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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 computationThu, 25 Nov 2010 15:05:18 +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/25/t1290697641hv84a1abcpop7ii.htm/, Retrieved Tue, 10 Feb 2026 03:28:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101075, Retrieved Tue, 10 Feb 2026 03:28:00 +0000
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Original text written by user:
IsPrivate?This computation is/was private until 2010-11-27
User-defined keywords
Estimated Impact357

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] [] [2010-11-25 15:05:18] [c474a97a96075919a678ad3d2290b00b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
'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'

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101075&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101075&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101075&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Tabulation of Results
Happiness x Depression
ABCD
A7101016
B1921812
C8254
D26752

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Happiness  x  Depression \tabularnewline
  & A & B & C & D \tabularnewline
A & 7 & 10 & 10 & 16 \tabularnewline
B & 19 & 21 & 8 & 12 \tabularnewline
C & 8 & 2 & 5 & 4 \tabularnewline
D & 26 & 7 & 5 & 2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101075&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Happiness  x  Depression[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]A[/C][C]7[/C][C]10[/C][C]10[/C][C]16[/C][/ROW]
[C]B[/C][C]19[/C][C]21[/C][C]8[/C][C]12[/C][/ROW]
[C]C[/C][C]8[/C][C]2[/C][C]5[/C][C]4[/C][/ROW]
[C]D[/C][C]26[/C][C]7[/C][C]5[/C][C]2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101075&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101075&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 Depression
ABCD
A7101016
B1921812
C8254
D26752






Tabulation of Expected Results
Happiness x Depression
ABCD
A15.9310.627.439.02
B22.2214.8110.3712.59
C7.044.693.283.99
D14.819.886.918.4

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Happiness  x  Depression \tabularnewline
  & A & B & C & D \tabularnewline
A & 15.93 & 10.62 & 7.43 & 9.02 \tabularnewline
B & 22.22 & 14.81 & 10.37 & 12.59 \tabularnewline
C & 7.04 & 4.69 & 3.28 & 3.99 \tabularnewline
D & 14.81 & 9.88 & 6.91 & 8.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101075&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Happiness  x  Depression[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]A[/C][C]15.93[/C][C]10.62[/C][C]7.43[/C][C]9.02[/C][/ROW]
[C]B[/C][C]22.22[/C][C]14.81[/C][C]10.37[/C][C]12.59[/C][/ROW]
[C]C[/C][C]7.04[/C][C]4.69[/C][C]3.28[/C][C]3.99[/C][/ROW]
[C]D[/C][C]14.81[/C][C]9.88[/C][C]6.91[/C][C]8.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101075&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101075&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 Depression
ABCD
A15.9310.627.439.02
B22.2214.8110.3712.59
C7.044.693.283.99
D14.819.886.918.4






Statistical Results
Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)
Chi Square Statistic32.19
P value0

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test with simulated p-value
	 (based on 2000 replicates) \tabularnewline
Chi Square Statistic & 32.19 \tabularnewline
P value & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101075&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]Chi Square Statistic[/C][C]32.19[/C][/ROW]
[ROW][C]P value[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101075&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101075&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 simulated p-value (based on 2000 replicates)
Chi Square Statistic32.19
P value0


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 5 ; par2 = 6 ; par3 = Exact Pearson Chi-Squared by Simulation ;
Parameters (R input):
par1 = 5 ; par2 = 6 ; 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 != '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')