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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 and McNemar Tests
Date of computationWed, 24 Nov 2010 12:59:30 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/24/t12906034478qagbdk41os1pvp.htm/, Retrieved Sat, 07 Feb 2026 01:55:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=100097, Retrieved Sat, 07 Feb 2026 01:55:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact369

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] [] [2010-11-24 12:59:30] [82d760768aff8bf374d9817688c406af] [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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100097&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100097&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100097&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Tabulation of Results
Happiness x Connected
HILO
HI6340
LO3425

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Happiness  x  Connected \tabularnewline
  & HI & LO \tabularnewline
HI & 63 & 40 \tabularnewline
LO & 34 & 25 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100097&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Happiness  x  Connected[/C][/ROW]
[ROW][C] [/C][C]HI[/C][C]LO[/C][/ROW]
[C]HI[/C][C]63[/C][C]40[/C][/ROW]
[C]LO[/C][C]34[/C][C]25[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100097&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100097&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
Happiness x Connected
HILO
HI6340
LO3425






Tabulation of Expected Results
Happiness x Connected
HILO
HI61.6741.33
LO35.3323.67

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Happiness  x  Connected \tabularnewline
  & HI & LO \tabularnewline
HI & 61.67 & 41.33 \tabularnewline
LO & 35.33 & 23.67 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100097&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Happiness  x  Connected[/C][/ROW]
[ROW][C] [/C][C]HI[/C][C]LO[/C][/ROW]
[C]HI[/C][C]61.67[/C][C]41.33[/C][/ROW]
[C]LO[/C][C]35.33[/C][C]23.67[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100097&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100097&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
Happiness x Connected
HILO
HI61.6741.33
LO35.3323.67






Statistical Results
Pearson's Chi-squared test with Yates' continuity correction
Chi Square Statistic0.08
Degrees of Freedom1
P value0.78

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test with Yates' continuity correction \tabularnewline
Chi Square Statistic & 0.08 \tabularnewline
Degrees of Freedom & 1 \tabularnewline
P value & 0.78 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100097&T=3

[TABLE]
[ROW][C]Statistical Results[/C][/ROW]
[ROW][C]Pearson's Chi-squared test with Yates' continuity correction[/C][/ROW]
[ROW][C]Chi Square Statistic[/C][C]0.08[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]1[/C][/ROW]
[ROW][C]P value[/C][C]0.78[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100097&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100097&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
Chi Square Statistic0.08
Degrees of Freedom1
P value0.78


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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 != 'McNemar Chi-Squared') {
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)
a<-table.element(a, 'Chi Square Statistic', 1, TRUE)
a<-table.element(a, round(cst$statistic, digits=2), 1,FALSE)
a<-table.row.end(a)
if(!simulate.p.value){
a<-table.row.start(a)
a<-table.element(a, 'Degrees of Freedom', 1, TRUE)
a<-table.element(a, cst$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')