Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_boxcoxnorm.wasp
Title produced by softwareBox-Cox Normality Plot
Date of computationMon, 12 Oct 2020 09:47:37 +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/2020/Oct/12/t1602496919kua7mdhjy2olhr5.htm/, Retrieved Fri, 29 Mar 2024 09:43:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319265, Retrieved Fri, 29 Mar 2024 09:43:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Box-Cox Normality Plot] [Transformation DV...] [2020-10-12 07:47:37] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
5
5
5
5
0




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=319265&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=319265&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319265&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 x84
maximum correlation0.870703111543209
optimal lambda1.47
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 84 \tabularnewline
maximum correlation & 0.870703111543209 \tabularnewline
optimal lambda & 1.47 \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=319265&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]84[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.870703111543209[/C][/ROW]
[ROW][C]optimal lambda[/C][C]1.47[/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=319265&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319265&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 x84
maximum correlation0.870703111543209
optimal lambda1.47
transformation formulafor all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda







Obs.OriginalTransformed
120.556.9911739392212
220.556.9911739392212
320.556.9911739392212
420.556.9911739392212
520.556.9911739392212
620.556.9911739392212
720.556.9911739392212
820.556.9911739392212
920.556.9911739392212
1020.556.9911739392212
1120.556.9911739392212
1220.556.9911739392212
1320.556.9911739392212
1420.556.9911739392212
1520.556.9911739392212
1620.556.9911739392212
1720.556.9911739392212
1820.556.9911739392212
1920.556.9911739392212
2020.556.9911739392212
2120.556.9911739392212
2220.556.9911739392212
2320.556.9911739392212
2420.556.9911739392212
2520.556.9911739392212
2620.556.9911739392212
2720.556.9911739392212
2820.556.9911739392212
2920.556.9911739392212
3020.556.9911739392212
3120.556.9911739392212
3220.556.9911739392212
3320.556.9911739392212
3420.556.9911739392212
3520.556.9911739392212
3620.556.9911739392212
3720.556.9911739392212
3820.556.9911739392212
3920.556.9911739392212
4020.556.9911739392212
4120.556.9911739392212
4220.556.9911739392212
4320.556.9911739392212
4420.556.9911739392212
4520.556.9911739392212
4620.556.9911739392212
4720.556.9911739392212
4815.537.5555349595888
4915.537.5555349595888
5015.537.5555349595888
5115.537.5555349595888
5215.537.5555349595888
5315.537.5555349595888
5415.537.5555349595888
5515.537.5555349595888
5615.537.5555349595888
5715.537.5555349595888
5815.537.5555349595888
5915.537.5555349595888
6015.537.5555349595888
6115.537.5555349595888
6215.537.5555349595888
6315.537.5555349595888
6415.537.5555349595888
6510.520.8887738029664
6610.520.8887738029664
6710.520.8887738029664
6810.520.8887738029664
6910.520.8887738029664
7010.520.8887738029664
7110.520.8887738029664
7210.520.8887738029664
7310.520.8887738029664
7410.520.8887738029664
7510.520.8887738029664
7610.520.8887738029664
7710.520.8887738029664
7810.520.8887738029664
7910.520.8887738029664
805.57.65684340418776
815.57.65684340418776
825.57.65684340418776
835.57.65684340418776
840.5-0.434705919128827

\begin{tabular}{lllllllll}
\hline
Obs. & Original & Transformed \tabularnewline
1 & 20.5 & 56.9911739392212 \tabularnewline
2 & 20.5 & 56.9911739392212 \tabularnewline
3 & 20.5 & 56.9911739392212 \tabularnewline
4 & 20.5 & 56.9911739392212 \tabularnewline
5 & 20.5 & 56.9911739392212 \tabularnewline
6 & 20.5 & 56.9911739392212 \tabularnewline
7 & 20.5 & 56.9911739392212 \tabularnewline
8 & 20.5 & 56.9911739392212 \tabularnewline
9 & 20.5 & 56.9911739392212 \tabularnewline
10 & 20.5 & 56.9911739392212 \tabularnewline
11 & 20.5 & 56.9911739392212 \tabularnewline
12 & 20.5 & 56.9911739392212 \tabularnewline
13 & 20.5 & 56.9911739392212 \tabularnewline
14 & 20.5 & 56.9911739392212 \tabularnewline
15 & 20.5 & 56.9911739392212 \tabularnewline
16 & 20.5 & 56.9911739392212 \tabularnewline
17 & 20.5 & 56.9911739392212 \tabularnewline
18 & 20.5 & 56.9911739392212 \tabularnewline
19 & 20.5 & 56.9911739392212 \tabularnewline
20 & 20.5 & 56.9911739392212 \tabularnewline
21 & 20.5 & 56.9911739392212 \tabularnewline
22 & 20.5 & 56.9911739392212 \tabularnewline
23 & 20.5 & 56.9911739392212 \tabularnewline
24 & 20.5 & 56.9911739392212 \tabularnewline
25 & 20.5 & 56.9911739392212 \tabularnewline
26 & 20.5 & 56.9911739392212 \tabularnewline
27 & 20.5 & 56.9911739392212 \tabularnewline
28 & 20.5 & 56.9911739392212 \tabularnewline
29 & 20.5 & 56.9911739392212 \tabularnewline
30 & 20.5 & 56.9911739392212 \tabularnewline
31 & 20.5 & 56.9911739392212 \tabularnewline
32 & 20.5 & 56.9911739392212 \tabularnewline
33 & 20.5 & 56.9911739392212 \tabularnewline
34 & 20.5 & 56.9911739392212 \tabularnewline
35 & 20.5 & 56.9911739392212 \tabularnewline
36 & 20.5 & 56.9911739392212 \tabularnewline
37 & 20.5 & 56.9911739392212 \tabularnewline
38 & 20.5 & 56.9911739392212 \tabularnewline
39 & 20.5 & 56.9911739392212 \tabularnewline
40 & 20.5 & 56.9911739392212 \tabularnewline
41 & 20.5 & 56.9911739392212 \tabularnewline
42 & 20.5 & 56.9911739392212 \tabularnewline
43 & 20.5 & 56.9911739392212 \tabularnewline
44 & 20.5 & 56.9911739392212 \tabularnewline
45 & 20.5 & 56.9911739392212 \tabularnewline
46 & 20.5 & 56.9911739392212 \tabularnewline
47 & 20.5 & 56.9911739392212 \tabularnewline
48 & 15.5 & 37.5555349595888 \tabularnewline
49 & 15.5 & 37.5555349595888 \tabularnewline
50 & 15.5 & 37.5555349595888 \tabularnewline
51 & 15.5 & 37.5555349595888 \tabularnewline
52 & 15.5 & 37.5555349595888 \tabularnewline
53 & 15.5 & 37.5555349595888 \tabularnewline
54 & 15.5 & 37.5555349595888 \tabularnewline
55 & 15.5 & 37.5555349595888 \tabularnewline
56 & 15.5 & 37.5555349595888 \tabularnewline
57 & 15.5 & 37.5555349595888 \tabularnewline
58 & 15.5 & 37.5555349595888 \tabularnewline
59 & 15.5 & 37.5555349595888 \tabularnewline
60 & 15.5 & 37.5555349595888 \tabularnewline
61 & 15.5 & 37.5555349595888 \tabularnewline
62 & 15.5 & 37.5555349595888 \tabularnewline
63 & 15.5 & 37.5555349595888 \tabularnewline
64 & 15.5 & 37.5555349595888 \tabularnewline
65 & 10.5 & 20.8887738029664 \tabularnewline
66 & 10.5 & 20.8887738029664 \tabularnewline
67 & 10.5 & 20.8887738029664 \tabularnewline
68 & 10.5 & 20.8887738029664 \tabularnewline
69 & 10.5 & 20.8887738029664 \tabularnewline
70 & 10.5 & 20.8887738029664 \tabularnewline
71 & 10.5 & 20.8887738029664 \tabularnewline
72 & 10.5 & 20.8887738029664 \tabularnewline
73 & 10.5 & 20.8887738029664 \tabularnewline
74 & 10.5 & 20.8887738029664 \tabularnewline
75 & 10.5 & 20.8887738029664 \tabularnewline
76 & 10.5 & 20.8887738029664 \tabularnewline
77 & 10.5 & 20.8887738029664 \tabularnewline
78 & 10.5 & 20.8887738029664 \tabularnewline
79 & 10.5 & 20.8887738029664 \tabularnewline
80 & 5.5 & 7.65684340418776 \tabularnewline
81 & 5.5 & 7.65684340418776 \tabularnewline
82 & 5.5 & 7.65684340418776 \tabularnewline
83 & 5.5 & 7.65684340418776 \tabularnewline
84 & 0.5 & -0.434705919128827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319265&T=2

[TABLE]
[ROW][C]Obs.[/C][C]Original[/C][C]Transformed[/C][/ROW]
[ROW][C]1[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]2[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]3[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]4[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]5[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]6[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]7[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]8[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]9[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]10[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]11[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]12[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]13[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]14[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]15[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]16[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]17[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]18[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]19[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]20[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]21[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]22[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]23[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]24[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]25[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]26[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]27[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]28[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]29[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]30[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]31[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]32[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]33[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]34[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]35[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]36[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]37[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]38[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]39[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]40[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]41[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]42[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]43[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]44[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]45[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]46[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]47[/C][C]20.5[/C][C]56.9911739392212[/C][/ROW]
[ROW][C]48[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]49[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]50[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]51[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]52[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]53[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]54[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]55[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]56[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]57[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]58[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]59[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]60[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]61[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]62[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]63[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]64[/C][C]15.5[/C][C]37.5555349595888[/C][/ROW]
[ROW][C]65[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]66[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]67[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]68[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]69[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]70[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]71[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]72[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]73[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]74[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]75[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]76[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]77[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]78[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]79[/C][C]10.5[/C][C]20.8887738029664[/C][/ROW]
[ROW][C]80[/C][C]5.5[/C][C]7.65684340418776[/C][/ROW]
[ROW][C]81[/C][C]5.5[/C][C]7.65684340418776[/C][/ROW]
[ROW][C]82[/C][C]5.5[/C][C]7.65684340418776[/C][/ROW]
[ROW][C]83[/C][C]5.5[/C][C]7.65684340418776[/C][/ROW]
[ROW][C]84[/C][C]0.5[/C][C]-0.434705919128827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319265&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319265&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
120.556.9911739392212
220.556.9911739392212
320.556.9911739392212
420.556.9911739392212
520.556.9911739392212
620.556.9911739392212
720.556.9911739392212
820.556.9911739392212
920.556.9911739392212
1020.556.9911739392212
1120.556.9911739392212
1220.556.9911739392212
1320.556.9911739392212
1420.556.9911739392212
1520.556.9911739392212
1620.556.9911739392212
1720.556.9911739392212
1820.556.9911739392212
1920.556.9911739392212
2020.556.9911739392212
2120.556.9911739392212
2220.556.9911739392212
2320.556.9911739392212
2420.556.9911739392212
2520.556.9911739392212
2620.556.9911739392212
2720.556.9911739392212
2820.556.9911739392212
2920.556.9911739392212
3020.556.9911739392212
3120.556.9911739392212
3220.556.9911739392212
3320.556.9911739392212
3420.556.9911739392212
3520.556.9911739392212
3620.556.9911739392212
3720.556.9911739392212
3820.556.9911739392212
3920.556.9911739392212
4020.556.9911739392212
4120.556.9911739392212
4220.556.9911739392212
4320.556.9911739392212
4420.556.9911739392212
4520.556.9911739392212
4620.556.9911739392212
4720.556.9911739392212
4815.537.5555349595888
4915.537.5555349595888
5015.537.5555349595888
5115.537.5555349595888
5215.537.5555349595888
5315.537.5555349595888
5415.537.5555349595888
5515.537.5555349595888
5615.537.5555349595888
5715.537.5555349595888
5815.537.5555349595888
5915.537.5555349595888
6015.537.5555349595888
6115.537.5555349595888
6215.537.5555349595888
6315.537.5555349595888
6415.537.5555349595888
6510.520.8887738029664
6610.520.8887738029664
6710.520.8887738029664
6810.520.8887738029664
6910.520.8887738029664
7010.520.8887738029664
7110.520.8887738029664
7210.520.8887738029664
7310.520.8887738029664
7410.520.8887738029664
7510.520.8887738029664
7610.520.8887738029664
7710.520.8887738029664
7810.520.8887738029664
7910.520.8887738029664
805.57.65684340418776
815.57.65684340418776
825.57.65684340418776
835.57.65684340418776
840.5-0.434705919128827







Maximum Likelihood Estimation of Lambda
> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x    2.1886           2       1.4363       2.9409
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 93.24308  1 < 2.22e-16
Likelihood ratio test that no transformation is needed
                          LRT df       pval
LR test, lambda = (1) 13.8563  1 0.00019733

\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    2.1886           2       1.4363       2.9409
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 93.24308  1 < 2.22e-16
Likelihood ratio test that no transformation is needed
                          LRT df       pval
LR test, lambda = (1) 13.8563  1 0.00019733
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=319265&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    2.1886           2       1.4363       2.9409
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 93.24308  1 < 2.22e-16
Likelihood ratio test that no transformation is needed
                          LRT df       pval
LR test, lambda = (1) 13.8563  1 0.00019733
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319265&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319265&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    2.1886           2       1.4363       2.9409
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 93.24308  1 < 2.22e-16
Likelihood ratio test that no transformation is needed
                          LRT df       pval
LR test, lambda = (1) 13.8563  1 0.00019733



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):
par5 <- 'Yes'
par4 <- '0,5'
par3 <- '5'
par2 <- '-5'
par1 <- 'Full Box-Cox transform'
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')