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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_twosampletests_mean.wasp
Title produced by softwarePaired and Unpaired Two Samples Tests about the Mean
Date of computationWed, 10 Dec 2014 13:29:55 +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/10/t1418218415gs02tg4o7ck7dpd.htm/, Retrieved Sun, 19 May 2024 15:54:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=265151, Retrieved Sun, 19 May 2024 15:54:46 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact53

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-       [Paired and Unpaired Two Samples Tests about the Mean] [zerefd] [2014-12-10 13:29:55] [a3e248f2ee98616f420122f2d0e2525c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1894.00 2132.00
1757.00 1964.00
3582.00 2209.00
5321.00 1965.00
5561.00 2631.00
5907.00 2583.00
4944.00 2714.00
4966.00 2248.00
3258.00 2364.00
1964.00 3042.00
1743.00 2316.00
1262.00 2735.00
2086.00 2493.00
1793.00 2136.00
3548.00 2467.00
5672.00 2414.00
6084.00 2556.00
4914.00 2768.00
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5139.00 2573.00
3218.00 3005.00
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2238.00 2540.00
1442.00 3187.00
2205.00 2689.00
2025.00 2154.00
3531.00 3065.00
4977.00 2397.00
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5202.00 3025.00
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2422.00 2261.00
1997.00 2590.00
3163.00 2624.00
5964.00 1860.00
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4500.00 2807.00
2939.00 2350.00
2702.00 3053.00
2090.00 2203.00
1504.00 2471.00
2549.00 1967.00
1931.00 2473.00
3013.00 2397.00
6204.00 1904.00
5788.00 2732.00
5611.00 2297.00
5594.00 2734.00
4647.00 2719.00
3490.00 2296.00
2487.00 3243.00
1992.00 2166.00
1507.00 2261.00
2306.00 2408.00
2002.00 2536.00
3075.00 2324.00
5331.00 2178.00
5589.00 2803.00
5813.00 2604.00
4876.00 2782.00
4665.00 2656.00
3601.00 2801.00
2192.00 3122.00
2111.00 2393.00
1580.00 2233.00
2288.00 2451.00
1993.00 2596.00
3228.00 2467.00
5000.00 2210.00
5480.00 2948.00
5770.00 2507.00
4962.00 3019.00
4685.00 2401.00
3607.00 2818.00
2222.00 3305.00
2467.00 2101.00
1594.00 2582.00
2228.00 2407.00
1910.00 2416.00
3157.00 2463.00
4809.00 2228.00
6249.00 2616.00
4607.00 2934.00
4975.00 2668.00
4784.00 2808.00
3028.00 2664.00
2461.00 3112.00
2218.00 2321.00
1351.00 2718.00
2070.00 2297.00
1887.00 2534.00
3024.00 2647.00
4596.00 2064.00
6398.00 2642.00
4459.00 2702.00
5382.00 2348.00
4359.00 2734.00
2687.00 2709.00
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1169.00 2531.00
2429.00 2119.00
1762.00 2369.00
2846.00 2682.00
5627.00 1840.00
5749.00 2622.00
4502.00 2570.00
5720.00 2447.00
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2635.00 2957.00
2059.00 2102.00
1511.00 2250.00
2359.00 2051.00
1741.00 2260.00
2917.00 2327.00
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5760.00 2631.00
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5134.00 2150.00
4831.00 2837.00
3695.00 1976.00
2462.00 2836.00
2146.00 2203.00
1579.00 1770.00

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'Sir Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265151&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265151&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265151&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Two Sample t-test (paired)
Difference: Mean1 - Mean21065.46212121212
t-stat7.34507824161356
df131
p-value1.95699436180567e-11
H0 value0
Alternativetwo.sided
CI Level0.95
CI[778.502859385534,1352.42138303871]
F-test to compare two variances
F-stat19.5804163685108
df131
p-value0
H0 value1
Alternativetwo.sided
CI Level0.95
CI[13.8813924050288,27.6191821380506]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & 1065.46212121212 \tabularnewline
t-stat & 7.34507824161356 \tabularnewline
df & 131 \tabularnewline
p-value & 1.95699436180567e-11 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [778.502859385534,1352.42138303871] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 19.5804163685108 \tabularnewline
df & 131 \tabularnewline
p-value & 0 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [13.8813924050288,27.6191821380506] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265151&T=1

[TABLE]
[ROW][C]Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]1065.46212121212[/C][/ROW]
[ROW][C]t-stat[/C][C]7.34507824161356[/C][/ROW]
[ROW][C]df[/C][C]131[/C][/ROW]
[ROW][C]p-value[/C][C]1.95699436180567e-11[/C][/ROW]
[ROW][C]H0 value[/C][C]0[/C][/ROW]
[ROW][C]Alternative[/C][C]two.sided[/C][/ROW]
[ROW][C]CI Level[/C][C]0.95[/C][/ROW]
[ROW][C]CI[/C][C][778.502859385534,1352.42138303871][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]19.5804163685108[/C][/ROW]
[ROW][C]df[/C][C]131[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]H0 value[/C][C]1[/C][/ROW]
[ROW][C]Alternative[/C][C]two.sided[/C][/ROW]
[ROW][C]CI Level[/C][C]0.95[/C][/ROW]
[ROW][C]CI[/C][C][13.8813924050288,27.6191821380506][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265151&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265151&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:

Two Sample t-test (paired)
Difference: Mean1 - Mean21065.46212121212
t-stat7.34507824161356
df131
p-value1.95699436180567e-11
H0 value0
Alternativetwo.sided
CI Level0.95
CI[778.502859385534,1352.42138303871]
F-test to compare two variances
F-stat19.5804163685108
df131
p-value0
H0 value1
Alternativetwo.sided
CI Level0.95
CI[13.8813924050288,27.6191821380506]






Welch Two Sample t-test (paired)
Difference: Mean1 - Mean21065.46212121212
t-stat7.34507824161356
df131
p-value1.95699436180567e-11
H0 value0
Alternativetwo.sided
CI Level0.95
CI[778.502859385534,1352.42138303871]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (paired) \tabularnewline
Difference: Mean1 - Mean2 & 1065.46212121212 \tabularnewline
t-stat & 7.34507824161356 \tabularnewline
df & 131 \tabularnewline
p-value & 1.95699436180567e-11 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [778.502859385534,1352.42138303871] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265151&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (paired)[/C][/ROW]
[ROW][C]Difference: Mean1 - Mean2[/C][C]1065.46212121212[/C][/ROW]
[ROW][C]t-stat[/C][C]7.34507824161356[/C][/ROW]
[ROW][C]df[/C][C]131[/C][/ROW]
[ROW][C]p-value[/C][C]1.95699436180567e-11[/C][/ROW]
[ROW][C]H0 value[/C][C]0[/C][/ROW]
[ROW][C]Alternative[/C][C]two.sided[/C][/ROW]
[ROW][C]CI Level[/C][C]0.95[/C][/ROW]
[ROW][C]CI[/C][C][778.502859385534,1352.42138303871][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265151&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265151&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:

Welch Two Sample t-test (paired)
Difference: Mean1 - Mean21065.46212121212
t-stat7.34507824161356
df131
p-value1.95699436180567e-11
H0 value0
Alternativetwo.sided
CI Level0.95
CI[778.502859385534,1352.42138303871]






Wicoxon rank sum test with continuity correction (paired)
W6836
p-value2.74956767817707e-08
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.462121212121212
p-value1.14430687148115e-12
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.439393939393939
p-value1.71040959173752e-11

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (paired) \tabularnewline
W & 6836 \tabularnewline
p-value & 2.74956767817707e-08 \tabularnewline
H0 value & 0 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.462121212121212 \tabularnewline
p-value & 1.14430687148115e-12 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.439393939393939 \tabularnewline
p-value & 1.71040959173752e-11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265151&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (paired)[/C][/ROW]
[ROW][C]W[/C][C]6836[/C][/ROW]
[ROW][C]p-value[/C][C]2.74956767817707e-08[/C][/ROW]
[ROW][C]H0 value[/C][C]0[/C][/ROW]
[ROW][C]Alternative[/C][C]two.sided[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributions of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.462121212121212[/C][/ROW]
[ROW][C]p-value[/C][C]1.14430687148115e-12[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.439393939393939[/C][/ROW]
[ROW][C]p-value[/C][C]1.71040959173752e-11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265151&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265151&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:

Wicoxon rank sum test with continuity correction (paired)
W6836
p-value2.74956767817707e-08
H0 value0
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.462121212121212
p-value1.14430687148115e-12
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.439393939393939
p-value1.71040959173752e-11


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = paired ; par6 = 0.0 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = paired ; par6 = 0.0 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #column number of first sample
par2 <- as.numeric(par2) #column number of second sample
par3 <- as.numeric(par3) #confidence (= 1 - alpha)
if (par5 == 'unpaired') paired <- FALSE else paired <- TRUE
par6 <- as.numeric(par6) #H0
z <- t(y)
if (par1 == par2) stop('Please, select two different column numbers')
if (par1 < 1) stop('Please, select a column number greater than zero for the first sample')
if (par2 < 1) stop('Please, select a column number greater than zero for the second sample')
if (par1 > length(z[1,])) stop('The column number for the first sample should be smaller')
if (par2 > length(z[1,])) stop('The column number for the second sample should be smaller')
if (par3 <= 0) stop('The confidence level should be larger than zero')
if (par3 >= 1) stop('The confidence level should be smaller than zero')
(r.t <- t.test(z[,par1],z[,par2],var.equal=TRUE,alternative=par4,paired=paired,mu=par6,conf.level=par3))
(v.t <- var.test(z[,par1],z[,par2],conf.level=par3))
(r.w <- t.test(z[,par1],z[,par2],var.equal=FALSE,alternative=par4,paired=paired,mu=par6,conf.level=par3))
(w.t <- wilcox.test(z[,par1],z[,par2],alternative=par4,paired=paired,mu=par6,conf.level=par3))
(ks.t <- ks.test(z[,par1],z[,par2],alternative=par4))
m1 <- mean(z[,par1],na.rm=T)
m2 <- mean(z[,par2],na.rm=T)
mdiff <- m1 - m2
newsam1 <- z[!is.na(z[,par1]),par1]
newsam2 <- z[,par2]+mdiff
newsam2 <- newsam2[!is.na(newsam2)]
(ks1.t <- ks.test(newsam1,newsam2,alternative=par4))
mydf <- data.frame(cbind(z[,par1],z[,par2]))
colnames(mydf) <- c('Variable 1','Variable 2')
bitmap(file='test1.png')
boxplot(mydf, notch=TRUE, ylab='value',main=main)
dev.off()
bitmap(file='test2.png')
qqnorm(z[,par1],main='Normal QQplot - Variable 1')
qqline(z[,par1])
dev.off()
bitmap(file='test3.png')
qqnorm(z[,par2],main='Normal QQplot - Variable 2')
qqline(z[,par2])
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,paste('Two Sample t-test (',par5,')',sep=''),2,TRUE)
a<-table.row.end(a)
if(!paired){
a<-table.row.start(a)
a<-table.element(a,'Mean of Sample 1',header=TRUE)
a<-table.element(a,r.t$estimate[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean of Sample 2',header=TRUE)
a<-table.element(a,r.t$estimate[[2]])
a<-table.row.end(a)
} else {
a<-table.row.start(a)
a<-table.element(a,'Difference: Mean1 - Mean2',header=TRUE)
a<-table.element(a,r.t$estimate)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,'t-stat',header=TRUE)
a<-table.element(a,r.t$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'df',header=TRUE)
a<-table.element(a,r.t$parameter[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,r.t$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'H0 value',header=TRUE)
a<-table.element(a,r.t$null.value[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Alternative',header=TRUE)
a<-table.element(a,r.t$alternative)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI Level',header=TRUE)
a<-table.element(a,attr(r.t$conf.int,'conf.level'))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI',header=TRUE)
a<-table.element(a,paste('[',r.t$conf.int[1],',',r.t$conf.int[2],']',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'F-test to compare two variances',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'F-stat',header=TRUE)
a<-table.element(a,v.t$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'df',header=TRUE)
a<-table.element(a,v.t$parameter[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,v.t$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'H0 value',header=TRUE)
a<-table.element(a,v.t$null.value[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Alternative',header=TRUE)
a<-table.element(a,v.t$alternative)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI Level',header=TRUE)
a<-table.element(a,attr(v.t$conf.int,'conf.level'))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI',header=TRUE)
a<-table.element(a,paste('[',v.t$conf.int[1],',',v.t$conf.int[2],']',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,paste('Welch Two Sample t-test (',par5,')',sep=''),2,TRUE)
a<-table.row.end(a)
if(!paired){
a<-table.row.start(a)
a<-table.element(a,'Mean of Sample 1',header=TRUE)
a<-table.element(a,r.w$estimate[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean of Sample 2',header=TRUE)
a<-table.element(a,r.w$estimate[[2]])
a<-table.row.end(a)
} else {
a<-table.row.start(a)
a<-table.element(a,'Difference: Mean1 - Mean2',header=TRUE)
a<-table.element(a,r.w$estimate)
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,'t-stat',header=TRUE)
a<-table.element(a,r.w$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'df',header=TRUE)
a<-table.element(a,r.w$parameter[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,r.w$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'H0 value',header=TRUE)
a<-table.element(a,r.w$null.value[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Alternative',header=TRUE)
a<-table.element(a,r.w$alternative)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI Level',header=TRUE)
a<-table.element(a,attr(r.w$conf.int,'conf.level'))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'CI',header=TRUE)
a<-table.element(a,paste('[',r.w$conf.int[1],',',r.w$conf.int[2],']',sep=''))
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,paste('Wicoxon rank sum test with continuity correction (',par5,')',sep=''),2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'W',header=TRUE)
a<-table.element(a,w.t$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,w.t$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'H0 value',header=TRUE)
a<-table.element(a,w.t$null.value[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Alternative',header=TRUE)
a<-table.element(a,w.t$alternative)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Kolmogorov-Smirnov Test to compare Distributions of two Samples',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'KS Statistic',header=TRUE)
a<-table.element(a,ks.t$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,ks.t$p.value)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'KS Statistic',header=TRUE)
a<-table.element(a,ks1.t$statistic[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,ks1.t$p.value)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')