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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

Thu, 11 Dec 2014 14:46:08 +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/11/t1418309200sx29xq030j0dzx1.htm/, Retrieved Tue, 18 Aug 2026 21:33:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266065, Retrieved Tue, 18 Aug 2026 21:33:54 +0000

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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 Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 14:46:08] [b4b65124834fa3a3e625dd03af063494] [Current]
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 19:17:35] [ccd66b5a2d6b0dd8c147f526ae5cbd1f] 
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 20:09:06] [ccd66b5a2d6b0dd8c147f526ae5cbd1f] 
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 21:30:54] [ccd66b5a2d6b0dd8c147f526ae5cbd1f] 
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 22:18:37] [ccd66b5a2d6b0dd8c147f526ae5cbd1f] 
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 22:26:47] [ccd66b5a2d6b0dd8c147f526ae5cbd1f] 
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 22:28:48] [ccd66b5a2d6b0dd8c147f526ae5cbd1f] 
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 22:30:09] [ccd66b5a2d6b0dd8c147f526ae5cbd1f] 
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 22:31:39] [ccd66b5a2d6b0dd8c147f526ae5cbd1f] 
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 22:32:28] [ccd66b5a2d6b0dd8c147f526ae5cbd1f] 
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-11 22:33:16] [ccd66b5a2d6b0dd8c147f526ae5cbd1f] 

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266065&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]2 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=266065&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266065&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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Tabulation of Results
IM4 x U4
	'A'	'B'	'C'	'D'
A	2	20	5	0
B	8	46	48	18
C	12	48	37	25
D	0	2	4	3

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
IM4  x  U4 \tabularnewline
  & 'A' & 'B' & 'C' & 'D' \tabularnewline
A & 2 & 20 & 5 & 0 \tabularnewline
B & 8 & 46 & 48 & 18 \tabularnewline
C & 12 & 48 & 37 & 25 \tabularnewline
D & 0 & 2 & 4 & 3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266065&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]IM4  x  U4[/C][/ROW]
[ROW][C] [/C][C]'A'[/C][C]'B'[/C][C]'C'[/C][C]'D'[/C][/ROW]
[C]A[/C][C]2[/C][C]20[/C][C]5[/C][C]0[/C][/ROW]
[C]B[/C][C]8[/C][C]46[/C][C]48[/C][C]18[/C][/ROW]
[C]C[/C][C]12[/C][C]48[/C][C]37[/C][C]25[/C][/ROW]
[C]D[/C][C]0[/C][C]2[/C][C]4[/C][C]3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266065&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266065&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
IM4 x U4
	'A'	'B'	'C'	'D'
A	2	20	5	0
B	8	46	48	18
C	12	48	37	25
D	0	2	4	3

Tabulation of Expected Results
IM4 x U4
	'A'	'B'	'C'	'D'
A	2.14	11.27	9.13	4.47
B	9.5	50.07	40.58	19.86
C	9.65	50.91	41.25	20.19
D	0.71	3.76	3.04	1.49

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
IM4  x  U4 \tabularnewline
  & 'A' & 'B' & 'C' & 'D' \tabularnewline
A & 2.14 & 11.27 & 9.13 & 4.47 \tabularnewline
B & 9.5 & 50.07 & 40.58 & 19.86 \tabularnewline
C & 9.65 & 50.91 & 41.25 & 20.19 \tabularnewline
D & 0.71 & 3.76 & 3.04 & 1.49 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266065&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]IM4  x  U4[/C][/ROW]
[ROW][C] [/C][C]'A'[/C][C]'B'[/C][C]'C'[/C][C]'D'[/C][/ROW]
[C]A[/C][C]2.14[/C][C]11.27[/C][C]9.13[/C][C]4.47[/C][/ROW]
[C]B[/C][C]9.5[/C][C]50.07[/C][C]40.58[/C][C]19.86[/C][/ROW]
[C]C[/C][C]9.65[/C][C]50.91[/C][C]41.25[/C][C]20.19[/C][/ROW]
[C]D[/C][C]0.71[/C][C]3.76[/C][C]3.04[/C][C]1.49[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266065&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266065&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
IM4 x U4
	'A'	'B'	'C'	'D'
A	2.14	11.27	9.13	4.47
B	9.5	50.07	40.58	19.86
C	9.65	50.91	41.25	20.19
D	0.71	3.76	3.04	1.49

Statistical Results
Pearson's Chi-squared test
Pearson Chi Square Statistic	20.9
Degrees of Freedom	9
P value	0.01

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Pearson Chi Square Statistic & 20.9 \tabularnewline
Degrees of Freedom & 9 \tabularnewline
P value & 0.01 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266065&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]20.9[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]9[/C][/ROW]
[ROW][C]P value[/C][C]0.01[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266065&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266065&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	20.9
Degrees of Freedom	9
P value	0.01

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

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

R code (references can be found in the software module):

par3 <- 'Pearson Chi-Squared'
par2 <- ''
par1 <- ''
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