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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_boxcoxnorm.wasp
Title produced by softwareBox-Cox Normality Plot
Date of computationThu, 29 Oct 2020 16:31:15 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/Oct/29/t1603986530sce3o6c7asjk34k.htm/, Retrieved Wed, 21 Apr 2021 07:42:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319281, Retrieved Wed, 21 Apr 2021 07:42:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact22
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Box-Cox Normality Plot] [] [2020-10-29 15:31:15] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
0
0
0
2
2
2
2
3
3
3
3
3
3
3
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10




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=319281&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=319281&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319281&T=0

As an alternative you can also use a 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







Box-Cox Normality Plot
# observations x163
maximum correlation0.908001200767898
optimal lambda1.29
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 163 \tabularnewline
maximum correlation & 0.908001200767898 \tabularnewline
optimal lambda & 1.29 \tabularnewline
transformation formula & for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319281&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]163[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.908001200767898[/C][/ROW]
[ROW][C]optimal lambda[/C][C]1.29[/C][/ROW]
[ROW][C]transformation formula[/C][C]for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319281&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319281&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Box-Cox Normality Plot
# observations x163
maximum correlation0.908001200767898
optimal lambda1.29
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda







Obs.OriginalTransformed
10.5-0.458177496683031
20.5-0.458177496683031
30.5-0.458177496683031
42.51.75266552089844
52.51.75266552089844
62.51.75266552089844
72.51.75266552089844
83.53.126543874166
93.53.126543874166
103.53.126543874166
113.53.126543874166
123.53.126543874166
133.53.126543874166
143.53.126543874166
154.54.62058866685531
164.54.62058866685531
174.54.62058866685531
184.54.62058866685531
194.54.62058866685531
204.54.62058866685531
214.54.62058866685531
225.56.21482202950251
235.56.21482202950251
245.56.21482202950251
255.56.21482202950251
265.56.21482202950251
275.56.21482202950251
285.56.21482202950251
295.56.21482202950251
305.56.21482202950251
315.56.21482202950251
325.56.21482202950251
335.56.21482202950251
345.56.21482202950251
355.56.21482202950251
365.56.21482202950251
375.56.21482202950251
385.56.21482202950251
395.56.21482202950251
405.56.21482202950251
416.57.8957928953427
426.57.8957928953427
436.57.8957928953427
446.57.8957928953427
456.57.8957928953427
466.57.8957928953427
476.57.8957928953427
486.57.8957928953427
496.57.8957928953427
506.57.8957928953427
516.57.8957928953427
526.57.8957928953427
536.57.8957928953427
546.57.8957928953427
556.57.8957928953427
566.57.8957928953427
577.59.65372580456229
587.59.65372580456229
597.59.65372580456229
607.59.65372580456229
617.59.65372580456229
627.59.65372580456229
637.59.65372580456229
647.59.65372580456229
657.59.65372580456229
668.511.4811434856536
678.511.4811434856536
688.511.4811434856536
698.511.4811434856536
708.511.4811434856536
718.511.4811434856536
728.511.4811434856536
738.511.4811434856536
748.511.4811434856536
758.511.4811434856536
768.511.4811434856536
778.511.4811434856536
788.511.4811434856536
798.511.4811434856536
808.511.4811434856536
819.513.3721119830928
829.513.3721119830928
839.513.3721119830928
849.513.3721119830928
859.513.3721119830928
869.513.3721119830928
879.513.3721119830928
889.513.3721119830928
8910.515.3217892054327
9010.515.3217892054327
9110.515.3217892054327
9210.515.3217892054327
9310.515.3217892054327
9410.515.3217892054327
9510.515.3217892054327
9610.515.3217892054327
9710.515.3217892054327
9810.515.3217892054327
9910.515.3217892054327
10010.515.3217892054327
10110.515.3217892054327
10210.515.3217892054327
10310.515.3217892054327
10410.515.3217892054327
10510.515.3217892054327
10610.515.3217892054327
10710.515.3217892054327
10810.515.3217892054327
10910.515.3217892054327
11010.515.3217892054327
11110.515.3217892054327
11210.515.3217892054327
11310.515.3217892054327
11410.515.3217892054327
11510.515.3217892054327
11610.515.3217892054327
11710.515.3217892054327
11810.515.3217892054327
11910.515.3217892054327
12010.515.3217892054327
12110.515.3217892054327
12210.515.3217892054327
12310.515.3217892054327
12410.515.3217892054327
12510.515.3217892054327
12610.515.3217892054327
12710.515.3217892054327
12810.515.3217892054327
12910.515.3217892054327
13010.515.3217892054327
13110.515.3217892054327
13210.515.3217892054327
13310.515.3217892054327
13410.515.3217892054327
13510.515.3217892054327
13610.515.3217892054327
13710.515.3217892054327
13810.515.3217892054327
13910.515.3217892054327
14010.515.3217892054327
14110.515.3217892054327
14210.515.3217892054327
14310.515.3217892054327
14410.515.3217892054327
14510.515.3217892054327
14610.515.3217892054327
14710.515.3217892054327
14810.515.3217892054327
14910.515.3217892054327
15010.515.3217892054327
15110.515.3217892054327
15210.515.3217892054327
15310.515.3217892054327
15410.515.3217892054327
15510.515.3217892054327
15610.515.3217892054327
15710.515.3217892054327
15810.515.3217892054327
15910.515.3217892054327
16010.515.3217892054327
16110.515.3217892054327
16210.515.3217892054327
16310.515.3217892054327

\begin{tabular}{lllllllll}
\hline
Obs. & Original & Transformed \tabularnewline
1 & 0.5 & -0.458177496683031 \tabularnewline
2 & 0.5 & -0.458177496683031 \tabularnewline
3 & 0.5 & -0.458177496683031 \tabularnewline
4 & 2.5 & 1.75266552089844 \tabularnewline
5 & 2.5 & 1.75266552089844 \tabularnewline
6 & 2.5 & 1.75266552089844 \tabularnewline
7 & 2.5 & 1.75266552089844 \tabularnewline
8 & 3.5 & 3.126543874166 \tabularnewline
9 & 3.5 & 3.126543874166 \tabularnewline
10 & 3.5 & 3.126543874166 \tabularnewline
11 & 3.5 & 3.126543874166 \tabularnewline
12 & 3.5 & 3.126543874166 \tabularnewline
13 & 3.5 & 3.126543874166 \tabularnewline
14 & 3.5 & 3.126543874166 \tabularnewline
15 & 4.5 & 4.62058866685531 \tabularnewline
16 & 4.5 & 4.62058866685531 \tabularnewline
17 & 4.5 & 4.62058866685531 \tabularnewline
18 & 4.5 & 4.62058866685531 \tabularnewline
19 & 4.5 & 4.62058866685531 \tabularnewline
20 & 4.5 & 4.62058866685531 \tabularnewline
21 & 4.5 & 4.62058866685531 \tabularnewline
22 & 5.5 & 6.21482202950251 \tabularnewline
23 & 5.5 & 6.21482202950251 \tabularnewline
24 & 5.5 & 6.21482202950251 \tabularnewline
25 & 5.5 & 6.21482202950251 \tabularnewline
26 & 5.5 & 6.21482202950251 \tabularnewline
27 & 5.5 & 6.21482202950251 \tabularnewline
28 & 5.5 & 6.21482202950251 \tabularnewline
29 & 5.5 & 6.21482202950251 \tabularnewline
30 & 5.5 & 6.21482202950251 \tabularnewline
31 & 5.5 & 6.21482202950251 \tabularnewline
32 & 5.5 & 6.21482202950251 \tabularnewline
33 & 5.5 & 6.21482202950251 \tabularnewline
34 & 5.5 & 6.21482202950251 \tabularnewline
35 & 5.5 & 6.21482202950251 \tabularnewline
36 & 5.5 & 6.21482202950251 \tabularnewline
37 & 5.5 & 6.21482202950251 \tabularnewline
38 & 5.5 & 6.21482202950251 \tabularnewline
39 & 5.5 & 6.21482202950251 \tabularnewline
40 & 5.5 & 6.21482202950251 \tabularnewline
41 & 6.5 & 7.8957928953427 \tabularnewline
42 & 6.5 & 7.8957928953427 \tabularnewline
43 & 6.5 & 7.8957928953427 \tabularnewline
44 & 6.5 & 7.8957928953427 \tabularnewline
45 & 6.5 & 7.8957928953427 \tabularnewline
46 & 6.5 & 7.8957928953427 \tabularnewline
47 & 6.5 & 7.8957928953427 \tabularnewline
48 & 6.5 & 7.8957928953427 \tabularnewline
49 & 6.5 & 7.8957928953427 \tabularnewline
50 & 6.5 & 7.8957928953427 \tabularnewline
51 & 6.5 & 7.8957928953427 \tabularnewline
52 & 6.5 & 7.8957928953427 \tabularnewline
53 & 6.5 & 7.8957928953427 \tabularnewline
54 & 6.5 & 7.8957928953427 \tabularnewline
55 & 6.5 & 7.8957928953427 \tabularnewline
56 & 6.5 & 7.8957928953427 \tabularnewline
57 & 7.5 & 9.65372580456229 \tabularnewline
58 & 7.5 & 9.65372580456229 \tabularnewline
59 & 7.5 & 9.65372580456229 \tabularnewline
60 & 7.5 & 9.65372580456229 \tabularnewline
61 & 7.5 & 9.65372580456229 \tabularnewline
62 & 7.5 & 9.65372580456229 \tabularnewline
63 & 7.5 & 9.65372580456229 \tabularnewline
64 & 7.5 & 9.65372580456229 \tabularnewline
65 & 7.5 & 9.65372580456229 \tabularnewline
66 & 8.5 & 11.4811434856536 \tabularnewline
67 & 8.5 & 11.4811434856536 \tabularnewline
68 & 8.5 & 11.4811434856536 \tabularnewline
69 & 8.5 & 11.4811434856536 \tabularnewline
70 & 8.5 & 11.4811434856536 \tabularnewline
71 & 8.5 & 11.4811434856536 \tabularnewline
72 & 8.5 & 11.4811434856536 \tabularnewline
73 & 8.5 & 11.4811434856536 \tabularnewline
74 & 8.5 & 11.4811434856536 \tabularnewline
75 & 8.5 & 11.4811434856536 \tabularnewline
76 & 8.5 & 11.4811434856536 \tabularnewline
77 & 8.5 & 11.4811434856536 \tabularnewline
78 & 8.5 & 11.4811434856536 \tabularnewline
79 & 8.5 & 11.4811434856536 \tabularnewline
80 & 8.5 & 11.4811434856536 \tabularnewline
81 & 9.5 & 13.3721119830928 \tabularnewline
82 & 9.5 & 13.3721119830928 \tabularnewline
83 & 9.5 & 13.3721119830928 \tabularnewline
84 & 9.5 & 13.3721119830928 \tabularnewline
85 & 9.5 & 13.3721119830928 \tabularnewline
86 & 9.5 & 13.3721119830928 \tabularnewline
87 & 9.5 & 13.3721119830928 \tabularnewline
88 & 9.5 & 13.3721119830928 \tabularnewline
89 & 10.5 & 15.3217892054327 \tabularnewline
90 & 10.5 & 15.3217892054327 \tabularnewline
91 & 10.5 & 15.3217892054327 \tabularnewline
92 & 10.5 & 15.3217892054327 \tabularnewline
93 & 10.5 & 15.3217892054327 \tabularnewline
94 & 10.5 & 15.3217892054327 \tabularnewline
95 & 10.5 & 15.3217892054327 \tabularnewline
96 & 10.5 & 15.3217892054327 \tabularnewline
97 & 10.5 & 15.3217892054327 \tabularnewline
98 & 10.5 & 15.3217892054327 \tabularnewline
99 & 10.5 & 15.3217892054327 \tabularnewline
100 & 10.5 & 15.3217892054327 \tabularnewline
101 & 10.5 & 15.3217892054327 \tabularnewline
102 & 10.5 & 15.3217892054327 \tabularnewline
103 & 10.5 & 15.3217892054327 \tabularnewline
104 & 10.5 & 15.3217892054327 \tabularnewline
105 & 10.5 & 15.3217892054327 \tabularnewline
106 & 10.5 & 15.3217892054327 \tabularnewline
107 & 10.5 & 15.3217892054327 \tabularnewline
108 & 10.5 & 15.3217892054327 \tabularnewline
109 & 10.5 & 15.3217892054327 \tabularnewline
110 & 10.5 & 15.3217892054327 \tabularnewline
111 & 10.5 & 15.3217892054327 \tabularnewline
112 & 10.5 & 15.3217892054327 \tabularnewline
113 & 10.5 & 15.3217892054327 \tabularnewline
114 & 10.5 & 15.3217892054327 \tabularnewline
115 & 10.5 & 15.3217892054327 \tabularnewline
116 & 10.5 & 15.3217892054327 \tabularnewline
117 & 10.5 & 15.3217892054327 \tabularnewline
118 & 10.5 & 15.3217892054327 \tabularnewline
119 & 10.5 & 15.3217892054327 \tabularnewline
120 & 10.5 & 15.3217892054327 \tabularnewline
121 & 10.5 & 15.3217892054327 \tabularnewline
122 & 10.5 & 15.3217892054327 \tabularnewline
123 & 10.5 & 15.3217892054327 \tabularnewline
124 & 10.5 & 15.3217892054327 \tabularnewline
125 & 10.5 & 15.3217892054327 \tabularnewline
126 & 10.5 & 15.3217892054327 \tabularnewline
127 & 10.5 & 15.3217892054327 \tabularnewline
128 & 10.5 & 15.3217892054327 \tabularnewline
129 & 10.5 & 15.3217892054327 \tabularnewline
130 & 10.5 & 15.3217892054327 \tabularnewline
131 & 10.5 & 15.3217892054327 \tabularnewline
132 & 10.5 & 15.3217892054327 \tabularnewline
133 & 10.5 & 15.3217892054327 \tabularnewline
134 & 10.5 & 15.3217892054327 \tabularnewline
135 & 10.5 & 15.3217892054327 \tabularnewline
136 & 10.5 & 15.3217892054327 \tabularnewline
137 & 10.5 & 15.3217892054327 \tabularnewline
138 & 10.5 & 15.3217892054327 \tabularnewline
139 & 10.5 & 15.3217892054327 \tabularnewline
140 & 10.5 & 15.3217892054327 \tabularnewline
141 & 10.5 & 15.3217892054327 \tabularnewline
142 & 10.5 & 15.3217892054327 \tabularnewline
143 & 10.5 & 15.3217892054327 \tabularnewline
144 & 10.5 & 15.3217892054327 \tabularnewline
145 & 10.5 & 15.3217892054327 \tabularnewline
146 & 10.5 & 15.3217892054327 \tabularnewline
147 & 10.5 & 15.3217892054327 \tabularnewline
148 & 10.5 & 15.3217892054327 \tabularnewline
149 & 10.5 & 15.3217892054327 \tabularnewline
150 & 10.5 & 15.3217892054327 \tabularnewline
151 & 10.5 & 15.3217892054327 \tabularnewline
152 & 10.5 & 15.3217892054327 \tabularnewline
153 & 10.5 & 15.3217892054327 \tabularnewline
154 & 10.5 & 15.3217892054327 \tabularnewline
155 & 10.5 & 15.3217892054327 \tabularnewline
156 & 10.5 & 15.3217892054327 \tabularnewline
157 & 10.5 & 15.3217892054327 \tabularnewline
158 & 10.5 & 15.3217892054327 \tabularnewline
159 & 10.5 & 15.3217892054327 \tabularnewline
160 & 10.5 & 15.3217892054327 \tabularnewline
161 & 10.5 & 15.3217892054327 \tabularnewline
162 & 10.5 & 15.3217892054327 \tabularnewline
163 & 10.5 & 15.3217892054327 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319281&T=2

[TABLE]
[ROW][C]Obs.[/C][C]Original[/C][C]Transformed[/C][/ROW]
[ROW][C]1[/C][C]0.5[/C][C]-0.458177496683031[/C][/ROW]
[ROW][C]2[/C][C]0.5[/C][C]-0.458177496683031[/C][/ROW]
[ROW][C]3[/C][C]0.5[/C][C]-0.458177496683031[/C][/ROW]
[ROW][C]4[/C][C]2.5[/C][C]1.75266552089844[/C][/ROW]
[ROW][C]5[/C][C]2.5[/C][C]1.75266552089844[/C][/ROW]
[ROW][C]6[/C][C]2.5[/C][C]1.75266552089844[/C][/ROW]
[ROW][C]7[/C][C]2.5[/C][C]1.75266552089844[/C][/ROW]
[ROW][C]8[/C][C]3.5[/C][C]3.126543874166[/C][/ROW]
[ROW][C]9[/C][C]3.5[/C][C]3.126543874166[/C][/ROW]
[ROW][C]10[/C][C]3.5[/C][C]3.126543874166[/C][/ROW]
[ROW][C]11[/C][C]3.5[/C][C]3.126543874166[/C][/ROW]
[ROW][C]12[/C][C]3.5[/C][C]3.126543874166[/C][/ROW]
[ROW][C]13[/C][C]3.5[/C][C]3.126543874166[/C][/ROW]
[ROW][C]14[/C][C]3.5[/C][C]3.126543874166[/C][/ROW]
[ROW][C]15[/C][C]4.5[/C][C]4.62058866685531[/C][/ROW]
[ROW][C]16[/C][C]4.5[/C][C]4.62058866685531[/C][/ROW]
[ROW][C]17[/C][C]4.5[/C][C]4.62058866685531[/C][/ROW]
[ROW][C]18[/C][C]4.5[/C][C]4.62058866685531[/C][/ROW]
[ROW][C]19[/C][C]4.5[/C][C]4.62058866685531[/C][/ROW]
[ROW][C]20[/C][C]4.5[/C][C]4.62058866685531[/C][/ROW]
[ROW][C]21[/C][C]4.5[/C][C]4.62058866685531[/C][/ROW]
[ROW][C]22[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]23[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]24[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]25[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]26[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]27[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]28[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]29[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]30[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]31[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]32[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]33[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]34[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]35[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]36[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]37[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]38[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]39[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]40[/C][C]5.5[/C][C]6.21482202950251[/C][/ROW]
[ROW][C]41[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]42[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]43[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]44[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]45[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]46[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]47[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]48[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]49[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]51[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]52[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]53[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]55[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]56[/C][C]6.5[/C][C]7.8957928953427[/C][/ROW]
[ROW][C]57[/C][C]7.5[/C][C]9.65372580456229[/C][/ROW]
[ROW][C]58[/C][C]7.5[/C][C]9.65372580456229[/C][/ROW]
[ROW][C]59[/C][C]7.5[/C][C]9.65372580456229[/C][/ROW]
[ROW][C]60[/C][C]7.5[/C][C]9.65372580456229[/C][/ROW]
[ROW][C]61[/C][C]7.5[/C][C]9.65372580456229[/C][/ROW]
[ROW][C]62[/C][C]7.5[/C][C]9.65372580456229[/C][/ROW]
[ROW][C]63[/C][C]7.5[/C][C]9.65372580456229[/C][/ROW]
[ROW][C]64[/C][C]7.5[/C][C]9.65372580456229[/C][/ROW]
[ROW][C]65[/C][C]7.5[/C][C]9.65372580456229[/C][/ROW]
[ROW][C]66[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]67[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]68[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]69[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]70[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]71[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]72[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]73[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]74[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]75[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]76[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]77[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]78[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]79[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]80[/C][C]8.5[/C][C]11.4811434856536[/C][/ROW]
[ROW][C]81[/C][C]9.5[/C][C]13.3721119830928[/C][/ROW]
[ROW][C]82[/C][C]9.5[/C][C]13.3721119830928[/C][/ROW]
[ROW][C]83[/C][C]9.5[/C][C]13.3721119830928[/C][/ROW]
[ROW][C]84[/C][C]9.5[/C][C]13.3721119830928[/C][/ROW]
[ROW][C]85[/C][C]9.5[/C][C]13.3721119830928[/C][/ROW]
[ROW][C]86[/C][C]9.5[/C][C]13.3721119830928[/C][/ROW]
[ROW][C]87[/C][C]9.5[/C][C]13.3721119830928[/C][/ROW]
[ROW][C]88[/C][C]9.5[/C][C]13.3721119830928[/C][/ROW]
[ROW][C]89[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]90[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]91[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]92[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]93[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]94[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]95[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]96[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]97[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]98[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]99[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]100[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]101[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]102[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]103[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]104[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]105[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]106[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]107[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]108[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]109[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]110[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]111[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]112[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]113[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]114[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]115[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]116[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]117[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]118[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]119[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]120[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]121[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]122[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]123[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]124[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]125[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]126[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]127[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]128[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]129[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]130[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]131[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]132[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]133[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]134[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]135[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]136[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]137[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]138[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]139[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]140[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]141[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]142[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]143[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]144[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]145[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]146[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]147[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]148[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]149[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]150[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]151[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]152[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]153[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]154[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]155[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]156[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]157[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]158[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]159[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]160[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]161[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]162[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[ROW][C]163[/C][C]10.5[/C][C]15.3217892054327[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319281&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319281&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Obs.OriginalTransformed
10.5-0.458177496683031
20.5-0.458177496683031
30.5-0.458177496683031
42.51.75266552089844
52.51.75266552089844
62.51.75266552089844
72.51.75266552089844
83.53.126543874166
93.53.126543874166
103.53.126543874166
113.53.126543874166
123.53.126543874166
133.53.126543874166
143.53.126543874166
154.54.62058866685531
164.54.62058866685531
174.54.62058866685531
184.54.62058866685531
194.54.62058866685531
204.54.62058866685531
214.54.62058866685531
225.56.21482202950251
235.56.21482202950251
245.56.21482202950251
255.56.21482202950251
265.56.21482202950251
275.56.21482202950251
285.56.21482202950251
295.56.21482202950251
305.56.21482202950251
315.56.21482202950251
325.56.21482202950251
335.56.21482202950251
345.56.21482202950251
355.56.21482202950251
365.56.21482202950251
375.56.21482202950251
385.56.21482202950251
395.56.21482202950251
405.56.21482202950251
416.57.8957928953427
426.57.8957928953427
436.57.8957928953427
446.57.8957928953427
456.57.8957928953427
466.57.8957928953427
476.57.8957928953427
486.57.8957928953427
496.57.8957928953427
506.57.8957928953427
516.57.8957928953427
526.57.8957928953427
536.57.8957928953427
546.57.8957928953427
556.57.8957928953427
566.57.8957928953427
577.59.65372580456229
587.59.65372580456229
597.59.65372580456229
607.59.65372580456229
617.59.65372580456229
627.59.65372580456229
637.59.65372580456229
647.59.65372580456229
657.59.65372580456229
668.511.4811434856536
678.511.4811434856536
688.511.4811434856536
698.511.4811434856536
708.511.4811434856536
718.511.4811434856536
728.511.4811434856536
738.511.4811434856536
748.511.4811434856536
758.511.4811434856536
768.511.4811434856536
778.511.4811434856536
788.511.4811434856536
798.511.4811434856536
808.511.4811434856536
819.513.3721119830928
829.513.3721119830928
839.513.3721119830928
849.513.3721119830928
859.513.3721119830928
869.513.3721119830928
879.513.3721119830928
889.513.3721119830928
8910.515.3217892054327
9010.515.3217892054327
9110.515.3217892054327
9210.515.3217892054327
9310.515.3217892054327
9410.515.3217892054327
9510.515.3217892054327
9610.515.3217892054327
9710.515.3217892054327
9810.515.3217892054327
9910.515.3217892054327
10010.515.3217892054327
10110.515.3217892054327
10210.515.3217892054327
10310.515.3217892054327
10410.515.3217892054327
10510.515.3217892054327
10610.515.3217892054327
10710.515.3217892054327
10810.515.3217892054327
10910.515.3217892054327
11010.515.3217892054327
11110.515.3217892054327
11210.515.3217892054327
11310.515.3217892054327
11410.515.3217892054327
11510.515.3217892054327
11610.515.3217892054327
11710.515.3217892054327
11810.515.3217892054327
11910.515.3217892054327
12010.515.3217892054327
12110.515.3217892054327
12210.515.3217892054327
12310.515.3217892054327
12410.515.3217892054327
12510.515.3217892054327
12610.515.3217892054327
12710.515.3217892054327
12810.515.3217892054327
12910.515.3217892054327
13010.515.3217892054327
13110.515.3217892054327
13210.515.3217892054327
13310.515.3217892054327
13410.515.3217892054327
13510.515.3217892054327
13610.515.3217892054327
13710.515.3217892054327
13810.515.3217892054327
13910.515.3217892054327
14010.515.3217892054327
14110.515.3217892054327
14210.515.3217892054327
14310.515.3217892054327
14410.515.3217892054327
14510.515.3217892054327
14610.515.3217892054327
14710.515.3217892054327
14810.515.3217892054327
14910.515.3217892054327
15010.515.3217892054327
15110.515.3217892054327
15210.515.3217892054327
15310.515.3217892054327
15410.515.3217892054327
15510.515.3217892054327
15610.515.3217892054327
15710.515.3217892054327
15810.515.3217892054327
15910.515.3217892054327
16010.515.3217892054327
16110.515.3217892054327
16210.515.3217892054327
16310.515.3217892054327







Maximum Likelihood Estimation of Lambda
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x     1.769           2       1.3221       2.2159
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 137.5186  1 < 2.22e-16
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 14.90063  1 0.00011333

\begin{tabular}{lllllllll}
\hline
Maximum Likelihood Estimation of Lambda \tabularnewline
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x     1.769           2       1.3221       2.2159
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 137.5186  1 < 2.22e-16
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 14.90063  1 0.00011333
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=319281&T=3

[TABLE]
[ROW][C]Maximum Likelihood Estimation of Lambda[/C][/ROW]
[ROW][C]
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x     1.769           2       1.3221       2.2159
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 137.5186  1 < 2.22e-16
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 14.90063  1 0.00011333
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319281&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319281&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Maximum Likelihood Estimation of Lambda
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x     1.769           2       1.3221       2.2159
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 137.5186  1 < 2.22e-16
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 14.90063  1 0.00011333



Parameters (Session):
par1 = Full Box-Cox transform ; par2 = -5 ; par3 = 5 ; par4 = 0.5 ; par5 = Yes ;
Parameters (R input):
par1 = Full Box-Cox transform ; par2 = -5 ; par3 = 5 ; par4 = 0.5 ; par5 = Yes ;
R code (references can be found in the software module):
library(car)
par2 <- abs(as.numeric(par2)*100)
par3 <- as.numeric(par3)*100
if(par4=='') par4 <- 0
par4 <- as.numeric(par4)
numlam <- par2 + par3 + 1
x <- x + par4
n <- length(x)
c <- array(NA,dim=c(numlam))
l <- array(NA,dim=c(numlam))
mx <- -1
mxli <- -999
for (i in 1:numlam)
{
l[i] <- (i-par2-1)/100
if (l[i] != 0)
{
if (par1 == 'Full Box-Cox transform') x1 <- (x^l[i] - 1) / l[i]
if (par1 == 'Simple Box-Cox transform') x1 <- x^l[i]
} else {
x1 <- log(x)
}
c[i] <- cor(qnorm(ppoints(x), mean=0, sd=1),sort(x1))
if (mx < c[i])
{
mx <- c[i]
mxli <- l[i]
x1.best <- x1
}
}
print(c)
print(mx)
print(mxli)
print(x1.best)
if (mxli != 0)
{
if (par1 == 'Full Box-Cox transform') x1 <- (x^mxli - 1) / mxli
if (par1 == 'Simple Box-Cox transform') x1 <- x^mxli
} else {
x1 <- log(x)
}
mypT <- powerTransform(x)
summary(mypT)
bitmap(file='test1.png')
plot(l,c,main='Box-Cox Normality Plot', xlab='Lambda',ylab='correlation')
mtext(paste('Optimal Lambda =',mxli))
grid()
dev.off()
bitmap(file='test2.png')
hist(x,main='Histogram of Original Data',xlab='X',ylab='frequency')
grid()
dev.off()
bitmap(file='test3.png')
hist(x1,main='Histogram of Transformed Data', xlab='X',ylab='frequency')
grid()
dev.off()
bitmap(file='test4.png')
qqPlot(x)
grid()
mtext('Original Data')
dev.off()
bitmap(file='test5.png')
qqPlot(x1)
grid()
mtext('Transformed Data')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Box-Cox Normality Plot',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'# observations x',header=TRUE)
a<-table.element(a,n)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'maximum correlation',header=TRUE)
a<-table.element(a,mx)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'optimal lambda',header=TRUE)
a<-table.element(a,mxli)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'transformation formula',header=TRUE)
if (par1 == 'Full Box-Cox transform') {
a<-table.element(a,'for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda')
} else {
a<-table.element(a,'for all lambda <> 0 : T(Y) = Y^lambda')
}
a<-table.row.end(a)
if(mx<0) {
a<-table.row.start(a)
a<-table.element(a,'Warning: maximum correlation is negative! The Box-Cox transformation must not be used.',2)
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
if(par5=='Yes') {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Obs.',header=T)
a<-table.element(a,'Original',header=T)
a<-table.element(a,'Transformed',header=T)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i)
a<-table.element(a,x[i])
a<-table.element(a,x1.best[i])
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,'Maximum Likelihood Estimation of Lambda',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,paste('
',RC.texteval('summary(mypT)'),'
',sep=''))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')