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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 computationWed, 13 Nov 2013 12:30:43 -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/2013/Nov/13/t1384363884dccwqvg8g4ycnks.htm/, Retrieved Tue, 10 Feb 2026 10:48:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=224840, Retrieved Tue, 10 Feb 2026 10:48:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact356

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] [Task 2] [2013-11-13 16:43:50] [947cbe24e101527daf12b807d6a22f40]
-   PD  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Task 2] [2013-11-13 16:53:21] [947cbe24e101527daf12b807d6a22f40]
-   PD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Task 2] [2013-11-13 16:57:24] [947cbe24e101527daf12b807d6a22f40]
-   PD      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Task 3] [2013-11-13 17:05:36] [947cbe24e101527daf12b807d6a22f40]
-    D        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Task 3] [2013-11-13 17:25:54] [947cbe24e101527daf12b807d6a22f40]
-    D            [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Task 4] [2013-11-13 17:30:43] [46d3d8bfbaf7691f7408e38ca0da8f78] [Current]
- RM                [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Task 4] [2013-11-13 17:31:32] [947cbe24e101527daf12b807d6a22f40]
- R  D              [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Task 4] [2013-11-13 17:40:45] [947cbe24e101527daf12b807d6a22f40]
-    D              [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Task 4] [2013-11-13 17:43:00] [947cbe24e101527daf12b807d6a22f40]
- RM                  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Task 4] [2013-11-13 17:44:32] [947cbe24e101527daf12b807d6a22f40]
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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'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224840&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224840&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224840&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'George Udny Yule' @ yule.wessa.net






Tabulation of Results
Depression4 x Connected4
ABCD
A12171516
B151357
C107101
D17674

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Depression4  x  Connected4 \tabularnewline
  & A & B & C & D \tabularnewline
A & 12 & 17 & 15 & 16 \tabularnewline
B & 15 & 13 & 5 & 7 \tabularnewline
C & 10 & 7 & 10 & 1 \tabularnewline
D & 17 & 6 & 7 & 4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224840&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Depression4  x  Connected4[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]A[/C][C]12[/C][C]17[/C][C]15[/C][C]16[/C][/ROW]
[C]B[/C][C]15[/C][C]13[/C][C]5[/C][C]7[/C][/ROW]
[C]C[/C][C]10[/C][C]7[/C][C]10[/C][C]1[/C][/ROW]
[C]D[/C][C]17[/C][C]6[/C][C]7[/C][C]4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224840&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224840&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
Depression4 x Connected4
ABCD
A12171516
B151357
C107101
D17674






Tabulation of Expected Results
Depression4 x Connected4
ABCD
A2015.9313.710.37
B13.3310.629.146.91
C9.337.436.44.84
D11.339.027.775.88

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Depression4  x  Connected4 \tabularnewline
  & A & B & C & D \tabularnewline
A & 20 & 15.93 & 13.7 & 10.37 \tabularnewline
B & 13.33 & 10.62 & 9.14 & 6.91 \tabularnewline
C & 9.33 & 7.43 & 6.4 & 4.84 \tabularnewline
D & 11.33 & 9.02 & 7.77 & 5.88 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224840&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Depression4  x  Connected4[/C][/ROW]
[ROW][C] [/C][C]A[/C][C]B[/C][C]C[/C][C]D[/C][/ROW]
[C]A[/C][C]20[/C][C]15.93[/C][C]13.7[/C][C]10.37[/C][/ROW]
[C]B[/C][C]13.33[/C][C]10.62[/C][C]9.14[/C][C]6.91[/C][/ROW]
[C]C[/C][C]9.33[/C][C]7.43[/C][C]6.4[/C][C]4.84[/C][/ROW]
[C]D[/C][C]11.33[/C][C]9.02[/C][C]7.77[/C][C]5.88[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224840&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224840&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
Depression4 x Connected4
ABCD
A2015.9313.710.37
B13.3310.629.146.91
C9.337.436.44.84
D11.339.027.775.88






Statistical Results
Pearson's Chi-squared test
Pearson Chi Square Statistic18.74
Degrees of Freedom9
P value0.03

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Pearson Chi Square Statistic & 18.74 \tabularnewline
Degrees of Freedom & 9 \tabularnewline
P value & 0.03 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224840&T=3

[TABLE]
[ROW][C]Statistical Results[/C][/ROW]
[ROW][C]Pearson's Chi-squared test[/C][/ROW]
[ROW][C]Pearson Chi Square Statistic[/C][C]18.74[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]9[/C][/ROW]
[ROW][C]P value[/C][C]0.03[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224840&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224840&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
Pearson Chi Square Statistic18.74
Degrees of Freedom9
P value0.03


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 5 ; par2 = 1 ; par3 = Pearson Chi-Squared ;
Parameters (R input):
par1 = 6 ; 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=='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')