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Author

*The author of this computation has been verified*

R Software Module

rwasp_chi_squared_tests.wasp

Title produced by software

Chi-Squared Test, McNemar Test, and Fisher Exact Test

Date of computation

Sun, 22 Nov 2015 14:58:29 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/22/t1448204367nx6v6s6st7g9ohn.htm/, Retrieved Mon, 03 Nov 2025 17:15:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283823, Retrieved Mon, 03 Nov 2025 17:15:52 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

581

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Notched Boxplots] [] [2015-08-02 10:20:32] [32b17a345b130fdf5cc88718ed94a974]
- RMPD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2015-11-22 14:58:29] [63a9f0ea7bb98050796b649e85481845] [Current]
-    D      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2015-11-28 20:03:11] [e7afe482707cd0d9e12999f107a77777] 
- R  D      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Task 10 - Chapter 5] [2015-11-29 17:09:05] [be3a328ac39a2f037654611efd7bd567] 
- RMPD      [One Sample Tests about the Mean] [Vraag 1] [2015-12-22 13:43:45] [2710f8dea95e981897be7c03387b4566] 
- RMPD      [Two-Way ANOVA] [Vraag 2] [2015-12-22 13:50:53] [2710f8dea95e981897be7c03387b4566] 
- RMPD      [Paired and Unpaired Two Samples Tests about the Mean] [Vraag 3] [2015-12-22 16:17:34] [2710f8dea95e981897be7c03387b4566] 
- R PD      [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Vraag 4] [2015-12-22 16:37:28] [2710f8dea95e981897be7c03387b4566] 
- RMPD      [Multiple Regression] [Vraag 5] [2015-12-22 16:42:13] [2710f8dea95e981897be7c03387b4566] 
- RMPD      [Skewness and Kurtosis Test] [Vraag 6.1] [2015-12-22 16:52:32] [2710f8dea95e981897be7c03387b4566] 
- RMPD      [Central Tendency] [Vraag 6.2] [2015-12-22 16:55:00] [2710f8dea95e981897be7c03387b4566] 
- RMPD      [Testing Mean with unknown Variance - Critical Value] [Vraag 6.3] [2015-12-22 17:00:26] [2710f8dea95e981897be7c03387b4566] 
- RMPD      [Exponential Smoothing] [Vraag 7] [2015-12-22 17:03:29] [2710f8dea95e981897be7c03387b4566] 
- RMPD      [Notched Boxplots] [Vraag 9] [2015-12-22 17:06:13] [2710f8dea95e981897be7c03387b4566] 
- RMPD      [Kendall tau Correlation Matrix] [Vraag 10] [2015-12-22 17:09:20] [2710f8dea95e981897be7c03387b4566] 

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Dataseries X:

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Boxplots

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'A' "'A'" "'HI'" "'HI'"
'A' "'D'" "'HI'" "'LO'"
'C' "'D'" "'LO'" "'LO'"
'C' "'A'" "'LO'" "'HI'"
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'C' "'B'" "'LO'" "'HI'"
'C' "'B'" "'LO'" "'HI'"
'A' "'A'" "'HI'" "'HI'"
'A' "'A'" "'HI'" "'HI'"
'A' "'D'" "'HI'" "'LO'"
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'A' "'A'" "'HI'" "'HI'"
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'A' "'A'" "'HI'" "'HI'"
'A' "'D'" "'HI'" "'LO'"
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'A' "'A'" "'HI'" "'HI'"
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'D' "'B'" "'LO'" "'HI'"
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'A' "'C'" "'HI'" "'LO'"
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'C' "'B'" "'LO'" "'HI'"
'D' "'C'" "'LO'" "'LO'"
'A' "'A'" "'HI'" "'HI'"
'A' "'D'" "'HI'" "'LO'"
'A' "'B'" "'HI'" "'HI'"
'A' "'A'" "'HI'" "'HI'"
'C' "'B'" "'LO'" "'HI'"
'A' "'A'" "'HI'" "'HI'"
'A' "'D'" "'HI'" "'LO'"
'A' "'A'" "'HI'" "'HI'"
'C' "'D'" "'LO'" "'LO'"
'A' "'B'" "'HI'" "'HI'"
'D' "'D'" "'LO'" "'LO'"
'A' "'A'" "'HI'" "'HI'"
'A' "'B'" "'HI'" "'HI'"
'A' "'D'" "'HI'" "'LO'"
'D' "'D'" "'LO'" "'LO'"
'A' "'B'" "'HI'" "'HI'"
'A' "'D'" "'HI'" "'LO'"
'A' "'C'" "'HI'" "'LO'"
'D' "'B'" "'LO'" "'HI'"
'D' "'A'" "'LO'" "'HI'"
'A' "'A'" "'HI'" "'HI'"
'C' "'B'" "'LO'" "'HI'"
'C' "'B'" "'LO'" "'HI'"
'D' "'B'" "'LO'" "'HI'"
'A' "'B'" "'HI'" "'HI'"
'D' "'D'" "'LO'" "'LO'"
'A' "'B'" "'HI'" "'HI'"
'D' "'B'" "'LO'" "'HI'"
'A' "'B'" "'HI'" "'HI'"
'C' "'B'" "'LO'" "'HI'"
'A' "'C'" "'HI'" "'LO'"
'C' "'A'" "'LO'" "'HI'"
'A' "'A'" "'HI'" "'HI'"
'C' "'A'" "'LO'" "'HI'"
'D' "'B'" "'LO'" "'HI'"
'A' "'C'" "'HI'" "'LO'"
'D' "'D'" "'LO'" "'LO'"
'A' "'B'" "'HI'" "'HI'"
'D' "'B'" "'LO'" "'HI'"
'C' "'B'" "'LO'" "'HI'"
'C' "'A'" "'LO'" "'HI'"
'D' "'D'" "'LO'" "'LO'"
'C' "'B'" "'LO'" "'HI'"
'D' "'D'" "'LO'" "'LO'"
'D' "'B'" "'LO'" "'HI'"
'D' "'C'" "'LO'" "'LO'"
'A' "'B'" "'HI'" "'HI'"
'C' "'A'" "'LO'" "'HI'"
'A' "'B'" "'HI'" "'HI'"
'A' "'B'" "'HI'" "'HI'"
'D' "'A'" "'LO'" "'HI'"
'A' "'A'" "'HI'" "'HI'"
'D' "'D'" "'LO'" "'LO'"
'A' "'D'" "'HI'" "'LO'"
'D' "'D'" "'LO'" "'LO'"
'D' "'A'" "'LO'" "'HI'"
'C' "'C'" "'LO'" "'LO'"
'A' "'A'" "'HI'" "'HI'"
'A' "'D'" "'HI'" "'LO'"
'C' "'D'" "'LO'" "'LO'"
'D' "'C'" "'LO'" "'LO'"
'A' "'C'" "'HI'" "'LO'"
'D' "'B'" "'LO'" "'HI'"
'C' "'A'" "'LO'" "'HI'"
'A' "'C'" "'HI'" "'LO'"
'D' "'D'" "'LO'" "'LO'"
'D' "'C'" "'LO'" "'LO'"

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283823&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283823&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283823&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Tabulation of Results
Learning4 x Happiness4
	'A'	'B'	'C'	'D'
A	26	27	12	18
C	11	22	2	8
D	6	11	5	14

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Learning4  x  Happiness4 \tabularnewline
  & 'A' & 'B' & 'C' & 'D' \tabularnewline
A & 26 & 27 & 12 & 18 \tabularnewline
C & 11 & 22 & 2 & 8 \tabularnewline
D & 6 & 11 & 5 & 14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283823&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Learning4  x  Happiness4[/C][/ROW]
[ROW][C] [/C][C]'A'[/C][C]'B'[/C][C]'C'[/C][C]'D'[/C][/ROW]
[C]A[/C][C]26[/C][C]27[/C][C]12[/C][C]18[/C][/ROW]
[C]C[/C][C]11[/C][C]22[/C][C]2[/C][C]8[/C][/ROW]
[C]D[/C][C]6[/C][C]11[/C][C]5[/C][C]14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283823&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283823&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Tabulation of Results
Learning4 x Happiness4
	'A'	'B'	'C'	'D'
A	26	27	12	18
C	11	22	2	8
D	6	11	5	14

Tabulation of Expected Results
Learning4 x Happiness4
	'A'	'B'	'C'	'D'
A	22.03	30.74	9.73	20.49
C	11.41	15.93	5.04	10.62
D	9.56	13.33	4.22	8.89

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Learning4  x  Happiness4 \tabularnewline
  & 'A' & 'B' & 'C' & 'D' \tabularnewline
A & 22.03 & 30.74 & 9.73 & 20.49 \tabularnewline
C & 11.41 & 15.93 & 5.04 & 10.62 \tabularnewline
D & 9.56 & 13.33 & 4.22 & 8.89 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283823&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Learning4  x  Happiness4[/C][/ROW]
[ROW][C] [/C][C]'A'[/C][C]'B'[/C][C]'C'[/C][C]'D'[/C][/ROW]
[C]A[/C][C]22.03[/C][C]30.74[/C][C]9.73[/C][C]20.49[/C][/ROW]
[C]C[/C][C]11.41[/C][C]15.93[/C][C]5.04[/C][C]10.62[/C][/ROW]
[C]D[/C][C]9.56[/C][C]13.33[/C][C]4.22[/C][C]8.89[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283823&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283823&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Tabulation of Expected Results
Learning4 x Happiness4
	'A'	'B'	'C'	'D'
A	22.03	30.74	9.73	20.49
C	11.41	15.93	5.04	10.62
D	9.56	13.33	4.22	8.89

Statistical Results
Pearson's Chi-squared test
Pearson Chi Square Statistic	11.63
Degrees of Freedom	6
P value	0.07

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Pearson Chi Square Statistic & 11.63 \tabularnewline
Degrees of Freedom & 6 \tabularnewline
P value & 0.07 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283823&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]11.63[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]6[/C][/ROW]
[ROW][C]P value[/C][C]0.07[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283823&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283823&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Statistical Results
Pearson's Chi-squared test
Pearson Chi Square Statistic	11.63
Degrees of Freedom	6
P value	0.07

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = Pearson Chi-Squared ;

Parameters (R input):

par1 = 1 ; par2 = 2 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code