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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationThu, 19 Aug 2010 16:35:49 +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/2010/Aug/19/t1282236252ekozph3cbm9ro4h.htm/, Retrieved Fri, 03 May 2024 05:41:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79331, Retrieved Fri, 03 May 2024 05:41:54 +0000
QR Codes:

Original text written by user:Data from Greatschools.net on schools in Santa Clara County, northern California. Question: What is the correlation between a school student population's median income and performance in science standardized achievement tests? How much variability is there across schools in science achievement, if you control for SES?
IsPrivate?No (this computation is public)
User-defined keywordspublic schools, science, achievement, ses, income, standardized testing
Estimated Impact115

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Pearson Correlation] [Median income and...] [2010-08-19 16:35:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum
2010-10-24 13:01:53 [] [reply] 
Great example!

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
47.071
47.071
47.071
47.071
47.071
50.322
50.322
50.322
50.322
50.322
50.322
50.322
50.322
50.322
50.322
50.322
50.322
50.322
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
54.567
55.321
55.321
55.709
57.513
57.513
57.513
57.513
57.513
58.807
58.807
58.807
58.807
58.807
58.807
58.807
58.807
58.807
58.807
58.807
58.807
58.807
58.807
58.807
58.807
64.119
66.905
66.905
66.905
66.905
66.905
66.905
66.905
66.905
66.905
66.905
66.905
66.905
66.905
67.491
67.491
67.491
74.264
74.264
74.264
74.264
74.264
74.264
74.264
74.264
74.264
74.264
74.264
74.264
74.911
78.287
78.613
78.613
78.613
78.613
78.745
78.745
78.745
78.745
78.745
78.745
80.335
80.335
80.335
80.335
80.335
80.335
80.335
80.335
80.335
80.335
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
80.616
82.559
83.934
83.934
83.934
83.934
83.934
85.508
85.508
85.508
85.97
85.97
85.97
85.97
85.97
85.97
85.97
85.97
85.97
85.97
85.97
85.97
86.291
86.291
86.291
86.291
86.921
86.921
86.921
89.543
89.543
89.543
89.543
89.543
89.543
89.543
89.543
89.543
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
93.342
96.505
96.505
96.505
96.505
96.505
97.527
97.527
97.527
97.527
97.527
97.527
97.527
97.527
97.527
102.115
102.422
102.422
102.422
102.422
102.422
102.422
102.422
102.422
102.422
102.422
102.422
102.422
105.76
105.76
105.76
105.76
105.76
105.76
105.76
105.76
105.76
105.76
105.76
105.76
112.731
112.731
112.731
112.731
112.731
113.496
118.657
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
120.012
125.604
125.604
137.855
137.855
137.855
137.855
137.855
137.855
137.855
137.855
137.855
137.855
137.855
151.481
151.481
151.481
151.481
151.481
151.481
151.481
151.481
186.848
Dataseries Y:
Download CSV
Histogram 
44
43
38
18
13
68
61
60
48
47
37
36
33
29
27
26
26
20
78
57
53
48
47
47
45
44
42
38
35
35
35
32
32
31
30
30
29
29
29
28
25
24
20
33
17
16
49
46
39
27
10
56
55
48
44
42
39
37
34
34
34
32
31
28
24
23
17
60
74
73
70
70
68
66
58
57
54
49
48
43
33
52
41
36
61
60
51
49
42
41
36
30
24
23
20
17
35
17
80
47
47
46
74
70
53
40
34
29
84
67
66
61
57
56
51
40
35
31
97
89
84
83
81
79
77
74
70
65
62
61
58
56
55
54
52
35
93
76
69
56
51
41
63
45
19
69
57
56
56
52
47
40
39
35
31
26
22
59
49
38
24
56
49
29
81
72
59
53
48
47
40
39
37
95
95
94
91
91
89
87
85
85
81
80
80
80
74
70
69
69
68
67
64
63
60
58
57
57
57
52
52
49
49
47
41
39
75
73
73
70
64
97
77
69
68
68
59
52
46
44
81
81
76
71
69
67
65
60
56
53
53
47
45
92
91
90
90
87
86
85
84
82
82
81
70
93
86
85
85
84
55
42
100
99
99
96
96
95
95
94
94
93
93
91
91
91
89
89
86
82
82
81
80
69
63
62
57
89
66
93
92
85
85
83
66
55
55
52
47
24
100
98
96
95
93
93
92
91
57

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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79331&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79331&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79331&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' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean87.21105016722458.4983277591973
Biased Variance668.54865585367516.938960414313
Biased Standard Deviation25.856307854248522.7362917032288
Covariance382.690256795583
Correlation0.648793273430934
Determination0.420932711649226
T-Test14.6933237235825
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom297
Number of Observations299

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 87.211050167224 & 58.4983277591973 \tabularnewline
Biased Variance & 668.54865585367 & 516.938960414313 \tabularnewline
Biased Standard Deviation & 25.8563078542485 & 22.7362917032288 \tabularnewline
Covariance & 382.690256795583 \tabularnewline
Correlation & 0.648793273430934 \tabularnewline
Determination & 0.420932711649226 \tabularnewline
T-Test & 14.6933237235825 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 297 \tabularnewline
Number of Observations & 299 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79331&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]87.211050167224[/C][C]58.4983277591973[/C][/ROW]
[ROW][C]Biased Variance[/C][C]668.54865585367[/C][C]516.938960414313[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]25.8563078542485[/C][C]22.7362917032288[/C][/ROW]
[ROW][C]Covariance[/C][C]382.690256795583[/C][/ROW]
[ROW][C]Correlation[/C][C]0.648793273430934[/C][/ROW]
[ROW][C]Determination[/C][C]0.420932711649226[/C][/ROW]
[ROW][C]T-Test[/C][C]14.6933237235825[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]297[/C][/ROW]
[ROW][C]Number of Observations[/C][C]299[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79331&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79331&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
Mean87.21105016722458.4983277591973
Biased Variance668.54865585367516.938960414313
Biased Standard Deviation25.856307854248522.7362917032288
Covariance382.690256795583
Correlation0.648793273430934
Determination0.420932711649226
T-Test14.6933237235825
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom297
Number of Observations299


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
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)
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')
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,'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')