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*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, 16 Dec 2014 12:45:20 +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/Dec/16/t1418734135i1jwkaan40abf3b.htm/, Retrieved Tue, 10 Feb 2026 13:14:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269433, Retrieved Tue, 10 Feb 2026 13:14:02 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

344

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] [] [2014-12-16 12:45:20] [1d338d9433eb3ecdb4d9d35f41140a45] [Current]
-    D    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 12:55:11] [8d160a85bfd9526a7d0e42afc5fb569b] 
- R PD      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 13:39:38] [8d160a85bfd9526a7d0e42afc5fb569b] 
-    D    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 12:56:49] [8d160a85bfd9526a7d0e42afc5fb569b] 
- R PD      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 13:40:20] [8d160a85bfd9526a7d0e42afc5fb569b] 
-   PD      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 13:52:29] [8d160a85bfd9526a7d0e42afc5fb569b] 
- R  D        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 13:53:08] [8d160a85bfd9526a7d0e42afc5fb569b] 
-    D        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 13:53:53] [8d160a85bfd9526a7d0e42afc5fb569b] 
- R  D          [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 13:54:51] [8d160a85bfd9526a7d0e42afc5fb569b] 
-  M D            [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 13:58:31] [8d160a85bfd9526a7d0e42afc5fb569b] 
-    D          [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 13:55:45] [8d160a85bfd9526a7d0e42afc5fb569b] 
- RM D            [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 13:56:06] [8d160a85bfd9526a7d0e42afc5fb569b] 
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-16 13:39:03] [8d160a85bfd9526a7d0e42afc5fb569b] 

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'George Udny Yule' @ yule.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 & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269433&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269433&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269433&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	7 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Tabulation of Results
code_I x lettercode_ex_res
	'A'	'B'	'C'	'D'
A	20	20	13	20
B	19	21	19	18
C	17	15	8	28
D	18	14	18	15

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
code_I  x  lettercode_ex_res \tabularnewline
  & 'A' & 'B' & 'C' & 'D' \tabularnewline
A & 20 & 20 & 13 & 20 \tabularnewline
B & 19 & 21 & 19 & 18 \tabularnewline
C & 17 & 15 & 8 & 28 \tabularnewline
D & 18 & 14 & 18 & 15 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269433&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]code_I  x  lettercode_ex_res[/C][/ROW]
[ROW][C] [/C][C]'A'[/C][C]'B'[/C][C]'C'[/C][C]'D'[/C][/ROW]
[C]A[/C][C]20[/C][C]20[/C][C]13[/C][C]20[/C][/ROW]
[C]B[/C][C]19[/C][C]21[/C][C]19[/C][C]18[/C][/ROW]
[C]C[/C][C]17[/C][C]15[/C][C]8[/C][C]28[/C][/ROW]
[C]D[/C][C]18[/C][C]14[/C][C]18[/C][C]15[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269433&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269433&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
code_I x lettercode_ex_res
	'A'	'B'	'C'	'D'
A	20	20	13	20
B	19	21	19	18
C	17	15	8	28
D	18	14	18	15

Tabulation of Expected Results
code_I x lettercode_ex_res
	'A'	'B'	'C'	'D'
A	19.09	18.06	14.96	20.89
B	20.13	19.05	15.78	22.04
C	17.78	16.82	13.94	19.46
D	17	16.08	13.32	18.6

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
code_I  x  lettercode_ex_res \tabularnewline
  & 'A' & 'B' & 'C' & 'D' \tabularnewline
A & 19.09 & 18.06 & 14.96 & 20.89 \tabularnewline
B & 20.13 & 19.05 & 15.78 & 22.04 \tabularnewline
C & 17.78 & 16.82 & 13.94 & 19.46 \tabularnewline
D & 17 & 16.08 & 13.32 & 18.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269433&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]code_I  x  lettercode_ex_res[/C][/ROW]
[ROW][C] [/C][C]'A'[/C][C]'B'[/C][C]'C'[/C][C]'D'[/C][/ROW]
[C]A[/C][C]19.09[/C][C]18.06[/C][C]14.96[/C][C]20.89[/C][/ROW]
[C]B[/C][C]20.13[/C][C]19.05[/C][C]15.78[/C][C]22.04[/C][/ROW]
[C]C[/C][C]17.78[/C][C]16.82[/C][C]13.94[/C][C]19.46[/C][/ROW]
[C]D[/C][C]17[/C][C]16.08[/C][C]13.32[/C][C]18.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269433&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269433&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
code_I x lettercode_ex_res
	'A'	'B'	'C'	'D'
A	19.09	18.06	14.96	20.89
B	20.13	19.05	15.78	22.04
C	17.78	16.82	13.94	19.46
D	17	16.08	13.32	18.6

Statistical Results
Pearson's Chi-squared test
Pearson Chi Square Statistic	11.38
Degrees of Freedom	9
P value	0.25

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Pearson Chi Square Statistic & 11.38 \tabularnewline
Degrees of Freedom & 9 \tabularnewline
P value & 0.25 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269433&T=3

[TABLE]
[ROW][C]Statistical Results[/C][/ROW]
[ROW][C]Pearson's Chi-squared test[/C][/ROW]
[ROW][C]Pearson Chi Square Statistic[/C][C]11.38[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]9[/C][/ROW]
[ROW][C]P value[/C][C]0.25[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269433&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269433&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
Pearson Chi Square Statistic	11.38
Degrees of Freedom	9
P value	0.25

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=='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