'A'"
'A' "'A'" "'C'" "'D'"
'D' "'A'" "'D'" "'D'"
'B' "'A'" "'B'" "'B'"
'D' "'A'" "'D'" "'B'"
'B' "'C'" "'B'" "'B'"
'C' "'B'" "'D'" "'B'"
'B' "'D'" "'C'" "'B'"
'A' "'A'" "'D'" "'B'"
'B' "'B'" "'D'" "'B'"
'B' "'B'" "'D'" "'D'"
'A' "'C'" "'A'" "'D'"
'A' "'B'" "'C'" "'D'"
'D' "'B'" "'B'" "'B'"
'D' "'C'" "'C'" "'D'"
'D' "'A'" "'B'" "'C'"
'A' "'B'" "'A'" "'A'"
'C' "'A'" "'A'" "'A'"
'A' "'D'" "'B'" "'A'"
'D' "'B'" "'B'" "'A'"
'D' "'A'" "'B'" "'B'"
'C' "'A'" "'C'" "'D'"
'C' "'A'" "'B'" "'C'"
'B' "'A'" "'C'" "'A'"
'A' "'C'" "'C'" "'B'"
'C' "'D'" "'B'" "'C'"
'D' "'A'" "'C'" "'B'"
'C' "'A'" "'B'" "'B'"

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=251290&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=251290&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=251290&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Tabulation of Results
Connected4 x Happiness4
	A	B	C	D
'A'	21	18	4	11
'B'	8	16	7	12
'C'	9	18	3	7
'D'	5	8	5	10

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Connected4  x  Happiness4 \tabularnewline
  & A & B & C & D \tabularnewline
'A' & 21 & 18 & 4 & 11 \tabularnewline
'B' & 8 & 16 & 7 & 12 \tabularnewline
'C' & 9 & 18 & 3 & 7 \tabularnewline
'D' & 5 & 8 & 5 & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=251290&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Connected4  x  Happiness4[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]'A'[/C][C]21[/C][C]18[/C][C]4[/C][C]11[/C][/ROW]
[C]'B'[/C][C]8[/C][C]16[/C][C]7[/C][C]12[/C][/ROW]
[C]'C'[/C][C]9[/C][C]18[/C][C]3[/C][C]7[/C][/ROW]
[C]'D'[/C][C]5[/C][C]8[/C][C]5[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=251290&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=251290&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
Connected4 x Happiness4
	A	B	C	D
'A'	21	18	4	11
'B'	8	16	7	12
'C'	9	18	3	7
'D'	5	8	5	10

Tabulation of Expected Results
Connected4 x Happiness4
	A	B	C	D
'A'	14.33	20	6.33	13.33
'B'	11.41	15.93	5.04	10.62
'C'	9.82	13.7	4.34	9.14
'D'	7.43	10.37	3.28	6.91

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Connected4  x  Happiness4 \tabularnewline
  & A & B & C & D \tabularnewline
'A' & 14.33 & 20 & 6.33 & 13.33 \tabularnewline
'B' & 11.41 & 15.93 & 5.04 & 10.62 \tabularnewline
'C' & 9.82 & 13.7 & 4.34 & 9.14 \tabularnewline
'D' & 7.43 & 10.37 & 3.28 & 6.91 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=251290&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Connected4  x  Happiness4[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]'A'[/C][C]14.33[/C][C]20[/C][C]6.33[/C][C]13.33[/C][/ROW]
[C]'B'[/C][C]11.41[/C][C]15.93[/C][C]5.04[/C][C]10.62[/C][/ROW]
[C]'C'[/C][C]9.82[/C][C]13.7[/C][C]4.34[/C][C]9.14[/C][/ROW]
[C]'D'[/C][C]7.43[/C][C]10.37[/C][C]3.28[/C][C]6.91[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=251290&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=251290&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
Connected4 x Happiness4
	A	B	C	D
'A'	14.33	20	6.33	13.33
'B'	11.41	15.93	5.04	10.62
'C'	9.82	13.7	4.34	9.14
'D'	7.43	10.37	3.28	6.91

Statistical Results
Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)
Exact Pearson Chi Square Statistic	12.47
P value	0.19

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test with simulated p-value
	 (based on 2000 replicates) \tabularnewline
Exact Pearson Chi Square Statistic & 12.47 \tabularnewline
P value & 0.19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=251290&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]Exact Pearson Chi Square Statistic[/C][C]12.47[/C][/ROW]
[ROW][C]P value[/C][C]0.19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=251290&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=251290&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 with simulated p-value (based on 2000 replicates)
Exact Pearson Chi Square Statistic	12.47
P value	0.19

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 3 ; par2 = 1 ; par3 = Exact Pearson Chi-Squared by Simulation ;

Parameters (R input):

par1 = 3 ; par2 = 1 ; par3 = Exact Pearson Chi-Squared by Simulation ;

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=='Fisher Exact Test') {
(cst <- fisher.test(table1))
}
if ((par3 != 'McNemar Chi-Squared') & (par3 != 'Fisher Exact Test')) {
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)
if (par3=='Pearson Chi-Squared') a<-table.element(a, 'Pearson Chi Square Statistic', 1, TRUE)
if (par3=='Exact Pearson Chi-Squared by Simulation') a<-table.element(a, 'Exact Pearson Chi Square Statistic', 1, TRUE)
if (par3=='McNemar Chi-Squared') a<-table.element(a, 'McNemar Chi Square Statistic', 1, TRUE)
if (par3=='Fisher Exact Test') a<-table.element(a, 'Odds Ratio', 1, TRUE)
if (par3=='Fisher Exact Test') {
if ((ncol(table1) == 2) & (nrow(table1) == 2)) {
a<-table.element(a, round(cst$estimate, digits=2), 1,FALSE)
} else {
a<-table.element(a, '--', 1,FALSE)
}
} else {
a<-table.element(a, round(cst$statistic, digits=2), 1,FALSE)
}
a<-table.row.end(a)
if(!simulate.p.value){
if(par3!='Fisher Exact Test') {
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