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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_chi_squared_tests.wasp
Title produced by softwareChi-Squared Test, McNemar Test, and Fisher Exact Test
Date of computationWed, 16 Nov 2011 09:26:56 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/16/t1321453656leovsc26rwxjshd.htm/, Retrieved Tue, 10 Feb 2026 04:55:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143971, Retrieved Tue, 10 Feb 2026 04:55:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact392

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Chi-Squared and McNemar Tests] [] [2010-11-23 13:43:08] [9315c5fa5df29386545a575306c6a452]
-       [Chi-Squared and McNemar Tests] [] [2010-11-25 10:55:25] [91de8b765895d6ee0c73f0d2e284be17]
-   P     [Chi-Squared and McNemar Tests] [] [2010-11-25 18:41:38] [2e1e44f0ae3cb9513dc28781dfdb387b]
- R  D        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Blog question 1 W...] [2011-11-16 14:26:56] [12a6074303e7dbf450a4f3ff6a9ce824] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
'HI'	'HI'	'LO'	'HI'	'HI'	'HI'
'HI'	'LO'	'HI'	'HI'	'HI'	'LO'
'LO'	'HI'	'HI'	'HI'	'LO'	'HI'
'LO'	'LO'	'LO'	'LO'	'LO'	'HI'
'HI'	'HI'	'LO'	'HI'	'HI'	'HI'
'HI'	'LO'	'LO'	'LO'	'HI'	'HI'
'HI'	'LO'	'HI'	'HI'	'HI'	'HI'
'HI'	'HI'	'LO'	'HI'	'HI'	'LO'
'HI'	'HI'	'LO'	'HI'	'HI'	'LO'
'HI'	'HI'	'LO'	'LO'	'HI'	'HI'
'HI'	'LO'	'HI'	'LO'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'LO'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'LO'	'HI'	'HI'	'HI'	'HI'	'LO'
'LO'	'LO'	'LO'	'HI'	'HI'	'HI'
'HI'	'LO'	'LO'	'LO'	'HI'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'LO'	'LO'	'HI'	'HI'	'HI'	'HI'
'LO'	'LO'	'HI'	'HI'	'HI'	'LO'
'LO'	'LO'	'HI'	'HI'	'LO'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'HI'	'HI'	'HI'	'HI'	'LO'	'HI'
'HI'	'LO'	'HI'	'LO'	'HI'	'LO'
'HI'	'LO'	'HI'	'HI'	'LO'	'LO'
'HI'	'HI'	'HI'	'LO'	'HI'	'LO'
'LO'	'HI'	'LO'	'HI'	'HI'	'HI'
'LO'	'LO'	'HI'	'HI'	'HI'	'HI'
'HI'	'LO'	'LO'	'LO'	'LO'	'HI'
'LO'	'LO'	'LO'	'HI'	'HI'	'LO'
'LO'	'LO'	'LO'	'LO'	'LO'	'HI'
'HI'	'LO'	'LO'	'LO'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'HI'	'LO'	'LO'	'HI'	'HI'	'HI'
'LO'	'LO'	'LO'	'LO'	'HI'	'LO'
'LO'	'LO'	'LO'	'LO'	'LO'	'HI'
'HI'	'LO'	'LO'	'HI'	'HI'	'HI'
'LO'	'LO'	'HI'	'LO'	'HI'	'LO'
'HI'	'LO'	'HI'	'LO'	'LO'	'LO'
'HI'	'LO'	'HI'	'LO'	'HI'	'LO'
'HI'	'LO'	'LO'	'HI'	'HI'	'HI'
'HI'	'LO'	'HI'	'HI'	'HI'	'LO'
'HI'	'LO'	'LO'	'LO'	'LO'	'HI'
'HI'	'LO'	'LO'	'LO'	'LO'	'LO'
'HI'	'HI'	'LO'	'HI'	'LO'	'HI'
'HI'	'HI'	'LO'	'HI'	'HI'	'LO'
'LO'	'HI'	'LO'	'HI'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'HI'	'LO'	'LO'	'HI'	'LO'	'LO'
'LO'	'HI'	'HI'	'HI'	'HI'	'LO'
'LO'	'LO'	'LO'	'LO'	'HI'	'HI'
'LO'	'LO'	'LO'	'HI'	'LO'	'HI'
'HI'	'HI'	'HI'	'HI'	'LO'	'HI'
'LO'	'LO'	'LO'	'LO'	'LO'	'LO'
'HI'	'LO'	'LO'	'LO'	'HI'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'LO'	'HI'	'HI'	'HI'	'HI'	'LO'
'HI'	'HI'	'LO'	'HI'	'LO'	'LO'
'HI'	'HI'	'HI'	'LO'	'LO'	'HI'
'LO'	'LO'	'LO'	'LO'	'LO'	'HI'
'HI'	'HI'	'HI'	'HI'	'LO'	'HI'
'HI'	'HI'	'HI'	'HI'	'LO'	'HI'
'LO'	'HI'	'LO'	'HI'	'HI'	'HI'
'HI'	'LO'	'HI'	'HI'	'HI'	'HI'
'HI'	'HI'	'HI'	'HI'	'LO'	'LO'
'HI'	'HI'	'HI'	'HI'	'LO'	'HI'
'LO'	'LO'	'HI'	'HI'	'LO'	'HI'
'HI'	'HI'	'LO'	'HI'	'HI'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'HI'	'HI'	'LO'	'LO'	'HI'	'HI'
'LO'	'HI'	'LO'	'HI'	'HI'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'HI'	'LO'	'HI'	'HI'	'LO'	'LO'
'HI'	'LO'	'HI'	'LO'	'LO'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'HI'	'LO'	'HI'	'HI'	'LO'	'HI'
'LO'	'LO'	'LO'	'HI'	'HI'	'HI'
'HI'	'LO'	'HI'	'HI'	'LO'	'LO'
'LO'	'HI'	'HI'	'HI'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'HI'	'LO'	'LO'	'HI'	'HI'	'HI'
'LO'	'HI'	'LO'	'HI'	'HI'	'HI'
'LO'	'LO'	'HI'	'LO'	'HI'	'HI'
'HI'	'HI'	'LO'	'LO'	'HI'	'HI'
'LO'	'HI'	'HI'	'HI'	'HI'	'HI'
'LO'	'LO'	'HI'	'HI'	'LO'	'HI'
'LO'	'LO'	'LO'	'HI'	'LO'	'HI'
'LO'	'HI'	'LO'	'LO'	'HI'	'HI'
'HI'	'LO'	'HI'	'HI'	'LO'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'LO'	'LO'	'LO'	'HI'	'HI'	'HI'
'LO'	'LO'	'LO'	'HI'	'LO'	'LO'
'HI'	'HI'	'HI'	'LO'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'LO'	'HI'
'HI'	'LO'	'HI'	'LO'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'LO'	'HI'	'LO'	'LO'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'LO'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'LO'	'LO'	'LO'	'HI'	'LO'	'LO'
'LO'	'HI'	'HI'	'HI'	'HI'	'HI'
'HI'	'LO'	'LO'	'HI'	'LO'	'HI'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'HI'	'HI'	'HI'	'HI'	'LO'	'HI'
'HI'	'HI'	'LO'	'LO'	'LO'	'HI'
'LO'	'HI'	'HI'	'HI'	'HI'	'HI'
'LO'	'LO'	'HI'	'HI'	'LO'	'HI'
'LO'	'HI'	'HI'	'HI'	'LO'	'LO'
'LO'	'LO'	'LO'	'HI'	'HI'	'HI'
'HI'	'HI'	'LO'	'LO'	'HI'	'HI'
'HI'	'LO'	'HI'	'HI'	'HI'	'LO'
'LO'	'HI'	'LO'	'HI'	'HI'	'HI'
'HI'	'HI'	'LO'	'LO'	'HI'	'HI'
'LO'	'HI'	'LO'	'HI'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'HI'
'LO'	'HI'	'LO'	'HI'	'LO'	'HI'
'LO'	'LO'	'HI'	'HI'	'HI'	'HI'
'HI'	'HI'	'LO'	'HI'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'LO'	'LO'	'LO'	'HI'	'HI'	'LO'
'LO'	'LO'	'HI'	'HI'	'LO'	'LO'
'HI'	'LO'	'LO'	'LO'	'HI'	'LO'
'HI'	'HI'	'HI'	'HI'	'HI'	'LO'
'LO'	'HI'	'LO'	'LO'	'HI'	'LO'
'HI'	'LO'	'LO'	'HI'	'HI'	'HI'
'LO'	'LO'	'HI'	'LO'	'LO'	'LO'
'LO'	'LO'	'LO'	'HI'	'LO'	'HI'
'HI'	'HI'	'HI'	'LO'	'HI'	'LO'
'LO'	'LO'	'LO'	'HI'	'HI'	'HI'
'HI'	'HI'	'LO'	'HI'	'HI'	'HI'
'LO'	'LO'	'LO'	'HI'	'HI'	'HI'
'LO'	'LO'	'LO'	'LO'	'LO'	'HI'
'HI'	'HI'	'LO'	'HI'	'HI'	'HI'
'LO'	'HI'	'LO'	'LO'	'LO'	'HI'
'HI'	'HI'	'LO'	'LO'	'HI'	'LO'
'LO'	'HI'	'LO'	'LO'	'LO'	'HI'
'LO'	'HI'	'HI'	'LO'	'HI'	'LO'
'LO'	'HI'	'LO'	'LO'	'HI'	'HI'
'LO'	'HI'	'HI'	'HI'	'HI'	'HI'
'LO'	'LO'	'HI'	'HI'	'HI'	'HI'
'HI'	'LO'	'LO'	'LO'	'HI'	'LO'
'LO'	'LO'	'HI'	'HI'	'HI'	'HI'
'HI'	'HI'	'LO'	'HI'	'LO'	'HI'
'LO'	'LO'	'HI'	'HI'	'LO'	'LO'
'HI'	'LO'	'LO'	'LO'	'LO'	'HI'
'HI'	'HI'	'LO'	'LO'	'HI'	'HI'
'HI'	'HI'	'LO'	'HI'	'LO'	'HI'
'HI'	'HI'	'HI'	'LO'	'HI'	'LO'
'HI'	'HI'	'HI'	'LO'	'LO'	'HI'
'HI'	'HI'	'LO'	'LO'	'LO'	'HI'
'LO'	'LO'	'LO'	'LO'	'LO'	'HI'
'HI'	'LO'	'HI'	'HI'	'LO'	'HI'
'LO'	'HI'	'LO'	'LO'	'HI'	'HI'
'LO'	'HI'	'LO'	'LO'	'HI'	'LO'
'HI'	'LO'	'HI'	'HI'	'LO'	'LO'
'LO'	'HI'	'LO'	'LO'	'LO'	'HI'
'HI'	'HI'	'LO'	'LO'	'LO'	'HI'

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143971&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143971&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Tabulation of Results
Connected x Separate
HILO
HI6235
LO2837

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Connected  x  Separate \tabularnewline
  & HI & LO \tabularnewline
HI & 62 & 35 \tabularnewline
LO & 28 & 37 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143971&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Connected  x  Separate[/C][/ROW]
[ROW][C] [/C][C]HI[/C][C]LO[/C][/ROW]
[C]HI[/C][C]62[/C][C]35[/C][/ROW]
[C]LO[/C][C]28[/C][C]37[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143971&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Tabulation of Results
Connected x Separate
HILO
HI6235
LO2837






Tabulation of Expected Results
Connected x Separate
HILO
HI53.8943.11
LO36.1128.89

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Connected  x  Separate \tabularnewline
  & HI & LO \tabularnewline
HI & 53.89 & 43.11 \tabularnewline
LO & 36.11 & 28.89 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143971&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Connected  x  Separate[/C][/ROW]
[ROW][C] [/C][C]HI[/C][C]LO[/C][/ROW]
[C]HI[/C][C]53.89[/C][C]43.11[/C][/ROW]
[C]LO[/C][C]36.11[/C][C]28.89[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143971&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143971&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Tabulation of Expected Results
Connected x Separate
HILO
HI53.8943.11
LO36.1128.89






Statistical Results
Pearson's Chi-squared test with Yates' continuity correction
Pearson Chi Square Statistic6.03
Degrees of Freedom1
P value0.01

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test with Yates' continuity correction \tabularnewline
Pearson Chi Square Statistic & 6.03 \tabularnewline
Degrees of Freedom & 1 \tabularnewline
P value & 0.01 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143971&T=3

[TABLE]
[ROW][C]Statistical Results[/C][/ROW]
[ROW][C]Pearson's Chi-squared test with Yates' continuity correction[/C][/ROW]
[ROW][C]Pearson Chi Square Statistic[/C][C]6.03[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]1[/C][/ROW]
[ROW][C]P value[/C][C]0.01[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143971&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143971&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Statistical Results
Pearson's Chi-squared test with Yates' continuity correction
Pearson Chi Square Statistic6.03
Degrees of Freedom1
P value0.01


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = 1 ; par2 = 2 ; 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')