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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

Tue, 15 Nov 2011 11:18:24 -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/2011/Nov/15/t1321373944ju8cffd0wob99jp.htm/, Retrieved Wed, 05 Nov 2025 02:19:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143135, Retrieved Wed, 05 Nov 2025 02:19:00 +0000

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Estimated Impact

124

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

-     [ECEL 2008] [ECEL2008 hypothes...] [2008-06-14 21:17:24] [74be16979710d4c4e7c6647856088456]
- RMPD  [Chi-Squared and McNemar Tests] [Chi squared 1] [2010-11-05 22:27:37] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
- R PD      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [C6 H-C1] [2011-11-15 16:18:24] [51aabe75794be7f34bed5d3096a085df] [Current]

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Boxplots

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

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	'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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143135&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143135&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143135&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	'George Udny Yule' @ yule.wessa.net

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

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
hapiness  x  connected \tabularnewline
  & A & B & C & D \tabularnewline
A & 21 & 8 & 9 & 5 \tabularnewline
B & 18 & 16 & 18 & 8 \tabularnewline
C & 4 & 7 & 3 & 5 \tabularnewline
D & 11 & 12 & 7 & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143135&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]hapiness  x  connected[/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]8[/C][C]9[/C][C]5[/C][/ROW]
[C]B[/C][C]18[/C][C]16[/C][C]18[/C][C]8[/C][/ROW]
[C]C[/C][C]4[/C][C]7[/C][C]3[/C][C]5[/C][/ROW]
[C]D[/C][C]11[/C][C]12[/C][C]7[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143135&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143135&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
hapiness x connected
	A	B	C	D
A	21	8	9	5
B	18	16	18	8
C	4	7	3	5
D	11	12	7	10

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

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
hapiness  x  connected \tabularnewline
  & A & B & C & D \tabularnewline
A & 14.33 & 11.41 & 9.82 & 7.43 \tabularnewline
B & 20 & 15.93 & 13.7 & 10.37 \tabularnewline
C & 6.33 & 5.04 & 4.34 & 3.28 \tabularnewline
D & 13.33 & 10.62 & 9.14 & 6.91 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143135&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]hapiness  x  connected[/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]11.41[/C][C]9.82[/C][C]7.43[/C][/ROW]
[C]B[/C][C]20[/C][C]15.93[/C][C]13.7[/C][C]10.37[/C][/ROW]
[C]C[/C][C]6.33[/C][C]5.04[/C][C]4.34[/C][C]3.28[/C][/ROW]
[C]D[/C][C]13.33[/C][C]10.62[/C][C]9.14[/C][C]6.91[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143135&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143135&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
hapiness x connected
	A	B	C	D
A	14.33	11.41	9.82	7.43
B	20	15.93	13.7	10.37
C	6.33	5.04	4.34	3.28
D	13.33	10.62	9.14	6.91

Statistical Results
Pearson's Chi-squared test
Pearson Chi Square Statistic	12.47
Degrees of Freedom	9
P value	0.19

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Pearson Chi Square Statistic & 12.47 \tabularnewline
Degrees of Freedom & 9 \tabularnewline
P value & 0.19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143135&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]12.47[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]9[/C][/ROW]
[ROW][C]P value[/C][C]0.19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143135&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143135&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	12.47
Degrees of Freedom	9
P value	0.19

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 5 ; par2 = 1 ; par3 = Pearson Chi-Squared ;

Parameters (R input):

par1 = 5 ; par2 = 1 ; 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