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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 computationMon, 01 Dec 2014 14:22:55 +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/01/t1417443801xbhzadkqhk7bmwt.htm/, Retrieved Thu, 16 May 2024 19:00:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261875, Retrieved Thu, 16 May 2024 19:00:24 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64

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-       [Paired and Unpaired Two Samples Tests about the Mean] [paper] [2014-12-01 14:22:55] [627bde65e5570be47fd7fc8a9f75ea40] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
72	50
61	68
68	62
61	54
64	71
65	54
69	65
63	73
75	52
63	84
73	42
75	66
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63	78
62	73
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68	71
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71	68
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63	63
59	70
73	66
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62	70
69	75
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74	65
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58	76
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62	64
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69	60
66	68
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66	62
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66	52
73	59
74	60
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84	60
64	55
58	62
59	69
78	68
67	72
60	19
66	68
74	79
72	71
55	71
49	74
74	75
53	53
64	50
65	70
57	78
51	59
80	72
67	70
70	63
74	74
75	67
70	66
69	62
65	73
71	67
65	61
68	74
67	32
66	69
59	60
72	57
52	60
65	68
68	68
67	73
73	69
65	65
75	81
57	55
62	69
59	48
63	69
73	68
55	74
64	67
78	65
60	63
66	74
68	39
78	68
60	69
64	63
72	70
71	68
80	70
74	78
69	59
75	62
73	75
60	74
76	73
53	62
78	69
67	65
59	67
73	73
70	52
59	61
76	53
66	63
64	78
72	65
57	77
74	69
66	68
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71	63
65	41
70	76
66	67
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72	73
65	63
67	78
72	56
58	56
84	64
63	68
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69	55
80	66
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71	61
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81	63
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	76
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	64
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	73
	75
	58
	51
	75
	71
	28

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261875&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261875&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261875&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'Herman Ole Andreas Wold' @ wold.wessa.net






Two Sample t-test (unpaired)
Mean of Sample 166.5745454545455
Mean of Sample 265.7054545454545
t-stat-73.8622270718196
df548
p-value4.93792018006541e-287
H0 value53
Alternativetwo.sided
CI Level0.95
CI[-0.517285752803829,2.25546757098565]
F-test to compare two variances
F-stat0.891172239318545
df274
p-value0.340862594187516
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.702912746767577,1.12985283562461]

\begin{tabular}{lllllllll}
\hline
Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 66.5745454545455 \tabularnewline
Mean of Sample 2 & 65.7054545454545 \tabularnewline
t-stat & -73.8622270718196 \tabularnewline
df & 548 \tabularnewline
p-value & 4.93792018006541e-287 \tabularnewline
H0 value & 53 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.517285752803829,2.25546757098565] \tabularnewline
F-test to compare two variances \tabularnewline
F-stat & 0.891172239318545 \tabularnewline
df & 274 \tabularnewline
p-value & 0.340862594187516 \tabularnewline
H0 value & 1 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [0.702912746767577,1.12985283562461] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261875&T=1

[TABLE]
[ROW][C]Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]66.5745454545455[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]65.7054545454545[/C][/ROW]
[ROW][C]t-stat[/C][C]-73.8622270718196[/C][/ROW]
[ROW][C]df[/C][C]548[/C][/ROW]
[ROW][C]p-value[/C][C]4.93792018006541e-287[/C][/ROW]
[ROW][C]H0 value[/C][C]53[/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][-0.517285752803829,2.25546757098565][/C][/ROW]
[ROW][C]F-test to compare two variances[/C][/ROW]
[ROW][C]F-stat[/C][C]0.891172239318545[/C][/ROW]
[ROW][C]df[/C][C]274[/C][/ROW]
[ROW][C]p-value[/C][C]0.340862594187516[/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][0.702912746767577,1.12985283562461][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261875&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261875&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 (unpaired)
Mean of Sample 166.5745454545455
Mean of Sample 265.7054545454545
t-stat-73.8622270718196
df548
p-value4.93792018006541e-287
H0 value53
Alternativetwo.sided
CI Level0.95
CI[-0.517285752803829,2.25546757098565]
F-test to compare two variances
F-stat0.891172239318545
df274
p-value0.340862594187516
H0 value1
Alternativetwo.sided
CI Level0.95
CI[0.702912746767577,1.12985283562461]






Welch Two Sample t-test (unpaired)
Mean of Sample 166.5745454545455
Mean of Sample 265.7054545454545
t-stat-73.8622270718197
df546.191318857488
p-value1.89676571390061e-286
H0 value53
Alternativetwo.sided
CI Level0.95
CI[-0.517295914435216,2.25547773261704]

\begin{tabular}{lllllllll}
\hline
Welch Two Sample t-test (unpaired) \tabularnewline
Mean of Sample 1 & 66.5745454545455 \tabularnewline
Mean of Sample 2 & 65.7054545454545 \tabularnewline
t-stat & -73.8622270718197 \tabularnewline
df & 546.191318857488 \tabularnewline
p-value & 1.89676571390061e-286 \tabularnewline
H0 value & 53 \tabularnewline
Alternative & two.sided \tabularnewline
CI Level & 0.95 \tabularnewline
CI & [-0.517295914435216,2.25547773261704] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261875&T=2

[TABLE]
[ROW][C]Welch Two Sample t-test (unpaired)[/C][/ROW]
[ROW][C]Mean of Sample 1[/C][C]66.5745454545455[/C][/ROW]
[ROW][C]Mean of Sample 2[/C][C]65.7054545454545[/C][/ROW]
[ROW][C]t-stat[/C][C]-73.8622270718197[/C][/ROW]
[ROW][C]df[/C][C]546.191318857488[/C][/ROW]
[ROW][C]p-value[/C][C]1.89676571390061e-286[/C][/ROW]
[ROW][C]H0 value[/C][C]53[/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][-0.517295914435216,2.25547773261704][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261875&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261875&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 (unpaired)
Mean of Sample 166.5745454545455
Mean of Sample 265.7054545454545
t-stat-73.8622270718197
df546.191318857488
p-value1.89676571390061e-286
H0 value53
Alternativetwo.sided
CI Level0.95
CI[-0.517295914435216,2.25547773261704]






Wicoxon rank sum test with continuity correction (unpaired)
W75
p-value3.1516506584163e-91
H0 value53
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.0618181818181818
p-value0.669513243311927
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.0618181818181818
p-value0.669513243311927

\begin{tabular}{lllllllll}
\hline
Wicoxon rank sum test with continuity correction (unpaired) \tabularnewline
W & 75 \tabularnewline
p-value & 3.1516506584163e-91 \tabularnewline
H0 value & 53 \tabularnewline
Alternative & two.sided \tabularnewline
Kolmogorov-Smirnov Test to compare Distributions of two Samples \tabularnewline
KS Statistic & 0.0618181818181818 \tabularnewline
p-value & 0.669513243311927 \tabularnewline
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples \tabularnewline
KS Statistic & 0.0618181818181818 \tabularnewline
p-value & 0.669513243311927 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261875&T=3

[TABLE]
[ROW][C]Wicoxon rank sum test with continuity correction (unpaired)[/C][/ROW]
[ROW][C]W[/C][C]75[/C][/ROW]
[ROW][C]p-value[/C][C]3.1516506584163e-91[/C][/ROW]
[ROW][C]H0 value[/C][C]53[/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]0.0618181818181818[/C][/ROW]
[ROW][C]p-value[/C][C]0.669513243311927[/C][/ROW]
[ROW][C]Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples[/C][/ROW]
[ROW][C]KS Statistic[/C][C]0.0618181818181818[/C][/ROW]
[ROW][C]p-value[/C][C]0.669513243311927[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261875&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261875&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 (unpaired)
W75
p-value3.1516506584163e-91
H0 value53
Alternativetwo.sided
Kolmogorov-Smirnov Test to compare Distributions of two Samples
KS Statistic0.0618181818181818
p-value0.669513243311927
Kolmogorov-Smirnov Test to compare Distributional Shape of two Samples
KS Statistic0.0618181818181818
p-value0.669513243311927


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 53 ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = 0.95 ; par4 = two.sided ; par5 = unpaired ; par6 = 53 ;
R code (references can be found in the software module):
par6 <- '53'
par5 <- 'unpaired'
par4 <- 'two.sided'
par3 <- '0.95'
par2 <- '2'
par1 <- '1'
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')