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*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

Wed, 21 Dec 2016 08:23:04 +0100

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/2016/Dec/21/t14823049894no2bvrcd0w71og.htm/, Retrieved Mon, 06 May 2024 14:08:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301861, Retrieved Mon, 06 May 2024 14:08:57 +0000

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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] [] [2016-12-21 07:23:04] [33afbfb1be031b32823b544e140562b9] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301861&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301861&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301861&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Tabulation of Results
GWSUM x ITHSUM
	10	11	12	13	14	15	16	17	18	19	20
5	0	0	0	0	0	0	0	1	0	0	0
8	0	0	1	0	0	0	0	0	0	0	0
9	0	0	0	0	0	1	4	1	2	2	0
10	0	0	1	0	3	6	2	2	2	2	1
11	0	1	0	1	3	5	4	1	4	2	3
12	1	0	1	1	8	9	11	12	10	9	6
13	0	0	1	2	0	2	3	6	4	3	3
14	0	0	0	1	0	0	2	1	1	2	0
15	0	0	0	1	0	0	0	0	1	0	1

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
GWSUM  x  ITHSUM \tabularnewline
  & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \tabularnewline
5 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \tabularnewline
8 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \tabularnewline
9 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 1 & 2 & 2 & 0 \tabularnewline
10 & 0 & 0 & 1 & 0 & 3 & 6 & 2 & 2 & 2 & 2 & 1 \tabularnewline
11 & 0 & 1 & 0 & 1 & 3 & 5 & 4 & 1 & 4 & 2 & 3 \tabularnewline
12 & 1 & 0 & 1 & 1 & 8 & 9 & 11 & 12 & 10 & 9 & 6 \tabularnewline
13 & 0 & 0 & 1 & 2 & 0 & 2 & 3 & 6 & 4 & 3 & 3 \tabularnewline
14 & 0 & 0 & 0 & 1 & 0 & 0 & 2 & 1 & 1 & 2 & 0 \tabularnewline
15 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301861&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]GWSUM  x  ITHSUM[/C][/ROW]
[ROW][C] [/C][C]10[/C][C]11[/C][C]12[/C][C]13[/C][C]14[/C][C]15[/C][C]16[/C][C]17[/C][C]18[/C][C]19[/C][C]20[/C][/ROW]
[C]5[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[C]8[/C][C]0[/C][C]0[/C][C]1[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[C]9[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][C]4[/C][C]1[/C][C]2[/C][C]2[/C][C]0[/C][/ROW]
[C]10[/C][C]0[/C][C]0[/C][C]1[/C][C]0[/C][C]3[/C][C]6[/C][C]2[/C][C]2[/C][C]2[/C][C]2[/C][C]1[/C][/ROW]
[C]11[/C][C]0[/C][C]1[/C][C]0[/C][C]1[/C][C]3[/C][C]5[/C][C]4[/C][C]1[/C][C]4[/C][C]2[/C][C]3[/C][/ROW]
[C]12[/C][C]1[/C][C]0[/C][C]1[/C][C]1[/C][C]8[/C][C]9[/C][C]11[/C][C]12[/C][C]10[/C][C]9[/C][C]6[/C][/ROW]
[C]13[/C][C]0[/C][C]0[/C][C]1[/C][C]2[/C][C]0[/C][C]2[/C][C]3[/C][C]6[/C][C]4[/C][C]3[/C][C]3[/C][/ROW]
[C]14[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][C]0[/C][C]0[/C][C]2[/C][C]1[/C][C]1[/C][C]2[/C][C]0[/C][/ROW]
[C]15[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][C]0[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301861&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301861&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
GWSUM x ITHSUM
	10	11	12	13	14	15	16	17	18	19	20
5	0	0	0	0	0	0	0	1	0	0	0
8	0	0	1	0	0	0	0	0	0	0	0
9	0	0	0	0	0	1	4	1	2	2	0
10	0	0	1	0	3	6	2	2	2	2	1
11	0	1	0	1	3	5	4	1	4	2	3
12	1	0	1	1	8	9	11	12	10	9	6
13	0	0	1	2	0	2	3	6	4	3	3
14	0	0	0	1	0	0	2	1	1	2	0
15	0	0	0	1	0	0	0	0	1	0	1

Tabulation of Expected Results
GWSUM x ITHSUM
	10	11	12	13	14	15	16	17	18	19	20
5	0.01	0.01	0.03	0.04	0.09	0.15	0.17	0.15	0.15	0.13	0.09
8	0.01	0.01	0.03	0.04	0.09	0.15	0.17	0.15	0.15	0.13	0.09
9	0.06	0.06	0.25	0.38	0.89	1.46	1.66	1.53	1.53	1.27	0.89
10	0.12	0.12	0.48	0.73	1.69	2.78	3.15	2.9	2.9	2.42	1.69
11	0.15	0.15	0.61	0.92	2.14	3.52	3.97	3.67	3.67	3.06	2.14
12	0.43	0.43	1.73	2.6	6.06	9.96	11.26	10.39	10.39	8.66	6.06
13	0.15	0.15	0.61	0.92	2.14	3.52	3.97	3.67	3.67	3.06	2.14
14	0.04	0.04	0.18	0.27	0.62	1.03	1.16	1.07	1.07	0.89	0.62
15	0.02	0.02	0.08	0.11	0.27	0.44	0.5	0.46	0.46	0.38	0.27

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
GWSUM  x  ITHSUM \tabularnewline
  & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \tabularnewline
5 & 0.01 & 0.01 & 0.03 & 0.04 & 0.09 & 0.15 & 0.17 & 0.15 & 0.15 & 0.13 & 0.09 \tabularnewline
8 & 0.01 & 0.01 & 0.03 & 0.04 & 0.09 & 0.15 & 0.17 & 0.15 & 0.15 & 0.13 & 0.09 \tabularnewline
9 & 0.06 & 0.06 & 0.25 & 0.38 & 0.89 & 1.46 & 1.66 & 1.53 & 1.53 & 1.27 & 0.89 \tabularnewline
10 & 0.12 & 0.12 & 0.48 & 0.73 & 1.69 & 2.78 & 3.15 & 2.9 & 2.9 & 2.42 & 1.69 \tabularnewline
11 & 0.15 & 0.15 & 0.61 & 0.92 & 2.14 & 3.52 & 3.97 & 3.67 & 3.67 & 3.06 & 2.14 \tabularnewline
12 & 0.43 & 0.43 & 1.73 & 2.6 & 6.06 & 9.96 & 11.26 & 10.39 & 10.39 & 8.66 & 6.06 \tabularnewline
13 & 0.15 & 0.15 & 0.61 & 0.92 & 2.14 & 3.52 & 3.97 & 3.67 & 3.67 & 3.06 & 2.14 \tabularnewline
14 & 0.04 & 0.04 & 0.18 & 0.27 & 0.62 & 1.03 & 1.16 & 1.07 & 1.07 & 0.89 & 0.62 \tabularnewline
15 & 0.02 & 0.02 & 0.08 & 0.11 & 0.27 & 0.44 & 0.5 & 0.46 & 0.46 & 0.38 & 0.27 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301861&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]GWSUM  x  ITHSUM[/C][/ROW]
[ROW][C] [/C][C]10[/C][C]11[/C][C]12[/C][C]13[/C][C]14[/C][C]15[/C][C]16[/C][C]17[/C][C]18[/C][C]19[/C][C]20[/C][/ROW]
[C]5[/C][C]0.01[/C][C]0.01[/C][C]0.03[/C][C]0.04[/C][C]0.09[/C][C]0.15[/C][C]0.17[/C][C]0.15[/C][C]0.15[/C][C]0.13[/C][C]0.09[/C][/ROW]
[C]8[/C][C]0.01[/C][C]0.01[/C][C]0.03[/C][C]0.04[/C][C]0.09[/C][C]0.15[/C][C]0.17[/C][C]0.15[/C][C]0.15[/C][C]0.13[/C][C]0.09[/C][/ROW]
[C]9[/C][C]0.06[/C][C]0.06[/C][C]0.25[/C][C]0.38[/C][C]0.89[/C][C]1.46[/C][C]1.66[/C][C]1.53[/C][C]1.53[/C][C]1.27[/C][C]0.89[/C][/ROW]
[C]10[/C][C]0.12[/C][C]0.12[/C][C]0.48[/C][C]0.73[/C][C]1.69[/C][C]2.78[/C][C]3.15[/C][C]2.9[/C][C]2.9[/C][C]2.42[/C][C]1.69[/C][/ROW]
[C]11[/C][C]0.15[/C][C]0.15[/C][C]0.61[/C][C]0.92[/C][C]2.14[/C][C]3.52[/C][C]3.97[/C][C]3.67[/C][C]3.67[/C][C]3.06[/C][C]2.14[/C][/ROW]
[C]12[/C][C]0.43[/C][C]0.43[/C][C]1.73[/C][C]2.6[/C][C]6.06[/C][C]9.96[/C][C]11.26[/C][C]10.39[/C][C]10.39[/C][C]8.66[/C][C]6.06[/C][/ROW]
[C]13[/C][C]0.15[/C][C]0.15[/C][C]0.61[/C][C]0.92[/C][C]2.14[/C][C]3.52[/C][C]3.97[/C][C]3.67[/C][C]3.67[/C][C]3.06[/C][C]2.14[/C][/ROW]
[C]14[/C][C]0.04[/C][C]0.04[/C][C]0.18[/C][C]0.27[/C][C]0.62[/C][C]1.03[/C][C]1.16[/C][C]1.07[/C][C]1.07[/C][C]0.89[/C][C]0.62[/C][/ROW]
[C]15[/C][C]0.02[/C][C]0.02[/C][C]0.08[/C][C]0.11[/C][C]0.27[/C][C]0.44[/C][C]0.5[/C][C]0.46[/C][C]0.46[/C][C]0.38[/C][C]0.27[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301861&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301861&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
GWSUM x ITHSUM
	10	11	12	13	14	15	16	17	18	19	20
5	0.01	0.01	0.03	0.04	0.09	0.15	0.17	0.15	0.15	0.13	0.09
8	0.01	0.01	0.03	0.04	0.09	0.15	0.17	0.15	0.15	0.13	0.09
9	0.06	0.06	0.25	0.38	0.89	1.46	1.66	1.53	1.53	1.27	0.89
10	0.12	0.12	0.48	0.73	1.69	2.78	3.15	2.9	2.9	2.42	1.69
11	0.15	0.15	0.61	0.92	2.14	3.52	3.97	3.67	3.67	3.06	2.14
12	0.43	0.43	1.73	2.6	6.06	9.96	11.26	10.39	10.39	8.66	6.06
13	0.15	0.15	0.61	0.92	2.14	3.52	3.97	3.67	3.67	3.06	2.14
14	0.04	0.04	0.18	0.27	0.62	1.03	1.16	1.07	1.07	0.89	0.62
15	0.02	0.02	0.08	0.11	0.27	0.44	0.5	0.46	0.46	0.38	0.27

Statistical Results
Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)
Exact Pearson Chi Square Statistic	95.62
P value	0.15

\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 & 95.62 \tabularnewline
P value & 0.15 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301861&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]95.62[/C][/ROW]
[ROW][C]P value[/C][C]0.15[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301861&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301861&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 with simulated p-value (based on 2000 replicates)
Exact Pearson Chi Square Statistic	95.62
P value	0.15

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = 1 ; par2 = 2 ; par3 = Exact Pearson Chi-Squared by Simulation ;

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