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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

Thu, 15 Dec 2016 21:18:40 +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/15/t14818332927tejg6f97y1wh6z.htm/, Retrieved Fri, 03 May 2024 09:00:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299995, Retrieved Fri, 03 May 2024 09:00:15 +0000

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User-defined keywords

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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] [Chi-Squared Test ...] [2016-12-15 20:18:40] [6fe662842930c5949e61d44eeb8a265b] [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	1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299995&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]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299995&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299995&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	Big Analytics Cloud Computing Center

Tabulation of Results
Usability x Tevredenheid
	10	11	12	13	14	15	16	17	18	19	20
19	0	1	0	0	0	0	0	0	0	0	0
20	0	0	0	0	1	0	0	0	0	0	0
21	1	0	0	0	0	0	1	0	0	0	0
22	0	1	1	3	1	1	0	1	0	0	0
23	0	0	1	1	3	2	3	3	1	0	0
24	0	0	0	1	4	5	10	1	0	0	0
25	0	0	1	2	3	4	7	4	4	0	1
26	0	1	0	1	1	2	3	4	0	1	0
27	0	0	0	0	0	2	1	3	2	0	0
28	0	0	0	0	0	1	2	3	1	0	0
29	0	0	0	0	0	0	0	0	0	1	0

\begin{tabular}{lllllllll}
\hline
Tabulation of Results \tabularnewline
Usability  x  Tevredenheid \tabularnewline
  & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \tabularnewline
19 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \tabularnewline
20 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \tabularnewline
21 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \tabularnewline
22 & 0 & 1 & 1 & 3 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \tabularnewline
23 & 0 & 0 & 1 & 1 & 3 & 2 & 3 & 3 & 1 & 0 & 0 \tabularnewline
24 & 0 & 0 & 0 & 1 & 4 & 5 & 10 & 1 & 0 & 0 & 0 \tabularnewline
25 & 0 & 0 & 1 & 2 & 3 & 4 & 7 & 4 & 4 & 0 & 1 \tabularnewline
26 & 0 & 1 & 0 & 1 & 1 & 2 & 3 & 4 & 0 & 1 & 0 \tabularnewline
27 & 0 & 0 & 0 & 0 & 0 & 2 & 1 & 3 & 2 & 0 & 0 \tabularnewline
28 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 3 & 1 & 0 & 0 \tabularnewline
29 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299995&T=1

[TABLE]
[ROW][C]Tabulation of Results[/C][/ROW]
[ROW][C]Usability  x  Tevredenheid[/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]19[/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][C]0[/C][/ROW]
[C]20[/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][C]0[/C][C]0[/C][C]0[/C][/ROW]
[C]21[/C][C]1[/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][C]0[/C][/ROW]
[C]22[/C][C]0[/C][C]1[/C][C]1[/C][C]3[/C][C]1[/C][C]1[/C][C]0[/C][C]1[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[C]23[/C][C]0[/C][C]0[/C][C]1[/C][C]1[/C][C]3[/C][C]2[/C][C]3[/C][C]3[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[C]24[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][C]4[/C][C]5[/C][C]10[/C][C]1[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[C]25[/C][C]0[/C][C]0[/C][C]1[/C][C]2[/C][C]3[/C][C]4[/C][C]7[/C][C]4[/C][C]4[/C][C]0[/C][C]1[/C][/ROW]
[C]26[/C][C]0[/C][C]1[/C][C]0[/C][C]1[/C][C]1[/C][C]2[/C][C]3[/C][C]4[/C][C]0[/C][C]1[/C][C]0[/C][/ROW]
[C]27[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]2[/C][C]1[/C][C]3[/C][C]2[/C][C]0[/C][C]0[/C][/ROW]
[C]28[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]1[/C][C]2[/C][C]3[/C][C]1[/C][C]0[/C][C]0[/C][/ROW]
[C]29[/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][C]0[/C][C]1[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299995&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299995&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
Usability x Tevredenheid
	10	11	12	13	14	15	16	17	18	19	20
19	0	1	0	0	0	0	0	0	0	0	0
20	0	0	0	0	1	0	0	0	0	0	0
21	1	0	0	0	0	0	1	0	0	0	0
22	0	1	1	3	1	1	0	1	0	0	0
23	0	0	1	1	3	2	3	3	1	0	0
24	0	0	0	1	4	5	10	1	0	0	0
25	0	0	1	2	3	4	7	4	4	0	1
26	0	1	0	1	1	2	3	4	0	1	0
27	0	0	0	0	0	2	1	3	2	0	0
28	0	0	0	0	0	1	2	3	1	0	0
29	0	0	0	0	0	0	0	0	0	1	0

Tabulation of Expected Results
Usability x Tevredenheid
	10	11	12	13	14	15	16	17	18	19	20
19	0.01	0.03	0.03	0.08	0.13	0.17	0.26	0.19	0.08	0.02	0.01
20	0.01	0.03	0.03	0.08	0.13	0.17	0.26	0.19	0.08	0.02	0.01
21	0.02	0.06	0.06	0.16	0.25	0.33	0.53	0.37	0.16	0.04	0.02
22	0.08	0.24	0.24	0.63	1.02	1.33	2.12	1.49	0.63	0.16	0.08
23	0.14	0.41	0.41	1.1	1.78	2.33	3.71	2.61	1.1	0.27	0.14
24	0.21	0.62	0.62	1.65	2.68	3.5	5.56	3.91	1.65	0.41	0.21
25	0.25	0.76	0.76	2.04	3.31	4.33	6.88	4.84	2.04	0.51	0.25
26	0.13	0.38	0.38	1.02	1.66	2.17	3.44	2.42	1.02	0.25	0.13
27	0.08	0.24	0.24	0.63	1.02	1.33	2.12	1.49	0.63	0.16	0.08
28	0.07	0.21	0.21	0.55	0.89	1.17	1.85	1.3	0.55	0.14	0.07
29	0.01	0.03	0.03	0.08	0.13	0.17	0.26	0.19	0.08	0.02	0.01

\begin{tabular}{lllllllll}
\hline
Tabulation of Expected Results \tabularnewline
Usability  x  Tevredenheid \tabularnewline
  & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \tabularnewline
19 & 0.01 & 0.03 & 0.03 & 0.08 & 0.13 & 0.17 & 0.26 & 0.19 & 0.08 & 0.02 & 0.01 \tabularnewline
20 & 0.01 & 0.03 & 0.03 & 0.08 & 0.13 & 0.17 & 0.26 & 0.19 & 0.08 & 0.02 & 0.01 \tabularnewline
21 & 0.02 & 0.06 & 0.06 & 0.16 & 0.25 & 0.33 & 0.53 & 0.37 & 0.16 & 0.04 & 0.02 \tabularnewline
22 & 0.08 & 0.24 & 0.24 & 0.63 & 1.02 & 1.33 & 2.12 & 1.49 & 0.63 & 0.16 & 0.08 \tabularnewline
23 & 0.14 & 0.41 & 0.41 & 1.1 & 1.78 & 2.33 & 3.71 & 2.61 & 1.1 & 0.27 & 0.14 \tabularnewline
24 & 0.21 & 0.62 & 0.62 & 1.65 & 2.68 & 3.5 & 5.56 & 3.91 & 1.65 & 0.41 & 0.21 \tabularnewline
25 & 0.25 & 0.76 & 0.76 & 2.04 & 3.31 & 4.33 & 6.88 & 4.84 & 2.04 & 0.51 & 0.25 \tabularnewline
26 & 0.13 & 0.38 & 0.38 & 1.02 & 1.66 & 2.17 & 3.44 & 2.42 & 1.02 & 0.25 & 0.13 \tabularnewline
27 & 0.08 & 0.24 & 0.24 & 0.63 & 1.02 & 1.33 & 2.12 & 1.49 & 0.63 & 0.16 & 0.08 \tabularnewline
28 & 0.07 & 0.21 & 0.21 & 0.55 & 0.89 & 1.17 & 1.85 & 1.3 & 0.55 & 0.14 & 0.07 \tabularnewline
29 & 0.01 & 0.03 & 0.03 & 0.08 & 0.13 & 0.17 & 0.26 & 0.19 & 0.08 & 0.02 & 0.01 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299995&T=2

[TABLE]
[ROW][C]Tabulation of Expected Results[/C][/ROW]
[ROW][C]Usability  x  Tevredenheid[/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]19[/C][C]0.01[/C][C]0.03[/C][C]0.03[/C][C]0.08[/C][C]0.13[/C][C]0.17[/C][C]0.26[/C][C]0.19[/C][C]0.08[/C][C]0.02[/C][C]0.01[/C][/ROW]
[C]20[/C][C]0.01[/C][C]0.03[/C][C]0.03[/C][C]0.08[/C][C]0.13[/C][C]0.17[/C][C]0.26[/C][C]0.19[/C][C]0.08[/C][C]0.02[/C][C]0.01[/C][/ROW]
[C]21[/C][C]0.02[/C][C]0.06[/C][C]0.06[/C][C]0.16[/C][C]0.25[/C][C]0.33[/C][C]0.53[/C][C]0.37[/C][C]0.16[/C][C]0.04[/C][C]0.02[/C][/ROW]
[C]22[/C][C]0.08[/C][C]0.24[/C][C]0.24[/C][C]0.63[/C][C]1.02[/C][C]1.33[/C][C]2.12[/C][C]1.49[/C][C]0.63[/C][C]0.16[/C][C]0.08[/C][/ROW]
[C]23[/C][C]0.14[/C][C]0.41[/C][C]0.41[/C][C]1.1[/C][C]1.78[/C][C]2.33[/C][C]3.71[/C][C]2.61[/C][C]1.1[/C][C]0.27[/C][C]0.14[/C][/ROW]
[C]24[/C][C]0.21[/C][C]0.62[/C][C]0.62[/C][C]1.65[/C][C]2.68[/C][C]3.5[/C][C]5.56[/C][C]3.91[/C][C]1.65[/C][C]0.41[/C][C]0.21[/C][/ROW]
[C]25[/C][C]0.25[/C][C]0.76[/C][C]0.76[/C][C]2.04[/C][C]3.31[/C][C]4.33[/C][C]6.88[/C][C]4.84[/C][C]2.04[/C][C]0.51[/C][C]0.25[/C][/ROW]
[C]26[/C][C]0.13[/C][C]0.38[/C][C]0.38[/C][C]1.02[/C][C]1.66[/C][C]2.17[/C][C]3.44[/C][C]2.42[/C][C]1.02[/C][C]0.25[/C][C]0.13[/C][/ROW]
[C]27[/C][C]0.08[/C][C]0.24[/C][C]0.24[/C][C]0.63[/C][C]1.02[/C][C]1.33[/C][C]2.12[/C][C]1.49[/C][C]0.63[/C][C]0.16[/C][C]0.08[/C][/ROW]
[C]28[/C][C]0.07[/C][C]0.21[/C][C]0.21[/C][C]0.55[/C][C]0.89[/C][C]1.17[/C][C]1.85[/C][C]1.3[/C][C]0.55[/C][C]0.14[/C][C]0.07[/C][/ROW]
[C]29[/C][C]0.01[/C][C]0.03[/C][C]0.03[/C][C]0.08[/C][C]0.13[/C][C]0.17[/C][C]0.26[/C][C]0.19[/C][C]0.08[/C][C]0.02[/C][C]0.01[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299995&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299995&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
Usability x Tevredenheid
	10	11	12	13	14	15	16	17	18	19	20
19	0.01	0.03	0.03	0.08	0.13	0.17	0.26	0.19	0.08	0.02	0.01
20	0.01	0.03	0.03	0.08	0.13	0.17	0.26	0.19	0.08	0.02	0.01
21	0.02	0.06	0.06	0.16	0.25	0.33	0.53	0.37	0.16	0.04	0.02
22	0.08	0.24	0.24	0.63	1.02	1.33	2.12	1.49	0.63	0.16	0.08
23	0.14	0.41	0.41	1.1	1.78	2.33	3.71	2.61	1.1	0.27	0.14
24	0.21	0.62	0.62	1.65	2.68	3.5	5.56	3.91	1.65	0.41	0.21
25	0.25	0.76	0.76	2.04	3.31	4.33	6.88	4.84	2.04	0.51	0.25
26	0.13	0.38	0.38	1.02	1.66	2.17	3.44	2.42	1.02	0.25	0.13
27	0.08	0.24	0.24	0.63	1.02	1.33	2.12	1.49	0.63	0.16	0.08
28	0.07	0.21	0.21	0.55	0.89	1.17	1.85	1.3	0.55	0.14	0.07
29	0.01	0.03	0.03	0.08	0.13	0.17	0.26	0.19	0.08	0.02	0.01

Statistical Results
Pearson's Chi-squared test with simulated p-value (based on 2000 replicates)
Exact Pearson Chi Square Statistic	196.53
P value	0.01

\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 & 196.53 \tabularnewline
P value & 0.01 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299995&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]196.53[/C][/ROW]
[ROW][C]P value[/C][C]0.01[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299995&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299995&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	196.53
P value	0.01

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

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

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