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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_One Factor ANOVA.wasp
Title produced by softwareOne-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)
Date of computationMon, 15 Dec 2014 13:58:38 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/15/t1418651925uw5unzunbstc8va.htm/, Retrieved Thu, 16 May 2024 08:31:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268414, Retrieved Thu, 16 May 2024 08:31:38 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [One-Way-Between-Groups ANOVA- Free Statistics Software (Calculator)] [] [2014-12-15 13:58:38] [58179e1d3a5a39b9daf58e365d8a3352] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21 12.9
21 12.8
21 7.4
21 6.7
21 12.6
21 14.8
23 13.3
22 11.1
25 8.2
21 11.4
23 6.4
21 12
21 6.3
25 11.3
21 11.9
21 9.3
24 10
21 13.8
24 10.8
21 11.7
22 10.9
20 16.1
21 9.9
22 11.5
22 8.3
21 11.7
21 9
22 10.8
20 10.4
21 12.7
21 11.8
24 13
22 10.8
22 12.3
21 11.3
20 11.6
23 10.9
20 12.1
23 13.3
21 10.1
21 14.3
22 9.3
21 12.5
21 7.6
21 9.2
22 14.5
21 12.3
21 12.6
21 13
21 12.6
20 13.2
21 7.7
19 10.5
19 10.9
20 4.3
19 10.3
20 11.4
21 5.6
18 8.8
21 9
20 9.6
21 6.4
19 11.6

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268414&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268414&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'Gwilym Jenkins' @ jenkins.wessa.net






ANOVA Model
TOT ~ age
means8.82.0252.2871.9162.2562.1752.4670.95

\begin{tabular}{lllllllll}
\hline
ANOVA Model \tabularnewline
TOT  ~  age \tabularnewline
means & 8.8 & 2.025 & 2.287 & 1.916 & 2.256 & 2.175 & 2.467 & 0.95 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268414&T=1

[TABLE]
[ROW][C]ANOVA Model[/C][/ROW]
[ROW][C]TOT  ~  age[/C][/ROW]
[ROW][C]means[/C][C]8.8[/C][C]2.025[/C][C]2.287[/C][C]1.916[/C][C]2.256[/C][C]2.175[/C][C]2.467[/C][C]0.95[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268414&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
TOT ~ age
means8.82.0252.2871.9162.2562.1752.4670.95






ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
age78.461.2090.1910.986
Residuals55348.626.339 

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
age & 7 & 8.46 & 1.209 & 0.191 & 0.986 \tabularnewline
Residuals & 55 & 348.62 & 6.339 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268414&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]7[/C][C]8.46[/C][C]1.209[/C][C]0.191[/C][C]0.986[/C][/ROW]
[ROW][C]Residuals[/C][C]55[/C][C]348.62[/C][C]6.339[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268414&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)
age78.461.2090.1910.986
Residuals55348.626.339






Tukey Honest Significant Difference Comparisons
difflwruprp adj
19-182.025-6.84310.8930.996
20-182.287-6.12510.70.989
21-181.916-6.1399.970.995
22-182.256-6.10510.6160.989
23-182.175-6.69311.0430.994
24-182.467-6.69211.6250.989
25-180.95-8.76410.6641
20-190.263-4.5955.121
21-19-0.109-4.3164.0971
22-190.231-4.5364.9971
23-190.15-5.4595.7591
24-190.442-5.6166.51
25-19-1.075-7.9445.7941
21-20-0.372-3.5072.7631
22-20-0.032-3.8863.8221
23-20-0.113-4.974.7451
24-200.179-5.1915.5491
25-20-1.338-7.6084.9330.997
22-210.34-2.6533.3331
23-210.259-3.9474.4661
24-210.551-4.2385.341
25-21-0.966-6.7474.8160.999
23-22-0.081-4.8474.6861
24-220.211-5.0775.4991
25-22-1.306-7.5064.8950.998
24-230.292-5.7666.351
25-23-1.225-8.0945.6440.999
25-24-1.517-8.7575.7240.998

\begin{tabular}{lllllllll}
\hline
Tukey Honest Significant Difference Comparisons \tabularnewline
  & diff & lwr & upr & p adj \tabularnewline
19-18 & 2.025 & -6.843 & 10.893 & 0.996 \tabularnewline
20-18 & 2.287 & -6.125 & 10.7 & 0.989 \tabularnewline
21-18 & 1.916 & -6.139 & 9.97 & 0.995 \tabularnewline
22-18 & 2.256 & -6.105 & 10.616 & 0.989 \tabularnewline
23-18 & 2.175 & -6.693 & 11.043 & 0.994 \tabularnewline
24-18 & 2.467 & -6.692 & 11.625 & 0.989 \tabularnewline
25-18 & 0.95 & -8.764 & 10.664 & 1 \tabularnewline
20-19 & 0.263 & -4.595 & 5.12 & 1 \tabularnewline
21-19 & -0.109 & -4.316 & 4.097 & 1 \tabularnewline
22-19 & 0.231 & -4.536 & 4.997 & 1 \tabularnewline
23-19 & 0.15 & -5.459 & 5.759 & 1 \tabularnewline
24-19 & 0.442 & -5.616 & 6.5 & 1 \tabularnewline
25-19 & -1.075 & -7.944 & 5.794 & 1 \tabularnewline
21-20 & -0.372 & -3.507 & 2.763 & 1 \tabularnewline
22-20 & -0.032 & -3.886 & 3.822 & 1 \tabularnewline
23-20 & -0.113 & -4.97 & 4.745 & 1 \tabularnewline
24-20 & 0.179 & -5.191 & 5.549 & 1 \tabularnewline
25-20 & -1.338 & -7.608 & 4.933 & 0.997 \tabularnewline
22-21 & 0.34 & -2.653 & 3.333 & 1 \tabularnewline
23-21 & 0.259 & -3.947 & 4.466 & 1 \tabularnewline
24-21 & 0.551 & -4.238 & 5.34 & 1 \tabularnewline
25-21 & -0.966 & -6.747 & 4.816 & 0.999 \tabularnewline
23-22 & -0.081 & -4.847 & 4.686 & 1 \tabularnewline
24-22 & 0.211 & -5.077 & 5.499 & 1 \tabularnewline
25-22 & -1.306 & -7.506 & 4.895 & 0.998 \tabularnewline
24-23 & 0.292 & -5.766 & 6.35 & 1 \tabularnewline
25-23 & -1.225 & -8.094 & 5.644 & 0.999 \tabularnewline
25-24 & -1.517 & -8.757 & 5.724 & 0.998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268414&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]19-18[/C][C]2.025[/C][C]-6.843[/C][C]10.893[/C][C]0.996[/C][/ROW]
[ROW][C]20-18[/C][C]2.287[/C][C]-6.125[/C][C]10.7[/C][C]0.989[/C][/ROW]
[ROW][C]21-18[/C][C]1.916[/C][C]-6.139[/C][C]9.97[/C][C]0.995[/C][/ROW]
[ROW][C]22-18[/C][C]2.256[/C][C]-6.105[/C][C]10.616[/C][C]0.989[/C][/ROW]
[ROW][C]23-18[/C][C]2.175[/C][C]-6.693[/C][C]11.043[/C][C]0.994[/C][/ROW]
[ROW][C]24-18[/C][C]2.467[/C][C]-6.692[/C][C]11.625[/C][C]0.989[/C][/ROW]
[ROW][C]25-18[/C][C]0.95[/C][C]-8.764[/C][C]10.664[/C][C]1[/C][/ROW]
[ROW][C]20-19[/C][C]0.263[/C][C]-4.595[/C][C]5.12[/C][C]1[/C][/ROW]
[ROW][C]21-19[/C][C]-0.109[/C][C]-4.316[/C][C]4.097[/C][C]1[/C][/ROW]
[ROW][C]22-19[/C][C]0.231[/C][C]-4.536[/C][C]4.997[/C][C]1[/C][/ROW]
[ROW][C]23-19[/C][C]0.15[/C][C]-5.459[/C][C]5.759[/C][C]1[/C][/ROW]
[ROW][C]24-19[/C][C]0.442[/C][C]-5.616[/C][C]6.5[/C][C]1[/C][/ROW]
[ROW][C]25-19[/C][C]-1.075[/C][C]-7.944[/C][C]5.794[/C][C]1[/C][/ROW]
[ROW][C]21-20[/C][C]-0.372[/C][C]-3.507[/C][C]2.763[/C][C]1[/C][/ROW]
[ROW][C]22-20[/C][C]-0.032[/C][C]-3.886[/C][C]3.822[/C][C]1[/C][/ROW]
[ROW][C]23-20[/C][C]-0.113[/C][C]-4.97[/C][C]4.745[/C][C]1[/C][/ROW]
[ROW][C]24-20[/C][C]0.179[/C][C]-5.191[/C][C]5.549[/C][C]1[/C][/ROW]
[ROW][C]25-20[/C][C]-1.338[/C][C]-7.608[/C][C]4.933[/C][C]0.997[/C][/ROW]
[ROW][C]22-21[/C][C]0.34[/C][C]-2.653[/C][C]3.333[/C][C]1[/C][/ROW]
[ROW][C]23-21[/C][C]0.259[/C][C]-3.947[/C][C]4.466[/C][C]1[/C][/ROW]
[ROW][C]24-21[/C][C]0.551[/C][C]-4.238[/C][C]5.34[/C][C]1[/C][/ROW]
[ROW][C]25-21[/C][C]-0.966[/C][C]-6.747[/C][C]4.816[/C][C]0.999[/C][/ROW]
[ROW][C]23-22[/C][C]-0.081[/C][C]-4.847[/C][C]4.686[/C][C]1[/C][/ROW]
[ROW][C]24-22[/C][C]0.211[/C][C]-5.077[/C][C]5.499[/C][C]1[/C][/ROW]
[ROW][C]25-22[/C][C]-1.306[/C][C]-7.506[/C][C]4.895[/C][C]0.998[/C][/ROW]
[ROW][C]24-23[/C][C]0.292[/C][C]-5.766[/C][C]6.35[/C][C]1[/C][/ROW]
[ROW][C]25-23[/C][C]-1.225[/C][C]-8.094[/C][C]5.644[/C][C]0.999[/C][/ROW]
[ROW][C]25-24[/C][C]-1.517[/C][C]-8.757[/C][C]5.724[/C][C]0.998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268414&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268414&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
19-182.025-6.84310.8930.996
20-182.287-6.12510.70.989
21-181.916-6.1399.970.995
22-182.256-6.10510.6160.989
23-182.175-6.69311.0430.994
24-182.467-6.69211.6250.989
25-180.95-8.76410.6641
20-190.263-4.5955.121
21-19-0.109-4.3164.0971
22-190.231-4.5364.9971
23-190.15-5.4595.7591
24-190.442-5.6166.51
25-19-1.075-7.9445.7941
21-20-0.372-3.5072.7631
22-20-0.032-3.8863.8221
23-20-0.113-4.974.7451
24-200.179-5.1915.5491
25-20-1.338-7.6084.9330.997
22-210.34-2.6533.3331
23-210.259-3.9474.4661
24-210.551-4.2385.341
25-21-0.966-6.7474.8160.999
23-22-0.081-4.8474.6861
24-220.211-5.0775.4991
25-22-1.306-7.5064.8950.998
24-230.292-5.7666.351
25-23-1.225-8.0945.6440.999
25-24-1.517-8.7575.7240.998






Levenes Test for Homogeneity of Variance
DfF valuePr(>F)
Group70.9490.477
55 

\begin{tabular}{lllllllll}
\hline
Levenes Test for Homogeneity of Variance \tabularnewline
  & Df & F value & Pr(>F) \tabularnewline
Group & 7 & 0.949 & 0.477 \tabularnewline
  & 55 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268414&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]7[/C][C]0.949[/C][C]0.477[/C][/ROW]
[ROW][C] [/C][C]55[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268414&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268414&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)
Group70.9490.477
55


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = 2 ; par2 = 1 ; par3 = TRUE ;
R code (references can be found in the software module):
par3 <- 'FALSE'
par2 <- '1'
par1 <- '2'
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){
'Tukey Plot'
thsd<-TukeyHSD(aov.xdf)
bitmap(file='TukeyHSDPlot.png')
plot(thsd)
dev.off()
}
if(intercept==TRUE){
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<-leveneTest(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')