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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationTue, 01 Dec 2015 11:39:55 +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/2015/Dec/01/t14489700314gym8whe3iptjmq.htm/, Retrieved Thu, 16 May 2024 16:15:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284680, Retrieved Thu, 16 May 2024 16:15:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2015-12-01 11:39:55] [417cd1fa2ccbc3df120e1b65b71e6aee] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
221
219
214
210
207
206
217
231
234
233
228
226
227
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191
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175
163
155
151
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167
177
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169
160
151
139
130
126
130
127
122
129
135
142
156
157
165
170
169
162
148
143
146
175
181
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166
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167
156
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174
181
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178
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192
182
163
157
167
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214
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183
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181
184
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197
189
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191
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184
203
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195
189
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190
190
190
193
185
173
176
170
163
170
171
173
171
162
152
142
136
146
179
191
181
170
161
168
180
182
176
164
154
160
189
196
186
171
169
181
198
202
196
183
173
175
198
203
197
191
182
172
158
147
143
146
147
152
177
184
174
162
157
155
159
158
156
157
156
158
173
179
172
169
168
172
180
182
182
181
178
178
196
199
192
187
184
184
188
183
176
168
163
166
189
195
192
189
187
187
190
187
179
168
160
161
177
182
176
Dataseries Y:
Download CSV
Histogram 
191
189
184
179
175
171
179
191
195
195
193
193
195
193
187
181
176
169
174
185
186
182
178
178
179
178
174
171
168
167
175
187
191
188
185
185
187
188
186
183
179
176
183
198
203
198
192
191
194
194
192
188
182
175
178
181
171
164
159
160
163
159
148
139
129
124
136
146
143
141
135
134
135
134
136
142
142
135
140
146
155
170
167
166
160
156
156
160
156
150
157
158
167
189
197
199
193
188
186
190
186
181
190
189
192
201
200
206
208
202
190
171
163
167
195
208
208
197
189
192
199
202
200
191
190
180
194
196
199
200
199
205
207
211
210
208
201
186
177
168
173
181
185
186
189
186
181
182
176
165
176
174
168
165
162
170
179
178
169
160
151
159
191
195
184
162
152
162
188
202
209
204
193
191
202
204
206
211
214
224
224
222
219
218
213
213
229
225
220
212
204
204
202
195
186
175
170
171
196
202
200
191
186
186
193
193
188
185
182
180
194
204
216
233
241
243
241
233
228
225
219
217
235
237
238
235
234
239
248
248
247
246
240
233
242
239
238
238
238
240
249
251
253
251
246
247
260
260
259

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284680&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]4 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=284680&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284680&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean182.630522088353190.89156626506
Biased Variance557.469911775617810.642860599023
Biased Standard Deviation23.610800744058128.4717906110421
Covariance192.568645549942
Correlation0.285306990199384
Determination0.0814000786566315
T-Test4.6784036196844
p-value (2 sided)4.76543145233599e-06
p-value (1 sided)2.38271572616799e-06
95% CI of Correlation[0.166910714603569, 0.395592314916767]
Degrees of Freedom247
Number of Observations249

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 182.630522088353 & 190.89156626506 \tabularnewline
Biased Variance & 557.469911775617 & 810.642860599023 \tabularnewline
Biased Standard Deviation & 23.6108007440581 & 28.4717906110421 \tabularnewline
Covariance & 192.568645549942 \tabularnewline
Correlation & 0.285306990199384 \tabularnewline
Determination & 0.0814000786566315 \tabularnewline
T-Test & 4.6784036196844 \tabularnewline
p-value (2 sided) & 4.76543145233599e-06 \tabularnewline
p-value (1 sided) & 2.38271572616799e-06 \tabularnewline
95% CI of Correlation & [0.166910714603569, 0.395592314916767] \tabularnewline
Degrees of Freedom & 247 \tabularnewline
Number of Observations & 249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284680&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]182.630522088353[/C][C]190.89156626506[/C][/ROW]
[ROW][C]Biased Variance[/C][C]557.469911775617[/C][C]810.642860599023[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]23.6108007440581[/C][C]28.4717906110421[/C][/ROW]
[ROW][C]Covariance[/C][C]192.568645549942[/C][/ROW]
[ROW][C]Correlation[/C][C]0.285306990199384[/C][/ROW]
[ROW][C]Determination[/C][C]0.0814000786566315[/C][/ROW]
[ROW][C]T-Test[/C][C]4.6784036196844[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.76543145233599e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.38271572616799e-06[/C][/ROW]
[ROW][C]95% CI of Correlation[/C][C][0.166910714603569, 0.395592314916767][/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]247[/C][/ROW]
[ROW][C]Number of Observations[/C][C]249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284680&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284680&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
Mean182.630522088353190.89156626506
Biased Variance557.469911775617810.642860599023
Biased Standard Deviation23.610800744058128.4717906110421
Covariance192.568645549942
Correlation0.285306990199384
Determination0.0814000786566315
T-Test4.6784036196844
p-value (2 sided)4.76543145233599e-06
p-value (1 sided)2.38271572616799e-06
95% CI of Correlation[0.166910714603569, 0.395592314916767]
Degrees of Freedom247
Number of Observations249






Normality Tests
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.9224, p-value = 0.3824
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2207, p-value = 0.1998
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.25427, p-value = 0.728

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.0329, p-value = 3.465e-05


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

> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.9224, p-value = 0.3824
alternative hypothesis: greater

 \tabularnewline

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2207, p-value = 0.1998
alternative hypothesis: greater

 \tabularnewline

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.25427, p-value = 0.728

 \tabularnewline

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.0329, p-value = 3.465e-05

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284680&T=2

[TABLE]
[ROW][C]Normality Tests[/C][/ROW]
[ROW][C]
> jarque.x
	Jarque-Bera Normality Test
data:  x
JB = 1.9224, p-value = 0.3824
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2207, p-value = 0.1998
alternative hypothesis: greater

[/C][/ROW]
[ROW][C]
> ad.x
	Anderson-Darling normality test
data:  x
A = 0.25427, p-value = 0.728

[/C][/ROW]
[ROW][C]
> ad.y
	Anderson-Darling normality test
data:  y
A = 2.0329, p-value = 3.465e-05

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284680&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284680&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 = 1.9224, p-value = 0.3824
alternative hypothesis: greater

> jarque.y
	Jarque-Bera Normality Test
data:  y
JB = 3.2207, p-value = 0.1998
alternative hypothesis: greater

> ad.x
	Anderson-Darling normality test
data:  x
A = 0.25427, p-value = 0.728

> ad.y
	Anderson-Darling normality test
data:  y
A = 2.0329, p-value = 3.465e-05


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$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$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')
qq.plot(x,main='QQplot of variable x')
dev.off()
bitmap(file='test3.png')
qq.plot(y,main='QQplot of variable y')
dev.off()