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Description of Statistical Computation

Author's title

THE EFFECTS OF LIMITED STUDENT ENGAGEMENT TO STUDENTS’ ACADEMIC PERFORMA...

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationFri, 13 May 2022 02:14:16 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2022/May/13/t1652401747cm3h9taqksmvcsk.htm/, Retrieved Fri, 28 Aug 2026 23:44:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319694, Retrieved Fri, 28 Aug 2026 23:44:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact416

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [THE EFFECTS OF L...] [2022-05-13 00:14:16] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
96
93.54
96
94
95.64
94
94.34
94
96.42
96.31
94.96
95.934
94.50
95.2
95.74
93.94
94.29
96.75
93
95.76
96.1
97.8
96.55
97.49
93
96.33
94.19
94.15
95
93.21
91
94
95.03
94.18
97.15
96.29
94.76
95.026
94.766
94
94.76
92.69
94.6
93.25
94.53
97
94
95.5
94
92
94
94.06
96.05
95.77
94
91.64
93
94
95
93.21
94
91.97
94.5
92
95.2
95.22
92.76
96.36
95.41
93.9
95.21
96.18
94.92
96
96.66
96.37
96.83
Dataseries Y:
Download CSV
Histogram 
97
96.36
97
97
97.09
96
96.81
96
97.47
97.54
97.13
97.18
97.25
96.5
97.65
96.83
96.6
97.74
95.66
96.67
98
98.69
98.37
98
95
97.68
95.95
96.67
97
96.95
93
96
95.05
96.58
97.87
97.86
97.16
97.08545455
95.915
97
96.83
96
95.9
94.31
94.31
97
95.5
95.5
94
93
95
94.51
97.56
97.17
95
91.38
95
95
96.63
94.81
95.37
94.96
96
93
95.2
96.13
93.53
97.8
97.4
95.63
97.04
97.7
97.08
93
97.47
98.11
97.88

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig 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=319694&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=319694&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319694&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean94.764883116883196.2470188902597
Biased Variance2.050103012312362.14751461045375
Biased Standard Deviation1.431818079335631.4654400739893
Covariance1.63062844483635
Correlation0.767046999733478
Determination0.588361099800131
T-Test10.3536720012344
p-value (2 sided)4.15568430806599e-16
p-value (1 sided)2.077842154033e-16
95% CI of Correlation[0.655722856916791, 0.845727849516412]
Degrees of Freedom75
Number of Observations77

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 94.7648831168831 & 96.2470188902597 \tabularnewline
Biased Variance & 2.05010301231236 & 2.14751461045375 \tabularnewline
Biased Standard Deviation & 1.43181807933563 & 1.4654400739893 \tabularnewline
Covariance & 1.63062844483635 \tabularnewline
Correlation & 0.767046999733478 \tabularnewline
Determination & 0.588361099800131 \tabularnewline
T-Test & 10.3536720012344 \tabularnewline
p-value (2 sided) & 4.15568430806599e-16 \tabularnewline
p-value (1 sided) & 2.077842154033e-16 \tabularnewline
95% CI of Correlation & [0.655722856916791, 0.845727849516412] \tabularnewline
Degrees of Freedom & 75 \tabularnewline
Number of Observations & 77 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319694&T=1

[TABLE]
[ROW][C]Pearson Product Moment Correlation - Ungrouped Data[/C][/ROW]
[ROW][C]Statistic[/C][C]Variable X[/C][C]Variable Y[/C][/ROW]
[ROW][C]Mean[/C][C]94.7648831168831[/C][C]96.2470188902597[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2.05010301231236[/C][C]2.14751461045375[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.43181807933563[/C][C]1.4654400739893[/C][/ROW]
[ROW][C]Covariance[/C][C]1.63062844483635[/C][/ROW]
[ROW][C]Correlation[/C][C]0.767046999733478[/C][/ROW]
[ROW][C]Determination[/C][C]0.588361099800131[/C][/ROW]
[ROW][C]T-Test[/C][C]10.3536720012344[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.15568430806599e-16[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.077842154033e-16[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.655722856916791, 0.845727849516412][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]75[/C][/ROW]
[ROW][C]Number of Observations[/C][C]77[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319694&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319694&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:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean94.764883116883196.2470188902597
Biased Variance2.050103012312362.14751461045375
Biased Standard Deviation1.431818079335631.4654400739893
Covariance1.63062844483635
Correlation0.767046999733478
Determination0.588361099800131
T-Test10.3536720012344
p-value (2 sided)4.15568430806599e-16
p-value (1 sided)2.077842154033e-16
95% CI of Correlation[0.655722856916791, 0.845727849516412]
Degrees of Freedom75
Number of Observations77






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0701, p-value = 0.5856
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.286, p-value = 0.001303
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.47837, p-value = 0.2294

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.6847, p-value = 0.0002323


\begin{tabular}{lllllllll}
\hline
Normality Tests \tabularnewline

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0701, p-value = 0.5856
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.286, p-value = 0.001303
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.47837, p-value = 0.2294

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.6847, p-value = 0.0002323

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319694&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0701, p-value = 0.5856
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.286, p-value = 0.001303
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.47837, p-value = 0.2294

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 1.6847, p-value = 0.0002323

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319694&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319694&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:

Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.0701, p-value = 0.5856
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 13.286, p-value = 0.001303
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.47837, p-value = 0.2294

> ad.y
	Anderson-Darling normality test
data:  y
A = 1.6847, p-value = 0.0002323


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
library(psychometric)
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
bitmap(file='test1.png')
histx <- hist(x, plot=FALSE)
histy <- hist(y, plot=FALSE)
maxcounts <- max(c(histx$counts, histx$counts))
xrange <- c(min(x),max(x))
yrange <- c(min(y),max(y))
nf <- layout(matrix(c(2,0,1,3),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE)
par(mar=c(4,4,1,1))
plot(x, y, xlim=xrange, ylim=yrange, xlab=xlab, ylab=ylab, sub=main)
par(mar=c(0,4,1,1))
barplot(histx$counts, axes=FALSE, ylim=c(0, maxcounts), space=0)
par(mar=c(4,0,1,1))
barplot(histy$counts, axes=FALSE, xlim=c(0, maxcounts), space=0, horiz=TRUE)
dev.off()
lx = length(x)
makebiased = (lx-1)/lx
varx = var(x)*makebiased
vary = var(y)*makebiased
corxy <- cor.test(x,y,method='pearson', na.rm = T)
cxy <- as.matrix(corxy$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Variance',header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biased Standard Deviation',header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Covariance',header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Correlation',header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Determination',header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-Test',header=TRUE)
a<-table.element(a,as.matrix(corxy$statistic)[1,1],2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (2 sided)',header=TRUE)
a<-table.element(a,(p2 <- as.matrix(corxy$p.value)[1,1]),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (1 sided)',header=TRUE)
a<-table.element(a,p2/2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'95% CI of Correlation',header=TRUE)
a<-table.element(a,paste('[',CIr(r=cxy, n = lx, level = .95)[1],', ', CIr(r=cxy, n = lx, level = .95)[2],']',sep=''),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degrees of Freedom',header=TRUE)
a<-table.element(a,lx-2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of Observations',header=TRUE)
a<-table.element(a,lx,2)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
library(moments)
library(nortest)
jarque.x <- jarque.test(x)
jarque.y <- jarque.test(y)
if(lx>7) {
ad.x <- ad.test(x)
ad.y <- ad.test(y)
}
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Normality Tests',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('jarque.y'),'
',sep=''))
a<-table.row.end(a)
if(lx>7) {
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.x'),'
',sep=''))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('ad.y'),'
',sep=''))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
library(car)
bitmap(file='test2.png')
qqPlot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qqPlot(y,main='QQplot of variable y')
dev.off()