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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software ModuleIan.Hollidayrwasp_One Factor ANOVA.wasp
Title produced by softwareChi Square Measure of Association- Free Statistics Software (Calculator)
Date of computationThu, 03 Dec 2009 14:47:54 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/03/t1259848103fq64o7e6yxcjj5i.htm/, Retrieved Fri, 22 Aug 2025 16:32:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62778, Retrieved Fri, 22 Aug 2025 16:32:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact425

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Chi Square Measure of Association- Free Statistics Software (Calculator)] [One Way ANOVA wit...] [2009-11-29 13:09:19] [98fd0e87c3eb04e0cc2efde01dbafab6]
-   PD  [Chi Square Measure of Association- Free Statistics Software (Calculator)] [One Way ANOVA for...] [2009-12-01 13:05:10] [3fdd735c61ad38cbc9b3393dc997cdb7]
- R P     [Chi Square Measure of Association- Free Statistics Software (Calculator)] [CARE date with Tu...] [2009-12-01 18:33:48] [98fd0e87c3eb04e0cc2efde01dbafab6]
-   PD      [Chi Square Measure of Association- Free Statistics Software (Calculator)] [comp9, 1] [2009-12-03 13:29:22] [e8bb49267f0b4e611f4778412d0811f2]
-    D        [Chi Square Measure of Association- Free Statistics Software (Calculator)] [comp 9, 2] [2009-12-03 13:38:11] [e8bb49267f0b4e611f4778412d0811f2]
-    D            [Chi Square Measure of Association- Free Statistics Software (Calculator)] [comp 3, 3] [2009-12-03 13:47:54] [5b58052098f4b0433c56ae9d9a4453be] [Current]
-    D              [Chi Square Measure of Association- Free Statistics Software (Calculator)] [comp 3, 4] [2009-12-03 13:50:36] [e8bb49267f0b4e611f4778412d0811f2]
-    D                [Chi Square Measure of Association- Free Statistics Software (Calculator)] [comp 9, 5] [2009-12-10 13:30:01] [e8bb49267f0b4e611f4778412d0811f2]
-    D                  [Chi Square Measure of Association- Free Statistics Software (Calculator)] [comp 9, 6] [2009-12-10 13:34:41] [e8bb49267f0b4e611f4778412d0811f2]
-    D                  [Chi Square Measure of Association- Free Statistics Software (Calculator)] [comp 9, 6] [2009-12-10 13:34:41] [e8bb49267f0b4e611f4778412d0811f2]
-    D                  [Chi Square Measure of Association- Free Statistics Software (Calculator)] [comp 9, 6] [2009-12-10 13:34:41] [e8bb49267f0b4e611f4778412d0811f2]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
36	1
36	2
56	2
48	3
32	1
44	1
39	2
34	1
41	1
50	3
39	1
62	3
52	2
37	1
50	2
41	2
55	2
41	1
56	3
39	2
52	1
46	1
44	1
48	1
41	2
50	3
50	3
44	2
52	3
54	2
44	2
52	3
37	2
52	2
50	2
36	1
50	2
52	2
55	3
31	1
36	2
49	1
42	2
37	3
41	2
30	2
52	3
30	1
41	1
44	2
66	2
48	1
43	3
57	1
46	1
54	1
48	2
48	2
52	3
62	1
58	1
58	3
62	3
48	3
46	2
34	2
66	3
52	3
55	1
55	1
57	2
56	2
55	3
56	3
54	2
55	2
46	3
52	1
32	2
44	1
46	2
59	2
46	2
46	2
54	3
66	3
56	2
59	2
57	2
52	2
48	2
44	2
41	1
50	1
48	1
48	3
59	2
34	2
46	2
54	2
55	1
54	3
59	2
44	2
54	1
52	3
66	3
44	2
57	1
39	1
60	1
45	1
41	2
50	2
39	3
43	2
48	2
37	2
58	3
46	1
43	3
44	1
34	2
30	3
50	3
39	1
37	2
55	1
48	3
41	3
39	1
36	2
43	1
50	3
55	2
43	1
60	1
48	1
30	1
43	2
39	3
52	2
39	2
39	1
56	2
59	1
46	1
57	2
50	2
54	3
50	2
60	3
59	3
41	3
48	2
59	2
60	2
56	1
56	2
51	1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62778&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62778&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62778&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






ANOVA Model
verbalIQ ~ Age
means46.2551.3545.095

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
verbalIQ  ~  Age \tabularnewline
means & 46.255 & 1.354 & 5.095 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62778&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]verbalIQ  ~  Age[/C][/ROW]
[ROW][C]means[/C][C]46.255[/C][C]1.354[/C][C]5.095[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62778&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62778&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:

ANOVA Model
verbalIQ ~ Age
means46.2551.3545.095






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Age2612.754306.3774.4520.013
Residuals15710805.22168.823 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Age & 2 & 612.754 & 306.377 & 4.452 & 0.013 \tabularnewline
Residuals & 157 & 10805.221 & 68.823 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62778&T=2

[TABLE]
[ROW][C]ANOVA Statistics[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]Sum Sq[/C][C]Mean Sq[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C]Age[/C][C]2[/C][C]612.754[/C][C]306.377[/C][C]4.452[/C][C]0.013[/C][/ROW]
[ROW][C]Residuals[/C][C]157[/C][C]10805.221[/C][C]68.823[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62778&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62778&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:

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Age2612.754306.3774.4520.013
Residuals15710805.22168.823






Tukey Honest Significant Difference Comparisons
difflwruprp adj
2-11.354-2.2714.9790.651
3-15.0950.9499.2410.012
3-23.741-0.167.6420.063

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
2-1 & 1.354 & -2.271 & 4.979 & 0.651 \tabularnewline
3-1 & 5.095 & 0.949 & 9.241 & 0.012 \tabularnewline
3-2 & 3.741 & -0.16 & 7.642 & 0.063 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62778&T=3

[TABLE]
[ROW][C]Tukey Honest Significant Difference Comparisons[/C][/ROW]
[ROW][C] [/C][C]diff[/C][C]lwr[/C][C]upr[/C][C]p adj[/C][/ROW]
[ROW][C]2-1[/C][C]1.354[/C][C]-2.271[/C][C]4.979[/C][C]0.651[/C][/ROW]
[ROW][C]3-1[/C][C]5.095[/C][C]0.949[/C][C]9.241[/C][C]0.012[/C][/ROW]
[ROW][C]3-2[/C][C]3.741[/C][C]-0.16[/C][C]7.642[/C][C]0.063[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62778&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62778&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:

Tukey Honest Significant Difference Comparisons
difflwruprp adj
2-11.354-2.2714.9790.651
3-15.0950.9499.2410.012
3-23.741-0.167.6420.063






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group20.4490.639
157 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 2 & 0.449 & 0.639 \tabularnewline
  & 157 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62778&T=4

[TABLE]
[ROW][C]Levenes Test for Homogeneity of Variance[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C]Group[/C][C]2[/C][C]0.449[/C][C]0.639[/C][/ROW]
[ROW][C] [/C][C]157[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62778&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62778&T=4

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group20.4490.639
157


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
R code (references can be found in the software module):
cat1 <- as.numeric(par1) #
cat2<- as.numeric(par2) #
intercept<-as.logical(par3)
x <- t(x)
x1<-as.numeric(x[,cat1])
f1<-as.character(x[,cat2])
xdf<-data.frame(x1,f1)
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
names(xdf)<-c('Response', 'Treatment')
if(intercept == FALSE) (lmxdf<-lm(Response ~ Treatment - 1, data = xdf) ) else (lmxdf<-lm(Response ~ Treatment, data = xdf) )
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Model', length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, paste(V1, ' ~ ', V2), length(lmxdf$coefficients)+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'means',,TRUE)
for(i in 1:length(lmxdf$coefficients)){
a<-table.element(a, round(lmxdf$coefficients[i], digits=3),,FALSE)
}
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Statistics', 5+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',,TRUE)
a<-table.element(a, 'Df',,FALSE)
a<-table.element(a, 'Sum Sq',,FALSE)
a<-table.element(a, 'Mean Sq',,FALSE)
a<-table.element(a, 'F value',,FALSE)
a<-table.element(a, 'Pr(>F)',,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, V2,,TRUE)
a<-table.element(a, anova.xdf$Df[1],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'F value'[1], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Pr(>F)'[1], digits=3),,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residuals',,TRUE)
a<-table.element(a, anova.xdf$Df[2],,FALSE)
a<-table.element(a, round(anova.xdf$'Sum Sq'[2], digits=3),,FALSE)
a<-table.element(a, round(anova.xdf$'Mean Sq'[2], digits=3),,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.element(a, ' ',,FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='anovaplot.png')
boxplot(Response ~ Treatment, data=xdf, xlab=V2, ylab=V1)
dev.off()
if(intercept==TRUE){
thsd<-TukeyHSD(aov.xdf)
bitmap(file='TukeyHSDPlot.png')
plot(thsd)
dev.off()
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Tukey Honest Significant Difference Comparisons', 5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ', 1, TRUE)
for(i in 1:4){
a<-table.element(a,colnames(thsd[[1]])[i], 1, TRUE)
}
a<-table.row.end(a)
for(i in 1:length(rownames(thsd[[1]]))){
a<-table.row.start(a)
a<-table.element(a,rownames(thsd[[1]])[i], 1, TRUE)
for(j in 1:4){
a<-table.element(a,round(thsd[[1]][i,j], digits=3), 1, FALSE)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
}
if(intercept==FALSE){
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'TukeyHSD Message', 1,TRUE)
a<-table.row.end(a)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Must Include Intercept to use Tukey Test ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')
}
library(car)
lt.lmxdf<-levene.test(lmxdf)
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Levenes Test for Homogeneity of Variance', 4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
for (i in 1:3){
a<-table.element(a,names(lt.lmxdf)[i], 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Group', 1, TRUE)
for (i in 1:3){
a<-table.element(a,round(lt.lmxdf[[i]][1], digits=3), 1, FALSE)
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ', 1, TRUE)
a<-table.element(a,lt.lmxdf[[1]][2], 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.element(a,' ', 1, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')