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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_chi_squared_tests.wasp

Title produced by software

Chi-Squared and McNemar Tests

Date of computation

Wed, 10 Nov 2010 15:02:30 +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/2010/Nov/10/t12894012731coiiam1di45oa3.htm/, Retrieved Fri, 21 Aug 2026 06:56:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=93059, Retrieved Fri, 21 Aug 2026 06:56:08 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

574

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

F       [Chi-Squared and McNemar Tests] [Connected - Depre...] [2010-11-10 15:02:30] [61e5ee05de011f44efa37f086a4e2271] [Current]
-   P     [Chi-Squared and McNemar Tests] [Depressions vs co...] [2010-11-15 12:18:26] [717f3d787904f94c39256c5c1fc72d4c] 
-           [Chi-Squared and McNemar Tests] [Depression vs Con...] [2010-11-16 09:38:54] [3df61981e9f4dafed65341be376c4457] 
-           [Chi-Squared and McNemar Tests] [Depression vs con...] [2010-11-16 09:41:54] [ff7c1e95cf99a1dae07ec89975494dde] 
-   P     [Chi-Squared and McNemar Tests] [Depression vs sep...] [2010-11-15 12:21:59] [717f3d787904f94c39256c5c1fc72d4c] 
-           [Chi-Squared and McNemar Tests] [Depression vs Con...] [2010-11-16 09:40:43] [3df61981e9f4dafed65341be376c4457] 
-           [Chi-Squared and McNemar Tests] [Depression vs Sep...] [2010-11-16 09:40:43] [3df61981e9f4dafed65341be376c4457] 
-           [Chi-Squared and McNemar Tests] [Depression vs sep...] [2010-11-16 09:43:40] [ff7c1e95cf99a1dae07ec89975494dde] 
-         [Chi-Squared and McNemar Tests] [workshop 6 part 1] [2010-11-16 19:55:11] [a90833f600c49a37df2affa5b2163a2e] 

Feedback Forum

2010-11-17 21:00:29 [] [reply] 
Ook hier gebruiken we de Chi-Squared test met gesimuleerde p-value. En er is inderdaad een verband, maar positief of negatief? Het verband is negatief. Dit kan je afleiden uit de grafiek. Als je naar de 2 uitersten kijkt (A-A en D-D), dus naar de hoofddiagonaal, zie je dat de 2 balkjes onder de lijn liggen. Dus dat aantal studenten dat daar terechtkomen, komen minder voor dan verwacht. Maar als we dan de berekening opnieuw doen, maar dan voor 2 onderverdelingen, zien we dat de p-value 0,43 is. Dus dit zegt ons dat er geen verband is. Het is beter om hier van uit te gaan omdat het betrouwbaarder is om minder categorieën te hebben en een hogere cell-count.

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Dataseries X:

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Histogram

Boxplots

'A'	'A'	'B'	'B'
'A'	'C'	'A'	'C'
'D'	'B'	'D'	'A'
'D'	'C'	'D'	'B'
'B'	'A'	'A'	'A'
'B'	'D'	'A'	'B'
'A'	'D'	'B'	'A'
'B'	'B'	'B'	'C'
'B'	'B'	'B'	'D'
'A'	'A'	'B'	'B'
'A'	'D'	'A'	'D'
'B'	'B'	'A'	'D'
'A'	'B'	'D'	'A'
'A'	'A'	'A'	'A'
'C'	'A'	'A'	'D'
'C'	'C'	'B'	'A'
'B'	'C'	'B'	'A'
'A'	'A'	'A'	'C'
'A'	'A'	'B'	'D'
'C'	'C'	'A'	'B'
'C'	'C'	'A'	'D'
'D'	'D'	'D'	'A'
'A'	'A'	'B'	'B'
'A'	'A'	'D'	'A'
'A'	'C'	'A'	'C'
'A'	'C'	'D'	'D'
'B'	'B'	'A'	'C'
'C'	'A'	'B'	'A'
'C'	'C'	'B'	'A'
'B'	'C'	'D'	'B'
'D'	'D'	'A'	'D'
'D'	'C'	'C'	'A'
'A'	'D'	'A'	'D'
'B'	'A'	'B'	'C'
'B'	'D'	'B'	'B'
'C'	'C'	'A'	'D'
'D'	'D'	'D'	'A'
'B'	'C'	'B'	'B'
'D'	'D'	'A'	'D'
'B'	'C'	'C'	'D'
'A'	'C'	'B'	'D'
'B'	'C'	'A'	'A'
'A'	'C'	'A'	'D'
'B'	'C'	'D'	'A'
'A'	'D'	'D'	'C'
'A'	'B'	'D'	'B'
'A'	'A'	'B'	'D'
'C'	'B'	'B'	'C'
'B'	'A'	'A'	'A'
'A'	'C'	'C'	'C'
'C'	'A'	'A'	'D'
'C'	'D'	'B'	'A'
'C'	'C'	'D'	'A'
'B'	'A'	'D'	'A'
'C'	'C'	'D'	'C'
'A'	'C'	'B'	'B'
'A'	'B'	'A'	'B'
'D'	'B'	'B'	'D'
'A'	'B'	'D'	'D'
'B'	'B'	'D'	'A'
'D'	'D'	'D'	'A'
'A'	'B'	'C'	'B'
'B'	'B'	'D'	'B'
'D'	'B'	'B'	'A'
'B'	'D'	'B'	'B'
'B'	'A'	'D'	'C'
'B'	'B'	'D'	'A'
'D'	'D'	'D'	'B'
'A'	'A'	'B'	'B'
'B'	'A'	'B'	'A'
'A'	'B'	'B'	'B'
'D'	'A'	'A'	'A'
'B'	'A'	'B'	'B'
'A'	'A'	'B'	'D'
'B'	'D'	'C'	'C'
'A'	'D'	'D'	'A'
'A'	'A'	'A'	'B'
'B'	'D'	'C'	'A'
'D'	'D'	'B'	'B'
'A'	'D'	'C'	'D'
'C'	'B'	'B'	'C'
'A'	'A'	'A'	'D'
'B'	'A'	'B'	'D'
'A'	'C'	'A'	'B'
'C'	'B'	'B'	'B'
'C'	'D'	'B'	'B'
'A'	'A'	'B'	'B'
'C'	'B'	'B'	'B'
'D'	'C'	'C'	'A'
'C'	'C'	'D'	'A'
'D'	'B'	'A'	'B'
'B'	'C'	'C'	'A'
'B'	'A'	'B'	'B'
'C'	'D'	'B'	'A'
'D'	'D'	'C'	'D'
'A'	'B'	'A'	'C'
'A'	'B'	'D'	'A'
'B'	'D'	'B'	'C'
'A'	'B'	'A'	'C'
'C'	'B'	'B'	'D'
'A'	'B'	'A'	'D'
'A'	'B'	'D'	'A'
'B'	'A'	'A'	'B'
'C'	'D'	'D'	'C'
'C'	'A'	'B'	'A'
'A'	'C'	'D'	'A'
'A'	'B'	'A'	'C'
'A'	'A'	'B'	'A'
'B'	'B'	'D'	'A'
'A'	'A'	'D'	'A'
'D'	'B'	'B'	'A'
'D'	'C'	'D'	'A'
'C'	'A'	'C'	'C'
'C'	'C'	'B'	'A'
'A'	'B'	'A'	'B'
'A'	'C'	'A'	'D'
'C'	'A'	'B'	'A'
'B'	'A'	'B'	'B'
'C'	'B'	'B'	'D'
'A'	'B'	'B'	'A'
'C'	'A'	'D'	'A'
'D'	'D'	'B'	'A'
'A'	'A'	'B'	'C'
'A'	'A'	'B'	'D'
'C'	'D'	'B'	'C'
'D'	'C'	'C'	'C'
'A'	'C'	'A'	'D'
'A'	'A'	'A'	'D'
'C'	'B'	'A'	'C'
'B'	'C'	'B'	'B'
'C'	'C'	'C'	'C'
'D'	'C'	'D'	'A'
'A'	'A'	'B'	'D'
'D'	'D'	'B'	'A'
'A'	'A'	'B'	'B'
'C'	'D'	'A'	'A'
'D'	'D'	'D'	'A'
'B'	'B'	'B'	'A'
'D'	'B'	'D'	'A'
'B'	'B'	'B'	'C'
'D'	'B'	'C'	'B'
'C'	'B'	'B'	'D'
'D'	'B'	'A'	'A'
'D'	'B'	'B'	'B'
'D'	'D'	'B'	'B'
'A'	'D'	'A'	'C'
'C'	'D'	'A'	'B'
'B'	'B'	'D'	'B'
'C'	'D'	'D'	'C'
'B'	'C'	'D'	'A'
'A'	'A'	'A'	'B'
'A'	'A'	'C'	'A'
'B'	'A'	'A'	'D'
'B'	'A'	'D'	'B'
'B'	'B'	'D'	'A'
'C'	'D'	'C'	'A'
'B'	'C'	'C'	'A'
'C'	'A'	'B'	'A'
'C'	'B'	'A'	'C'
'B'	'C'	'C'	'D'
'C'	'B'	'D'	'A'
'B'	'B'	'C'	'A'

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \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=93059&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/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=93059&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93059&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24
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
Connected x Depression
	A	B	C	D
A	12	15	10	17
B	17	13	7	6
C	15	5	10	7
D	16	7	1	4

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Connected  x  Depression
 \tabularnewline
  & A & B & C & D \tabularnewline
A & 12 & 15 & 10 & 17 \tabularnewline
B & 17 & 13 & 7 & 6 \tabularnewline
C & 15 & 5 & 10 & 7 \tabularnewline
D & 16 & 7 & 1 & 4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93059&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Connected  x  Depression
[/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]15[/C][C]10[/C][C]17[/C][/ROW]
[C]B[/C][C]17[/C][C]13[/C][C]7[/C][C]6[/C][/ROW]
[C]C[/C][C]15[/C][C]5[/C][C]10[/C][C]7[/C][/ROW]
[C]D[/C][C]16[/C][C]7[/C][C]1[/C][C]4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93059&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93059&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
Connected x Depression
	A	B	C	D
A	12	15	10	17
B	17	13	7	6
C	15	5	10	7
D	16	7	1	4

Tabulation of Expected Results
Connected x Depression
	A	B	C	D
A	20	13.33	9.33	11.33
B	15.93	10.62	7.43	9.02
C	13.7	9.14	6.4	7.77
D	10.37	6.91	4.84	5.88

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Connected  x  Depression
 \tabularnewline
  & A & B & C & D \tabularnewline
A & 20 & 13.33 & 9.33 & 11.33 \tabularnewline
B & 15.93 & 10.62 & 7.43 & 9.02 \tabularnewline
C & 13.7 & 9.14 & 6.4 & 7.77 \tabularnewline
D & 10.37 & 6.91 & 4.84 & 5.88 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=93059&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Connected  x  Depression
[/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]13.33[/C][C]9.33[/C][C]11.33[/C][/ROW]
[C]B[/C][C]15.93[/C][C]10.62[/C][C]7.43[/C][C]9.02[/C][/ROW]
[C]C[/C][C]13.7[/C][C]9.14[/C][C]6.4[/C][C]7.77[/C][/ROW]
[C]D[/C][C]10.37[/C][C]6.91[/C][C]4.84[/C][C]5.88[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=93059&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93059&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
Connected x Depression
	A	B	C	D
A	20	13.33	9.33	11.33
B	15.93	10.62	7.43	9.02
C	13.7	9.14	6.4	7.77
D	10.37	6.91	4.84	5.88

Statistical Results
Pearson's Chi-squared test
Chi Square Statistic	18.74
Degrees of Freedom	9
P value	0.03

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
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=93059&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]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=93059&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=93059&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
Chi Square Statistic	18.74
Degrees of Freedom	9
P value	0.03

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 4 ; par3 = Pearson Chi-Squared ;

Parameters (R input):

par1 = 1 ; par2 = 4 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code