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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_chi_squared_tests.wasp
Title produced by softwareChi-Squared Test, McNemar Test, and Fisher Exact Test
Date of computationThu, 17 Nov 2011 09:43:55 -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/17/t13215412045iov9907g7o9gpo.htm/, Retrieved Wed, 11 Feb 2026 19:18:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=144781, Retrieved Wed, 11 Feb 2026 19:18:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact354

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
- RMPD  [Chi-Squared and McNemar Tests] [ws6 vraag 1- Happ...] [2010-11-25 09:47:50] [ca50229b6b451ac8f5a30a9e3154d674]
- R P       [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Happiness versus ...] [2011-11-17 14:43:55] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=144781&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=144781&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=144781&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.






Tabulation of Results
Happiness x Connected
ABCD
A21895
B1816188
C4735
D1112710

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Happiness  x  Connected \tabularnewline
  & A & B & C & D \tabularnewline
A & 21 & 8 & 9 & 5 \tabularnewline
B & 18 & 16 & 18 & 8 \tabularnewline
C & 4 & 7 & 3 & 5 \tabularnewline
D & 11 & 12 & 7 & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=144781&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Happiness  x  Connected[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]A[/C][C]21[/C][C]8[/C][C]9[/C][C]5[/C][/ROW]
[C]B[/C][C]18[/C][C]16[/C][C]18[/C][C]8[/C][/ROW]
[C]C[/C][C]4[/C][C]7[/C][C]3[/C][C]5[/C][/ROW]
[C]D[/C][C]11[/C][C]12[/C][C]7[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=144781&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=144781&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
ABCD
A21895
B1816188
C4735
D1112710






Tabulation of Expected Results
Happiness x Connected
ABCD
A14.3311.419.827.43
B2015.9313.710.37
C6.335.044.343.28
D13.3310.629.146.91

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Happiness  x  Connected \tabularnewline
  & A & B & C & D \tabularnewline
A & 14.33 & 11.41 & 9.82 & 7.43 \tabularnewline
B & 20 & 15.93 & 13.7 & 10.37 \tabularnewline
C & 6.33 & 5.04 & 4.34 & 3.28 \tabularnewline
D & 13.33 & 10.62 & 9.14 & 6.91 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=144781&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Happiness  x  Connected[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]A[/C][C]14.33[/C][C]11.41[/C][C]9.82[/C][C]7.43[/C][/ROW]
[C]B[/C][C]20[/C][C]15.93[/C][C]13.7[/C][C]10.37[/C][/ROW]
[C]C[/C][C]6.33[/C][C]5.04[/C][C]4.34[/C][C]3.28[/C][/ROW]
[C]D[/C][C]13.33[/C][C]10.62[/C][C]9.14[/C][C]6.91[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=144781&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=144781&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
ABCD
A14.3311.419.827.43
B2015.9313.710.37
C6.335.044.343.28
D13.3310.629.146.91






Statistical Results
Pearson's Chi-squared test
Chi Square Statistic12.47
Degrees of Freedom9
P value0.19

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Chi Square Statistic & 12.47 \tabularnewline
Degrees of Freedom & 9 \tabularnewline
P value & 0.19 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=144781&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]12.47[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]9[/C][/ROW]
[ROW][C]P value[/C][C]0.19[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=144781&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=144781&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 Statistic12.47
Degrees of Freedom9
P value0.19


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 5 ; par2 = 1 ; par3 = Pearson Chi-Squared ;
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')