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rwasp_chi_squared_tests.wasp

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

Date of computation

Mon, 15 Dec 2014 17:47:48 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/15/t1418665705iqpd5anvqzatjnl.htm/, Retrieved Wed, 11 Feb 2026 13:36:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268809, Retrieved Wed, 11 Feb 2026 13:36:51 +0000

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Estimated Impact

306

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-       [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2014-12-15 17:47:48] [6c0da333d5967ad7c023c95d07a1face] [Current]

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

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	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268809&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268809&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268809&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Tabulation of Results
cat_AMS.E x cat_algebraic
	'A'	'B'	'C'	'D'
A	12	39	107	8
B	4	6	27	2
C	0	0	2	1

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
cat_AMS.E  x  cat_algebraic \tabularnewline
  & 'A' & 'B' & 'C' & 'D' \tabularnewline
A & 12 & 39 & 107 & 8 \tabularnewline
B & 4 & 6 & 27 & 2 \tabularnewline
C & 0 & 0 & 2 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268809&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]cat_AMS.E  x  cat_algebraic[/C][/ROW]
[ROW][C] [/C][C]'A'[/C][C]'B'[/C][C]'C'[/C][C]'D'[/C][/ROW]
[C]A[/C][C]12[/C][C]39[/C][C]107[/C][C]8[/C][/ROW]
[C]B[/C][C]4[/C][C]6[/C][C]27[/C][C]2[/C][/ROW]
[C]C[/C][C]0[/C][C]0[/C][C]2[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268809&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268809&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
cat_AMS.E x cat_algebraic
	'A'	'B'	'C'	'D'
A	12	39	107	8
B	4	6	27	2
C	0	0	2	1

Tabulation of Expected Results
cat_AMS.E x cat_algebraic
	'A'	'B'	'C'	'D'
A	12.77	35.91	108.54	8.78
B	3	8.44	25.5	2.06
C	0.23	0.65	1.96	0.16

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
cat_AMS.E  x  cat_algebraic \tabularnewline
  & 'A' & 'B' & 'C' & 'D' \tabularnewline
A & 12.77 & 35.91 & 108.54 & 8.78 \tabularnewline
B & 3 & 8.44 & 25.5 & 2.06 \tabularnewline
C & 0.23 & 0.65 & 1.96 & 0.16 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268809&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]cat_AMS.E  x  cat_algebraic[/C][/ROW]
[ROW][C] [/C][C]'A'[/C][C]'B'[/C][C]'C'[/C][C]'D'[/C][/ROW]
[C]A[/C][C]12.77[/C][C]35.91[/C][C]108.54[/C][C]8.78[/C][/ROW]
[C]B[/C][C]3[/C][C]8.44[/C][C]25.5[/C][C]2.06[/C][/ROW]
[C]C[/C][C]0.23[/C][C]0.65[/C][C]1.96[/C][C]0.16[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268809&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268809&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
cat_AMS.E x cat_algebraic
	'A'	'B'	'C'	'D'
A	12.77	35.91	108.54	8.78
B	3	8.44	25.5	2.06
C	0.23	0.65	1.96	0.16

Statistical Results
Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)
Exact Pearson Chi Square Statistic	6.87
P value	0.31

\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 & 6.87 \tabularnewline
P value & 0.31 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268809&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]6.87[/C][/ROW]
[ROW][C]P value[/C][C]0.31[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268809&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268809&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	6.87
P value	0.31

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 4 ; par3 = Exact Pearson Chi-Squared by Simulation ;

Parameters (R input):

par1 = 1 ; par2 = 4 ; 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