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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 14:56:55 +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/t129069693670tj6gl4mg2705i.htm/, Retrieved Tue, 10 Feb 2026 14:26:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101066, Retrieved Tue, 10 Feb 2026 14:26:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact363

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Chi-Squared and McNemar Tests] [Happiness x Conne...] [2010-11-25 14:11:16] [14bb7b0a8b81eed6207eeab240457b45]
F   P     [Chi-Squared and McNemar Tests] [Happiness x separ...] [2010-11-25 14:56:55] [186d70462ffc26ec970915be294cb975] [Current]
Feedback Forum
2010-12-02 11:38:19 [cd1371e651d5ceb0aaa1282036220853] [reply] 
Voor de berekening moet de simulatie worden gebruikt

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
'A'	'A'	'D'	'A'	'B'	'B'	'D'
'A'	'C'	'A'	'B'	'A'	'C'	'A'
'D'	'B'	'A'	'A'	'D'	'A'	'C'
'D'	'C'	'C'	'D'	'D'	'B'	'C'
'B'	'A'	'C'	'A'	'A'	'A'	'B'
'B'	'D'	'D'	'C'	'A'	'B'	'A'
'A'	'D'	'A'	'A'	'B'	'A'	'D'
'B'	'B'	'C'	'A'	'B'	'C'	'A'
'B'	'B'	'C'	'A'	'B'	'D'	'B'
'A'	'A'	'C'	'D'	'B'	'B'	'B'
'A'	'D'	'A'	'C'	'A'	'D'	'A'
'B'	'B'	'A'	'A'	'A'	'D'	'D'
'A'	'B'	'A'	'A'	'D'	'A'	'C'
'A'	'A'	'A'	'B'	'A'	'A'	'D'
'C'	'A'	'A'	'A'	'A'	'D'	'A'
'C'	'C'	'C'	'A'	'B'	'A'	'D'
'B'	'C'	'C'	'C'	'B'	'A'	'B'
'A'	'A'	'A'	'A'	'A'	'C'	'A'
'A'	'A'	'A'	'B'	'B'	'D'	'D'
'C'	'C'	'A'	'A'	'A'	'B'	'D'
'C'	'C'	'A'	'B'	'A'	'D'	'C'
'D'	'D'	'A'	'A'	'D'	'A'	'C'
'A'	'A'	'A'	'A'	'B'	'B'	'D'
'A'	'A'	'A'	'B'	'D'	'A'	'D'
'A'	'C'	'A'	'D'	'A'	'C'	'A'
'A'	'C'	'A'	'A'	'D'	'D'	'A'
'B'	'B'	'A'	'C'	'A'	'C'	'B'
'C'	'A'	'C'	'A'	'B'	'A'	'C'
'C'	'C'	'A'	'A'	'B'	'A'	'A'
'B'	'C'	'C'	'C'	'D'	'B'	'C'
'D'	'D'	'C'	'A'	'A'	'D'	'A'
'D'	'C'	'D'	'D'	'C'	'A'	'D'
'A'	'D'	'C'	'C'	'A'	'D'	'C'
'B'	'A'	'A'	'A'	'B'	'C'	'A'
'B'	'D'	'C'	'A'	'B'	'B'	'B'
'C'	'C'	'D'	'D'	'A'	'D'	'C'
'D'	'D'	'D'	'D'	'D'	'A'	'D'
'B'	'C'	'C'	'A'	'B'	'B'	'C'
'D'	'D'	'A'	'C'	'A'	'D'	'B'
'B'	'C'	'A'	'C'	'C'	'D'	'C'
'A'	'C'	'A'	'C'	'B'	'D'	'B'
'B'	'C'	'C'	'A'	'A'	'A'	'B'
'A'	'C'	'A'	'A'	'A'	'D'	'D'
'B'	'C'	'C'	'C'	'D'	'A'	'D'
'A'	'D'	'C'	'C'	'D'	'C'	'C'
'A'	'B'	'D'	'A'	'D'	'B'	'C'
'A'	'A'	'C'	'A'	'B'	'D'	'D'
'C'	'B'	'C'	'B'	'B'	'C'	'B'
'B'	'A'	'A'	'B'	'A'	'A'	'B'
'A'	'C'	'C'	'A'	'C'	'C'	'B'
'C'	'A'	'A'	'A'	'A'	'D'	'C'
'C'	'D'	'C'	'C'	'B'	'A'	'C'
'C'	'C'	'D'	'A'	'D'	'A'	'D'
'B'	'A'	'A'	'A'	'D'	'A'	'D'
'C'	'C'	'D'	'D'	'D'	'C'	'D'
'A'	'C'	'C'	'D'	'B'	'B'	'B'
'A'	'B'	'A'	'A'	'A'	'B'	'B'
'D'	'B'	'A'	'A'	'B'	'D'	'C'
'A'	'B'	'C'	'B'	'D'	'D'	'B'
'B'	'B'	'A'	'C'	'D'	'A'	'C'
'D'	'D'	'D'	'D'	'D'	'A'	'D'
'A'	'B'	'A'	'A'	'C'	'B'	'B'
'B'	'B'	'A'	'A'	'D'	'B'	'B'
'D'	'B'	'C'	'B'	'B'	'A'	'D'
'B'	'D'	'A'	'A'	'B'	'B'	'D'
'B'	'A'	'A'	'A'	'D'	'C'	'A'
'B'	'B'	'A'	'A'	'D'	'A'	'C'
'D'	'D'	'A'	'B'	'D'	'B'	'B'
'A'	'A'	'D'	'A'	'B'	'B'	'D'
'B'	'A'	'A'	'A'	'B'	'A'	'C'
'A'	'B'	'D'	'D'	'B'	'B'	'C'
'D'	'A'	'C'	'B'	'A'	'A'	'D'
'B'	'A'	'A'	'A'	'B'	'B'	'A'
'A'	'A'	'A'	'A'	'B'	'D'	'C'
'B'	'D'	'A'	'A'	'C'	'C'	'A'
'A'	'D'	'A'	'D'	'D'	'A'	'A'
'A'	'A'	'A'	'A'	'A'	'B'	'C'
'B'	'D'	'A'	'B'	'C'	'A'	'C'
'D'	'D'	'D'	'A'	'B'	'B'	'B'
'A'	'D'	'A'	'A'	'C'	'D'	'D'
'C'	'B'	'A'	'A'	'B'	'C'	'A'
'A'	'A'	'A'	'A'	'A'	'D'	'D'
'B'	'A'	'A'	'A'	'B'	'D'	'C'
'A'	'C'	'C'	'A'	'A'	'B'	'B'
'C'	'B'	'C'	'B'	'B'	'B'	'C'
'C'	'D'	'A'	'C'	'B'	'B'	'B'
'A'	'A'	'C'	'D'	'B'	'B'	'B'
'C'	'B'	'A'	'A'	'B'	'B'	'C'
'D'	'C'	'A'	'A'	'C'	'A'	'D'
'C'	'C'	'C'	'A'	'D'	'A'	'C'
'D'	'B'	'D'	'D'	'A'	'B'	'B'
'B'	'C'	'A'	'A'	'C'	'A'	'D'
'B'	'A'	'A'	'A'	'B'	'B'	'B'
'C'	'D'	'C'	'A'	'B'	'A'	'A'
'D'	'D'	'D'	'A'	'C'	'D'	'A'
'A'	'B'	'A'	'C'	'A'	'C'	'A'
'A'	'B'	'A'	'A'	'D'	'A'	'C'
'B'	'D'	'A'	'D'	'B'	'C'	'A'
'A'	'B'	'A'	'A'	'A'	'C'	'A'
'C'	'B'	'C'	'C'	'B'	'D'	'B'
'A'	'B'	'A'	'A'	'A'	'D'	'B'
'A'	'B'	'A'	'B'	'D'	'A'	'B'
'B'	'A'	'A'	'A'	'A'	'B'	'A'
'C'	'D'	'C'	'B'	'D'	'C'	'C'
'C'	'A'	'A'	'B'	'B'	'A'	'A'
'A'	'C'	'D'	'A'	'D'	'A'	'C'
'A'	'B'	'A'	'A'	'A'	'C'	'B'
'A'	'A'	'A'	'A'	'B'	'A'	'C'
'B'	'B'	'A'	'B'	'D'	'A'	'D'
'A'	'A'	'D'	'D'	'D'	'A'	'D'
'D'	'B'	'A'	'A'	'B'	'A'	'A'
'D'	'C'	'A'	'A'	'D'	'A'	'B'
'C'	'A'	'A'	'B'	'C'	'C'	'A'
'C'	'C'	'D'	'B'	'B'	'A'	'D'
'A'	'B'	'D'	'C'	'A'	'B'	'B'
'A'	'C'	'A'	'A'	'A'	'D'	'A'
'C'	'A'	'C'	'A'	'B'	'A'	'D'
'B'	'A'	'C'	'D'	'B'	'B'	'C'
'C'	'B'	'D'	'B'	'B'	'D'	'C'
'A'	'B'	'A'	'A'	'B'	'A'	'A'
'C'	'A'	'D'	'B'	'D'	'A'	'D'
'D'	'D'	'A'	'A'	'B'	'A'	'B'
'A'	'A'	'D'	'A'	'B'	'C'	'A'
'A'	'A'	'A'	'A'	'B'	'D'	'B'
'C'	'D'	'C'	'A'	'B'	'C'	'B'
'D'	'C'	'A'	'A'	'C'	'C'	'A'
'A'	'C'	'C'	'C'	'A'	'D'	'A'
'A'	'A'	'A'	'B'	'A'	'D'	'B'
'C'	'B'	'C'	'D'	'A'	'C'	'A'
'B'	'C'	'D'	'B'	'B'	'B'	'C'
'C'	'C'	'A'	'C'	'C'	'C'	'C'
'D'	'C'	'D'	'B'	'D'	'A'	'C'
'A'	'A'	'A'	'D'	'B'	'D'	'B'
'D'	'D'	'D'	'B'	'B'	'A'	'D'
'A'	'A'	'C'	'A'	'B'	'B'	'B'
'C'	'D'	'C'	'A'	'A'	'A'	'A'
'D'	'D'	'D'	'D'	'D'	'A'	'D'
'B'	'B'	'C'	'B'	'B'	'A'	'D'
'D'	'B'	'D'	'C'	'D'	'A'	'D'
'B'	'B'	'D'	'D'	'B'	'C'	'D'
'D'	'B'	'D'	'D'	'C'	'B'	'C'
'C'	'B'	'A'	'D'	'B'	'D'	'D'
'D'	'B'	'C'	'D'	'A'	'A'	'A'
'D'	'B'	'A'	'A'	'B'	'B'	'A'
'D'	'D'	'A'	'B'	'B'	'B'	'B'
'A'	'D'	'D'	'D'	'A'	'C'	'A'
'C'	'D'	'A'	'A'	'A'	'B'	'B'
'B'	'B'	'D'	'A'	'D'	'B'	'D'
'C'	'D'	'A'	'A'	'D'	'C'	'B'
'B'	'C'	'D'	'D'	'D'	'A'	'B'
'A'	'A'	'D'	'D'	'A'	'B'	'A'
'A'	'A'	'C'	'A'	'C'	'A'	'A'
'B'	'A'	'A'	'D'	'A'	'D'	'C'
'B'	'A'	'A'	'D'	'D'	'B'	'C'
'B'	'B'	'C'	'D'	'D'	'A'	'C'
'C'	'D'	'D'	'D'	'C'	'A'	'A'
'B'	'C'	'A'	'A'	'C'	'A'	'D'
'C'	'A'	'D'	'D'	'B'	'A'	'C'
'C'	'B'	'C'	'D'	'A'	'C'	'A'
'B'	'C'	'A'	'B'	'C'	'D'	'A'
'C'	'B'	'D'	'D'	'D'	'A'	'A'
'B'	'B'	'D'	'D'	'C'	'A'	'C'

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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101066&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101066&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101066&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






Tabulation of Results
Separate x Happiness
ABCD
A132326
B1217314
C108911
D81259

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Separate  x  Happiness \tabularnewline
  & A & B & C & D \tabularnewline
A & 13 & 23 & 2 & 6 \tabularnewline
B & 12 & 17 & 3 & 14 \tabularnewline
C & 10 & 8 & 9 & 11 \tabularnewline
D & 8 & 12 & 5 & 9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101066&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Separate  x  Happiness[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]A[/C][C]13[/C][C]23[/C][C]2[/C][C]6[/C][/ROW]
[C]B[/C][C]12[/C][C]17[/C][C]3[/C][C]14[/C][/ROW]
[C]C[/C][C]10[/C][C]8[/C][C]9[/C][C]11[/C][/ROW]
[C]D[/C][C]8[/C][C]12[/C][C]5[/C][C]9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101066&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101066&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
Separate x Happiness
ABCD
A132326
B1217314
C108911
D81259






Tabulation of Expected Results
Separate x Happiness
ABCD
A11.6816.35.1610.86
B12.2117.045.411.36
C10.0914.074.469.38
D9.0212.593.998.4

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Separate  x  Happiness \tabularnewline
  & A & B & C & D \tabularnewline
A & 11.68 & 16.3 & 5.16 & 10.86 \tabularnewline
B & 12.21 & 17.04 & 5.4 & 11.36 \tabularnewline
C & 10.09 & 14.07 & 4.46 & 9.38 \tabularnewline
D & 9.02 & 12.59 & 3.99 & 8.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101066&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Separate  x  Happiness[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]A[/C][C]11.68[/C][C]16.3[/C][C]5.16[/C][C]10.86[/C][/ROW]
[C]B[/C][C]12.21[/C][C]17.04[/C][C]5.4[/C][C]11.36[/C][/ROW]
[C]C[/C][C]10.09[/C][C]14.07[/C][C]4.46[/C][C]9.38[/C][/ROW]
[C]D[/C][C]9.02[/C][C]12.59[/C][C]3.99[/C][C]8.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101066&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101066&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
Separate x Happiness
ABCD
A11.6816.35.1610.86
B12.2117.045.411.36
C10.0914.074.469.38
D9.0212.593.998.4






Statistical Results
Pearson's Chi-squared test
Chi Square Statistic16.68
Degrees of Freedom9
P value0.05

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Chi Square Statistic & 16.68 \tabularnewline
Degrees of Freedom & 9 \tabularnewline
P value & 0.05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101066&T=3

[TABLE]
[ROW][C]Statistical Results[/C][/ROW]
[ROW][C]Pearson's Chi-squared test[/C][/ROW]
[ROW][C]Chi Square Statistic[/C][C]16.68[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]9[/C][/ROW]
[ROW][C]P value[/C][C]0.05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101066&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101066&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
Chi Square Statistic16.68
Degrees of Freedom9
P value0.05


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = 5 ; par3 = Pearson Chi-Squared ;
Parameters (R input):
par1 = 2 ; par2 = 5 ; 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')