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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 computationMon, 21 Oct 2013 09:42:37 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/21/t138236298417oycfbargwc4su.htm/, Retrieved Wed, 11 Feb 2026 00:37:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=217465, Retrieved Wed, 11 Feb 2026 00:37:12 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact346

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [WS6 (H-D)] [2013-10-21 13:15:32] [5656c69feb9996d30e47ca36e253d413]
- R PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2013-10-21 13:42:37] [0147fd68123b42babc023061627c5370] [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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=217465&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=217465&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=217465&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'Sir Maurice George Kendall' @ kendall.wessa.net






Tabulation of Results
Happiness2 x Depression2
HILO
HI5746
LO4316

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Happiness2  x  Depression2 \tabularnewline
  & HI & LO \tabularnewline
HI & 57 & 46 \tabularnewline
LO & 43 & 16 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=217465&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Happiness2  x  Depression2[/C][/ROW]
[ROW][C] [/C][C]HI[/C][C]LO[/C][/ROW]
[C]HI[/C][C]57[/C][C]46[/C][/ROW]
[C]LO[/C][C]43[/C][C]16[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=217465&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=217465&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
Happiness2 x Depression2
HILO
HI5746
LO4316






Tabulation of Expected Results
Happiness2 x Depression2
HILO
HI63.5839.42
LO36.4222.58

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Happiness2  x  Depression2 \tabularnewline
  & HI & LO \tabularnewline
HI & 63.58 & 39.42 \tabularnewline
LO & 36.42 & 22.58 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=217465&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Happiness2  x  Depression2[/C][/ROW]
[ROW][C] [/C][C]HI[/C][C]LO[/C][/ROW]
[C]HI[/C][C]63.58[/C][C]39.42[/C][/ROW]
[C]LO[/C][C]36.42[/C][C]22.58[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=217465&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=217465&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
Happiness2 x Depression2
HILO
HI63.5839.42
LO36.4222.58






Statistical Results
Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)
Exact Pearson Chi Square Statistic4.89
P value0.03

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test with simulated p-value
	 (based on 2000 replicates) \tabularnewline
Exact Pearson Chi Square Statistic & 4.89 \tabularnewline
P value & 0.03 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=217465&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]Exact Pearson Chi Square Statistic[/C][C]4.89[/C][/ROW]
[ROW][C]P value[/C][C]0.03[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=217465&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=217465&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)
Exact Pearson Chi Square Statistic4.89
P value0.03


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):
par3 <- 'Pearson Chi-Squared'
par2 <- '6'
par1 <- '5'
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')