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

Date of computation

Sat, 22 Aug 2015 22:09:47 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Aug/22/t14402777993xrcn5bfa5zq89f.htm/, Retrieved Thu, 16 May 2024 15:25:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280307, Retrieved Thu, 16 May 2024 15:25:11 +0000

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Estimated Impact

167

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] [hi i2] [2015-08-19 11:04:54] [5b73c907efdd91cd8d467e65f28ae5f1]
-    D  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2015-08-19 12:26:09] [5b73c907efdd91cd8d467e65f28ae5f1]
- RM        [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2015-08-22 21:09:47] [8145b3fe416df466b077d26de89041cd] [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	'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280307&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280307&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280307&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Tabulation of Results
E2 x B-S
	0	1
5	1	0
6	1	0
8	0	2
9	3	2
11	2	1
12	6	1
13	1	3
14	2	3
15	9	4
16	6	6
17	2	10
18	10	17
19	11	6
20	14	18
21	15	15
22	11	12
23	15	12
24	16	11
25	10	6
26	5	5
27	4	1
28	5	2

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
E2  x  B-S \tabularnewline
  & 0 & 1 \tabularnewline
5 & 1 & 0 \tabularnewline
6 & 1 & 0 \tabularnewline
8 & 0 & 2 \tabularnewline
9 & 3 & 2 \tabularnewline
11 & 2 & 1 \tabularnewline
12 & 6 & 1 \tabularnewline
13 & 1 & 3 \tabularnewline
14 & 2 & 3 \tabularnewline
15 & 9 & 4 \tabularnewline
16 & 6 & 6 \tabularnewline
17 & 2 & 10 \tabularnewline
18 & 10 & 17 \tabularnewline
19 & 11 & 6 \tabularnewline
20 & 14 & 18 \tabularnewline
21 & 15 & 15 \tabularnewline
22 & 11 & 12 \tabularnewline
23 & 15 & 12 \tabularnewline
24 & 16 & 11 \tabularnewline
25 & 10 & 6 \tabularnewline
26 & 5 & 5 \tabularnewline
27 & 4 & 1 \tabularnewline
28 & 5 & 2 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280307&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]E2  x  B-S[/C][/ROW]
[ROW][C] [/C][C]0[/C][C]1[/C][/ROW]
[C]5[/C][C]1[/C][C]0[/C][/ROW]
[C]6[/C][C]1[/C][C]0[/C][/ROW]
[C]8[/C][C]0[/C][C]2[/C][/ROW]
[C]9[/C][C]3[/C][C]2[/C][/ROW]
[C]11[/C][C]2[/C][C]1[/C][/ROW]
[C]12[/C][C]6[/C][C]1[/C][/ROW]
[C]13[/C][C]1[/C][C]3[/C][/ROW]
[C]14[/C][C]2[/C][C]3[/C][/ROW]
[C]15[/C][C]9[/C][C]4[/C][/ROW]
[C]16[/C][C]6[/C][C]6[/C][/ROW]
[C]17[/C][C]2[/C][C]10[/C][/ROW]
[C]18[/C][C]10[/C][C]17[/C][/ROW]
[C]19[/C][C]11[/C][C]6[/C][/ROW]
[C]20[/C][C]14[/C][C]18[/C][/ROW]
[C]21[/C][C]15[/C][C]15[/C][/ROW]
[C]22[/C][C]11[/C][C]12[/C][/ROW]
[C]23[/C][C]15[/C][C]12[/C][/ROW]
[C]24[/C][C]16[/C][C]11[/C][/ROW]
[C]25[/C][C]10[/C][C]6[/C][/ROW]
[C]26[/C][C]5[/C][C]5[/C][/ROW]
[C]27[/C][C]4[/C][C]1[/C][/ROW]
[C]28[/C][C]5[/C][C]2[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280307&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280307&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
E2 x B-S
	0	1
5	1	0
6	1	0
8	0	2
9	3	2
11	2	1
12	6	1
13	1	3
14	2	3
15	9	4
16	6	6
17	2	10
18	10	17
19	11	6
20	14	18
21	15	15
22	11	12
23	15	12
24	16	11
25	10	6
26	5	5
27	4	1
28	5	2

Tabulation of Expected Results
E2 x B-S
	0	1
5	0.52	0.48
6	0.52	0.48
8	1.04	0.96
9	2.6	2.4
11	1.56	1.44
12	3.65	3.35
13	2.08	1.92
14	2.6	2.4
15	6.77	6.23
16	6.25	5.75
17	6.25	5.75
18	14.07	12.93
19	8.86	8.14
20	16.67	15.33
21	15.63	14.37
22	11.98	11.02
23	14.07	12.93
24	14.07	12.93
25	8.34	7.66
26	5.21	4.79
27	2.6	2.4
28	3.65	3.35

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
E2  x  B-S \tabularnewline
  & 0 & 1 \tabularnewline
5 & 0.52 & 0.48 \tabularnewline
6 & 0.52 & 0.48 \tabularnewline
8 & 1.04 & 0.96 \tabularnewline
9 & 2.6 & 2.4 \tabularnewline
11 & 1.56 & 1.44 \tabularnewline
12 & 3.65 & 3.35 \tabularnewline
13 & 2.08 & 1.92 \tabularnewline
14 & 2.6 & 2.4 \tabularnewline
15 & 6.77 & 6.23 \tabularnewline
16 & 6.25 & 5.75 \tabularnewline
17 & 6.25 & 5.75 \tabularnewline
18 & 14.07 & 12.93 \tabularnewline
19 & 8.86 & 8.14 \tabularnewline
20 & 16.67 & 15.33 \tabularnewline
21 & 15.63 & 14.37 \tabularnewline
22 & 11.98 & 11.02 \tabularnewline
23 & 14.07 & 12.93 \tabularnewline
24 & 14.07 & 12.93 \tabularnewline
25 & 8.34 & 7.66 \tabularnewline
26 & 5.21 & 4.79 \tabularnewline
27 & 2.6 & 2.4 \tabularnewline
28 & 3.65 & 3.35 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280307&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]E2  x  B-S[/C][/ROW]
[ROW][C] [/C][C]0[/C][C]1[/C][/ROW]
[C]5[/C][C]0.52[/C][C]0.48[/C][/ROW]
[C]6[/C][C]0.52[/C][C]0.48[/C][/ROW]
[C]8[/C][C]1.04[/C][C]0.96[/C][/ROW]
[C]9[/C][C]2.6[/C][C]2.4[/C][/ROW]
[C]11[/C][C]1.56[/C][C]1.44[/C][/ROW]
[C]12[/C][C]3.65[/C][C]3.35[/C][/ROW]
[C]13[/C][C]2.08[/C][C]1.92[/C][/ROW]
[C]14[/C][C]2.6[/C][C]2.4[/C][/ROW]
[C]15[/C][C]6.77[/C][C]6.23[/C][/ROW]
[C]16[/C][C]6.25[/C][C]5.75[/C][/ROW]
[C]17[/C][C]6.25[/C][C]5.75[/C][/ROW]
[C]18[/C][C]14.07[/C][C]12.93[/C][/ROW]
[C]19[/C][C]8.86[/C][C]8.14[/C][/ROW]
[C]20[/C][C]16.67[/C][C]15.33[/C][/ROW]
[C]21[/C][C]15.63[/C][C]14.37[/C][/ROW]
[C]22[/C][C]11.98[/C][C]11.02[/C][/ROW]
[C]23[/C][C]14.07[/C][C]12.93[/C][/ROW]
[C]24[/C][C]14.07[/C][C]12.93[/C][/ROW]
[C]25[/C][C]8.34[/C][C]7.66[/C][/ROW]
[C]26[/C][C]5.21[/C][C]4.79[/C][/ROW]
[C]27[/C][C]2.6[/C][C]2.4[/C][/ROW]
[C]28[/C][C]3.65[/C][C]3.35[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280307&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280307&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
E2 x B-S
	0	1
5	0.52	0.48
6	0.52	0.48
8	1.04	0.96
9	2.6	2.4
11	1.56	1.44
12	3.65	3.35
13	2.08	1.92
14	2.6	2.4
15	6.77	6.23
16	6.25	5.75
17	6.25	5.75
18	14.07	12.93
19	8.86	8.14
20	16.67	15.33
21	15.63	14.37
22	11.98	11.02
23	14.07	12.93
24	14.07	12.93
25	8.34	7.66
26	5.21	4.79
27	2.6	2.4
28	3.65	3.35

Statistical Results
Pearson's Chi-squared test
25.28
Degrees of Freedom	21
P value	0.24

\begin{tabular}{lllllllll}
\hline
Statistical Results \tabularnewline
Pearson's Chi-squared test \tabularnewline
25.28 \tabularnewline
Degrees of Freedom & 21 \tabularnewline
P value & 0.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280307&T=3

[TABLE]
[ROW][C]Statistical Results[/C][/ROW]
[ROW][C]Pearson's Chi-squared test[/C][/ROW]
[ROW][C]25.28[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]21[/C][/ROW]
[ROW][C]P value[/C][C]0.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280307&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280307&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
25.28
Degrees of Freedom	21
P value	0.24

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 2 ; par2 = 1 ; par3 = TRUE ;

Parameters (R input):

par1 = 2 ; par2 = 1 ; par3 = TRUE ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code