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R Software Module

rwasp_chi_squared_tests.wasp

Title produced by software

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

Date of computation

Wed, 05 Nov 2014 15:11:03 +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/05/t1415200270bpjs6nxvu4mabhp.htm/, Retrieved Mon, 27 Apr 2026 14:52:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=251926, Retrieved Mon, 27 Apr 2026 14:52:38 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

302

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] [] [2014-11-05 15:11:03] [b4b65124834fa3a3e625dd03af063494] [Current]

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'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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=251926&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=251926&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=251926&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	'Gertrude Mary Cox' @ cox.wessa.net

Tabulation of Results
Learning4 x Software4
	'A'	'B'	'C'	'D'
'A'	52	15	9	7
'C'	19	7	8	9
'D'	9	6	3	18

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Learning4  x  Software4 \tabularnewline
  & 'A' & 'B' & 'C' & 'D' \tabularnewline
'A' & 52 & 15 & 9 & 7 \tabularnewline
'C' & 19 & 7 & 8 & 9 \tabularnewline
'D' & 9 & 6 & 3 & 18 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=251926&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Learning4  x  Software4[/C][/ROW]
[ROW][C] [/C][C]'A'[/C][C]'B'[/C][C]'C'[/C][C]'D'[/C][/ROW]
[C]'A'[/C][C]52[/C][C]15[/C][C]9[/C][C]7[/C][/ROW]
[C]'C'[/C][C]19[/C][C]7[/C][C]8[/C][C]9[/C][/ROW]
[C]'D'[/C][C]9[/C][C]6[/C][C]3[/C][C]18[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=251926&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=251926&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
Learning4 x Software4
	'A'	'B'	'C'	'D'
'A'	52	15	9	7
'C'	19	7	8	9
'D'	9	6	3	18

Tabulation of Expected Results
Learning4 x Software4
	'A'	'B'	'C'	'D'
'A'	40.99	14.35	10.25	17.42
'C'	21.23	7.43	5.31	9.02
'D'	17.78	6.22	4.44	7.56

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Learning4  x  Software4 \tabularnewline
  & 'A' & 'B' & 'C' & 'D' \tabularnewline
'A' & 40.99 & 14.35 & 10.25 & 17.42 \tabularnewline
'C' & 21.23 & 7.43 & 5.31 & 9.02 \tabularnewline
'D' & 17.78 & 6.22 & 4.44 & 7.56 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=251926&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Learning4  x  Software4[/C][/ROW]
[ROW][C] [/C][C]'A'[/C][C]'B'[/C][C]'C'[/C][C]'D'[/C][/ROW]
[C]'A'[/C][C]40.99[/C][C]14.35[/C][C]10.25[/C][C]17.42[/C][/ROW]
[C]'C'[/C][C]21.23[/C][C]7.43[/C][C]5.31[/C][C]9.02[/C][/ROW]
[C]'D'[/C][C]17.78[/C][C]6.22[/C][C]4.44[/C][C]7.56[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=251926&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=251926&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
Learning4 x Software4
	'A'	'B'	'C'	'D'
'A'	40.99	14.35	10.25	17.42
'C'	21.23	7.43	5.31	9.02
'D'	17.78	6.22	4.44	7.56

Statistical Results
Pearson's Chi-squared test
Pearson Chi Square Statistic	30.25
Degrees of Freedom	6
P value	0

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Pearson Chi Square Statistic & 30.25 \tabularnewline
Degrees of Freedom & 6 \tabularnewline
P value & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=251926&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]30.25[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]6[/C][/ROW]
[ROW][C]P value[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=251926&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=251926&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	30.25
Degrees of Freedom	6
P value	0

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 3 ; par2 = 4 ; par3 = Pearson Chi-Squared ;

Parameters (R input):

par1 = 3 ; par2 = 4 ; 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