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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 computationFri, 02 Dec 2011 08:49:54 -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/Dec/02/t1322833809y1ljk78sjod0tcm.htm/, Retrieved Thu, 12 Feb 2026 12:36:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150199, Retrieved Thu, 12 Feb 2026 12:36:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact400

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Cronbach Alpha] [Intrinsic Motivat...] [2010-10-12 11:46:14] [b98453cac15ba1066b407e146608df68]
- R  D  [Cronbach Alpha] [] [2011-10-13 12:23:05] [d49626b9c7bd91ce0b695b5077c2942f]
-         [Cronbach Alpha] [] [2011-10-13 12:53:23] [d49626b9c7bd91ce0b695b5077c2942f]
- RMPD        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2011-12-02 13:49:54] [8a7cc4cdacda1fa59fc196ea0735b051] [Current]
- R P           [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2011-12-02 14:02:46] [d49626b9c7bd91ce0b695b5077c2942f]
-  M              [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2011-12-02 14:03:41] [d49626b9c7bd91ce0b695b5077c2942f]
- R P           [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2011-12-02 14:09:04] [d49626b9c7bd91ce0b695b5077c2942f]
- R P           [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2011-12-15 13:30:28] [d49626b9c7bd91ce0b695b5077c2942f]
- RMP           [Central Tendency] [] [2011-12-15 14:21:05] [d49626b9c7bd91ce0b695b5077c2942f]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7	7	7	5
5	5	5	5
6	5	4	4
4	5	5	5
5	5	5	5
6	6	6	7
7	4	7	7
6	5	5	6
6	7	7	6
6	5	5	6
5	2	4	6
5	5	6	6
4	5	4	6
6	6	6	6
6	6	7	7
5	5	6	5
3	3	4	3
7	6	6	7
3	5	6	6
5	5	6	6
3	3	4	4
5	5	5	6
2	1	2	2
6	5	6	6
3	4	5	5
6	6	6	7
6	6	6	7
5	4	5	5
5	4	5	6
7	5	5	6
6	4	6	6
5	5	6	6
5	6	5	5
4	3	4	4
4	5	6	5
6	5	5	6
5	3	5	5
5	5	5	5
7	7	7	7
5	6	5	6
5	4	5	4
6	5	7	5
5	5	5	5
6	6	7	6
7	7	6	6
5	3	3	4
5	4	4	4
5	6	6	6
6	5	5	5
2	2	4	5
4	4	4	6
4	4	6	5
6	5	5	6
3	4	4	5
6	6	6	6
6	2	5	5
5	4	5	6
6	6	6	6
1	4	6	3
5	5	6	6
7	6	5	6
4	4	5	5
5	6	5	5
6	6	5	6
4	5	4	4
6	6	5	5
6	6	6	6
5	4	6	6
5	6	5	6
3	3	5	5
5	5	5	6
6	5	6	6
5	5	6	6
6	6	6	6
6	6	6	6
4	4	4	4
4	4	4	4
6	5	5	5
7	6	6	7
4	3	3	5
5	6	7	7
6	2	5	5
6	5	6	6
5	3	6	6
3	4	5	5
7	6	6	6
6	5	6	7
4	4	4	5
4	5	6	4
5	5	5	5
3	4	4	4
7	7	7	6
6	4	6	6
6	6	6	5
4	4	4	4
5	4	5	5
6	6	6	7
5	3	5	6
6	4	4	5
6	7	7	6
4	5	6	6
5	5	5	5
6	6	6	6
5	5	6	6
5	5	5	5
4	4	5	5
4	5	5	4
6	6	5	7
5	5	7	7
6	5	6	5
5	4	7	7
6	4	6	6
5	5	5	5
4	5	4	5
6	6	6	7
4	5	4	5
5	3	3	5
5	5	5	5
6	3	5	5
3	4	5	3
5	4	5	5
4	5	5	5
5	2	5	4
5	5	3	4
7	7	7	7
5	6	6	6
7	6	6	6
5	5	4	6
4	4	4	5
6	6	6	5
4	3	4	5
4	7	6	6
4	3	2	2
4	4	5	5
6	6	5	7
6	5	6	6
5	6	5	5
3	4	4	5
6	6	6	6
5	6	6	6
4	4	5	5
5	5	5	5
2	3	2	2
5	6	6	7
7	5	6	7
4	6	5	5
4	5	6	6
7	6	7	5
6	5	5	6
5	6	5	5
5	5	5	6
5	5	6	6
7	6	7	7
6	5	7	6
6	6	6	6
5	5	5	6
2	4	6	6
4	4	4	4
6	4	6	6
5	5	6	4
5	4	4	5
5	5	5	5

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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150199&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150199&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






Tabulation of Results
Q2 x Q9
1234567
10001000
21111000
30036100
4004121111
50251027110
6021516222
70001275

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Q2  x  Q9 \tabularnewline
  & 1 & 2 & 3 & 4 & 5 & 6 & 7 \tabularnewline
1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \tabularnewline
2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \tabularnewline
3 & 0 & 0 & 3 & 6 & 1 & 0 & 0 \tabularnewline
4 & 0 & 0 & 4 & 12 & 11 & 1 & 1 \tabularnewline
5 & 0 & 2 & 5 & 10 & 27 & 11 & 0 \tabularnewline
6 & 0 & 2 & 1 & 5 & 16 & 22 & 2 \tabularnewline
7 & 0 & 0 & 0 & 1 & 2 & 7 & 5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150199&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Q2  x  Q9[/C][/ROW]
[ROW][C] [/C][C]1[/C][C]2[/C][C]3[/C][C]4[/C][C]5[/C][C]6[/C][C]7[/C][/ROW]
[C]1[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[C]2[/C][C]1[/C][C]1[/C][C]1[/C][C]1[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[C]3[/C][C]0[/C][C]0[/C][C]3[/C][C]6[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[C]4[/C][C]0[/C][C]0[/C][C]4[/C][C]12[/C][C]11[/C][C]1[/C][C]1[/C][/ROW]
[C]5[/C][C]0[/C][C]2[/C][C]5[/C][C]10[/C][C]27[/C][C]11[/C][C]0[/C][/ROW]
[C]6[/C][C]0[/C][C]2[/C][C]1[/C][C]5[/C][C]16[/C][C]22[/C][C]2[/C][/ROW]
[C]7[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][C]2[/C][C]7[/C][C]5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150199&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
Q2 x Q9
1234567
10001000
21111000
30036100
4004121111
50251027110
6021516222
70001275






Tabulation of Expected Results
Q2 x Q9
1234567
10.010.030.090.220.350.250.05
20.020.120.350.891.411.010.2
30.060.310.862.223.522.530.49
40.180.92.516.4410.27.341.43
50.341.74.7512.2219.3513.922.72
60.31.484.1510.6716.8912.152.37
70.090.461.33.335.283.80.74

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Q2  x  Q9 \tabularnewline
  & 1 & 2 & 3 & 4 & 5 & 6 & 7 \tabularnewline
1 & 0.01 & 0.03 & 0.09 & 0.22 & 0.35 & 0.25 & 0.05 \tabularnewline
2 & 0.02 & 0.12 & 0.35 & 0.89 & 1.41 & 1.01 & 0.2 \tabularnewline
3 & 0.06 & 0.31 & 0.86 & 2.22 & 3.52 & 2.53 & 0.49 \tabularnewline
4 & 0.18 & 0.9 & 2.51 & 6.44 & 10.2 & 7.34 & 1.43 \tabularnewline
5 & 0.34 & 1.7 & 4.75 & 12.22 & 19.35 & 13.92 & 2.72 \tabularnewline
6 & 0.3 & 1.48 & 4.15 & 10.67 & 16.89 & 12.15 & 2.37 \tabularnewline
7 & 0.09 & 0.46 & 1.3 & 3.33 & 5.28 & 3.8 & 0.74 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150199&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Q2  x  Q9[/C][/ROW]
[ROW][C] [/C][C]1[/C][C]2[/C][C]3[/C][C]4[/C][C]5[/C][C]6[/C][C]7[/C][/ROW]
[C]1[/C][C]0.01[/C][C]0.03[/C][C]0.09[/C][C]0.22[/C][C]0.35[/C][C]0.25[/C][C]0.05[/C][/ROW]
[C]2[/C][C]0.02[/C][C]0.12[/C][C]0.35[/C][C]0.89[/C][C]1.41[/C][C]1.01[/C][C]0.2[/C][/ROW]
[C]3[/C][C]0.06[/C][C]0.31[/C][C]0.86[/C][C]2.22[/C][C]3.52[/C][C]2.53[/C][C]0.49[/C][/ROW]
[C]4[/C][C]0.18[/C][C]0.9[/C][C]2.51[/C][C]6.44[/C][C]10.2[/C][C]7.34[/C][C]1.43[/C][/ROW]
[C]5[/C][C]0.34[/C][C]1.7[/C][C]4.75[/C][C]12.22[/C][C]19.35[/C][C]13.92[/C][C]2.72[/C][/ROW]
[C]6[/C][C]0.3[/C][C]1.48[/C][C]4.15[/C][C]10.67[/C][C]16.89[/C][C]12.15[/C][C]2.37[/C][/ROW]
[C]7[/C][C]0.09[/C][C]0.46[/C][C]1.3[/C][C]3.33[/C][C]5.28[/C][C]3.8[/C][C]0.74[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150199&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150199&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
Q2 x Q9
1234567
10.010.030.090.220.350.250.05
20.020.120.350.891.411.010.2
30.060.310.862.223.522.530.49
40.180.92.516.4410.27.341.43
50.341.74.7512.2219.3513.922.72
60.31.484.1510.6716.8912.152.37
70.090.461.33.335.283.80.74






Statistical Results
Pearson's Chi-squared test
Pearson Chi Square Statistic135.29
Degrees of Freedom36
P value0

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
Pearson Chi Square Statistic & 135.29 \tabularnewline
Degrees of Freedom & 36 \tabularnewline
P value & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150199&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]135.29[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]36[/C][/ROW]
[ROW][C]P value[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150199&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150199&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 Statistic135.29
Degrees of Freedom36
P value0


Figures (Output of Computation)

Input Parameters & R Code

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')