Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

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

Sat, 16 Dec 2017 16:55:19 +0100

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/2017/Dec/16/t15134398447ij0zp9i3s5hmkz.htm/, Retrieved Tue, 10 Feb 2026 13:58:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309914, Retrieved Tue, 10 Feb 2026 13:58:50 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Group vs. Intention to use

Estimated Impact

267

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] [Chi squared test] [2017-12-16 15:55:19] [97ca58e32232a99e44a6c848c7facc09] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

'AVERAGE'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'B'
'HIGH'	'S'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'B'
'HIGH'	'B'
'HIGH'	'S'
'AVERAGE'	'B'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'LOW'	'B'
'HIGH'	'B'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'B'
'HIGH'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'HIGH'	'S'
'AVERAGE'	'B'
'LOW'	'B'
'LOW'	'B'
'AVERAGE'	'B'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'HIGH'	'S'
'AVERAGE'	'B'
'LOW'	'S'
'AVERAGE'	'B'
'AVERAGE'	'B'
'LOW'	'B'
'HIGH'	'B'
'HIGH'	'B'
'HIGH'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'S'
'HIGH'	'B'
'HIGH'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'B'
'AVERAGE'	'S'
'LOW'	'B'
'HIGH'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'LOW'	'S'
'HIGH'	'B'
'LOW'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'B'
'LOW'	'S'
'LOW'	'B'
'HIGH'	'S'
'HIGH'	'B'
'AVERAGE'	'B'
'LOW'	'B'
'LOW'	'B'
'HIGH'	'B'
'LOW'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'HIGH'	'S'
'HIGH'	'B'
'AVERAGE'	'S'
'HIGH'	'B'
'LOW'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'HIGH'	'B'
'LOW'	'S'
'LOW'	'B'
'AVERAGE'	'B'
'HIGH'	'S'
'LOW'	'S'
'AVERAGE'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'HIGH'	'B'
'HIGH'	'B'
'LOW'	'B'
'AVERAGE'	'B'
'LOW'	'S'
'LOW'	'S'
'LOW'	'S'
'LOW'	'S'
'HIGH'	'B'
'HIGH'	'S'
'HIGH'	'B'
'LOW'	'B'
'LOW'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'LOW'	'S'
'LOW'	'S'
'LOW'	'S'
'HIGH'	'B'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'B'
'LOW'	'B'
'LOW'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'LOW'	'S'
'HIGH'	'S'
'HIGH'	'S'
'LOW'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'B'
'LOW'	'B'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'S'
'LOW'	'B'
'AVERAGE'	'S'
'LOW'	'B'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'B'
'HIGH'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'LOW'	'B'
'LOW'	'B'
'HIGH'	'B'
'LOW'	'S'
'LOW'	'S'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'S'
'LOW'	'B'
'LOW'	'S'
'AVERAGE'	'S'
'AVERAGE'	'B'
'HIGH'	'B'
'LOW'	'B'
'LOW'	'S'
'LOW'	'B'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'LOW'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'B'
'AVERAGE'	'B'
'AVERAGE'	'S'
'HIGH'	'S'
'HIGH'	'S'
'HIGH'	'B'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'B'
'AVERAGE'	'B'
'AVERAGE'	'S'
'AVERAGE'	'B'
'HIGH'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'LOW'	'B'
'LOW'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'LOW'	'B'
'HIGH'	'S'
'LOW'	'S'
'LOW'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'HIGH'	'B'
'LOW'	'S'
'HIGH'	'S'
'LOW'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'B'
'HIGH'	'S'
'LOW'	'S'
'AVERAGE'	'B'
'LOW'	'B'
'LOW'	'B'
'LOW'	'B'
'HIGH'	'S'
'HIGH'	'S'
'LOW'	'S'
'HIGH'	'S'
'HIGH'	'B'
'LOW'	'S'
'HIGH'	'S'
'HIGH'	'S'
'LOW'	'S'
'LOW'	'S'
'LOW'	'B'
'LOW'	'S'
'LOW'	'S'
'LOW'	'S'
'AVERAGE'	'B'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'B'
'LOW'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'LOW'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'HIGH'	'S'
'HIGH'	'S'
'LOW'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'LOW'	'B'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'LOW'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'HIGH'	'S'
'AVERAGE'	'B'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'LOW'	'B'
'LOW'	'S'
'AVERAGE'	'S'
'AVERAGE'	'B'
'AVERAGE'	'B'
'AVERAGE'	'S'
'LOW'	'S'
'HIGH'	'S'
'HIGH'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'LOW'	'B'
'LOW'	'B'
'LOW'	'B'
'LOW'	'B'
'LOW'	'B'
'LOW'	'B'
'LOW'	'B'
'AVERAGE'	'S'
'AVERAGE'	'S'
'LOW'	'B'
'HIGH'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'LOW'	'S'
'LOW'	'S'
'HIGH'	'S'
'HIGH'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'LOW'	'B'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'B'
'HIGH'	'B'
'AVERAGE'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'LOW'	'S'
'AVERAGE'	'S'
'HIGH'	'S'
'HIGH'	'S'
'AVERAGE'	'S'
'LOW'	'B'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'B'
'HIGH'	'S'
'HIGH'	'B'
'HIGH'	'S'
'LOW'	'B'
'LOW'	'S'
'LOW'	'S'
'LOW'	'B'
'AVERAGE'	'S'
'LOW'	'B'
'AVERAGE'	'B'
'AVERAGE'	'B'
'LOW'	'B'
'HIGH'	'S'
'LOW'	'B'
'HIGH'	'B'
'LOW'	'B'
'LOW'	'B'
'LOW'	'B'
'LOW'	'B'
'AVERAGE'	'S'
'LOW'	'B'
'AVERAGE'	'B'
'LOW'	'B'
'HIGH'	'B'
'LOW'	'S'
'LOW'	'B'
'AVERAGE'	'B'
'LOW'	'B'
'AVERAGE'	'S'
'HIGH'	'S'
'LOW'	'S'
'LOW'	'B'
'AVERAGE'	'B'
'AVERAGE'	'S'
'LOW'	'S'
'HIGH'	'B'
'HIGH'	'S'
'HIGH'	'B'
'AVERAGE'	'B'
'LOW'	'S'
'AVERAGE'	'B'
'HIGH'	'S'
'AVERAGE'	'S'
'LOW'	'B'
'HIGH'	'B'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'S'
'AVERAGE'	'B'
'AVERAGE'	'S'
'HIGH'	'S'
'LOW'	'B'
'LOW'	'B'

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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309914&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309914&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309914&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	Big Analytics Cloud Computing Center

Tabulation of Results
score x group
	B	S
AVERAGE	70	120
HIGH	47	78
LOW	60	71

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
score  x  group \tabularnewline
  & B & S \tabularnewline
AVERAGE & 70 & 120 \tabularnewline
HIGH & 47 & 78 \tabularnewline
LOW & 60 & 71 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309914&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]score  x  group[/C][/ROW]
[ROW][C] [/C][C]B[/C][C]S[/C][/ROW]
[C]AVERAGE[/C][C]70[/C][C]120[/C][/ROW]
[C]HIGH[/C][C]47[/C][C]78[/C][/ROW]
[C]LOW[/C][C]60[/C][C]71[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309914&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309914&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
score x group
	B	S
AVERAGE	70	120
HIGH	47	78
LOW	60	71

Tabulation of Expected Results
score x group
	B	S
AVERAGE	75.4	114.6
HIGH	49.61	75.39
LOW	51.99	79.01

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
score  x  group \tabularnewline
  & B & S \tabularnewline
AVERAGE & 75.4 & 114.6 \tabularnewline
HIGH & 49.61 & 75.39 \tabularnewline
LOW & 51.99 & 79.01 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309914&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]score  x  group[/C][/ROW]
[ROW][C] [/C][C]B[/C][C]S[/C][/ROW]
[C]AVERAGE[/C][C]75.4[/C][C]114.6[/C][/ROW]
[C]HIGH[/C][C]49.61[/C][C]75.39[/C][/ROW]
[C]LOW[/C][C]51.99[/C][C]79.01[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309914&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309914&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
score x group
	B	S
AVERAGE	75.4	114.6
HIGH	49.61	75.39
LOW	51.99	79.01

Statistical Results
Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)
Exact Pearson Chi Square Statistic	2.92
P value	0.24

\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 & 2.92 \tabularnewline
P value & 0.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309914&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]2.92[/C][/ROW]
[ROW][C]P value[/C][C]0.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309914&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309914&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	2.92
P value	0.24

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = 1 ; par2 = 2 ; 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