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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_boxcoxnorm.wasp

Title produced by software

Box-Cox Normality Plot

Date of computation

Fri, 11 Dec 2015 21:57:36 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/11/t1449871067loyxsuof5r4tyhh.htm/, Retrieved Thu, 16 May 2024 15:31:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286040, Retrieved Thu, 16 May 2024 15:31:37 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Two-Way ANOVA] [] [2015-11-16 17:14:42] [32b17a345b130fdf5cc88718ed94a974]
- RMPD  [Exponential Smoothing] [] [2015-12-11 21:11:55] [0e2e3dbefef1c665f3752d42409bac25]
- RM D    [(Partial) Autocorrelation Function] [] [2015-12-11 21:47:51] [0e2e3dbefef1c665f3752d42409bac25]
- RM D        [Box-Cox Normality Plot] [] [2015-12-11 21:57:36] [074449c5cdcdb4dafd7dd3585d12ae02] [Current]

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Dataseries X:

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Histogram

Boxplots

1.4
1.5
1.8
1.8
1.8
1.7
1.5
1.1
1.3
1.6
1.9
1.9
2
2.2
2.2
2
2.3
2.6
3.2
3.2
3.1
2.8
2.3
1.9
1.9
2
2
1.8
1.6
1.4
0.2
0.3
0.4
0.7
1
1.1
0.8
0.8
1
1.1
1
0.8
1.6
1.5
1.6
1.6
1.6
1.9
2
1.9
2
2.1
2.3
2.3
2.6
2.6
2.7
2.6
2.6
2.4
2.5
2.5
2.5
2.4
2.1
2.1
2.3
2.3
2.3
2.9
2.8
2.9
3
3
2.9
2.6
2.8
2.9
3.1
2.8
2.4
1.6
1.5
1.7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'George Udny Yule' @ yule.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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286040&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286040&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286040&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 Output	view raw output of R engine
Computing time	5 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Box-Cox Normality Plot
# observations x	84
maximum correlation	0.992613173536299
optimal lambda	1.37
transformation formula	for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 84 \tabularnewline
maximum correlation & 0.992613173536299 \tabularnewline
optimal lambda & 1.37 \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=286040&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]0.992613173536299[/C][/ROW]
[ROW][C]optimal lambda[/C][C]1.37[/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=286040&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286040&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 x	84
maximum correlation	0.992613173536299
optimal lambda	1.37
transformation formula	for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

Obs.	Original	Transformed
1	1.4	0.427449977073897
2	1.5	0.542182380945475
3	1.8	0.903135337074741
4	1.8	0.903135337074741
5	1.8	0.903135337074741
6	1.7	0.780133866993087
7	1.5	0.542182380945475
8	1.1	0.101812654591103
9	1.3	0.31571211889867
10	1.6	0.65978179747346
11	1.9	1.02869241874922
12	1.9	1.02869241874922
13	2	1.15671946078466
14	2.2	1.41987520549572
15	2.2	1.41987520549572
16	2	1.15671946078466
17	2.3	1.55486445994355
18	2.6	1.97274236183518
19	3.2	2.8620612079205
20	3.2	2.8620612079205
21	3.1	2.70917417456483
22	2.8	2.26155183643942
23	2.3	1.55486445994355
24	1.9	1.02869241874922
25	1.9	1.02869241874922
26	2	1.15671946078466
27	2	1.15671946078466
28	1.8	0.903135337074741
29	1.6	0.65978179747346
30	1.4	0.427449977073897
31	0.2	-0.649446533048873
32	0.3	-0.589666452695153
33	0.4	-0.521908669882174
34	0.7	-0.282147980962377
35	1	0
36	1.1	0.101812654591103
37	0.8	-0.192260832928292
38	0.8	-0.192260832928292
39	1	0
40	1.1	0.101812654591103
41	1	0
42	0.8	-0.192260832928292
43	1.6	0.65978179747346
44	1.5	0.542182380945475
45	1.6	0.65978179747346
46	1.6	0.65978179747346
47	1.6	0.65978179747346
48	1.9	1.02869241874922
49	2	1.15671946078466
50	1.9	1.02869241874922
51	2	1.15671946078466
52	2.1	1.28713786745724
53	2.3	1.55486445994355
54	2.3	1.55486445994355
55	2.6	1.97274236183518
56	2.6	1.97274236183518
57	2.7	2.11615749031873
58	2.6	1.97274236183518
59	2.6	1.97274236183518
60	2.4	1.69204340864528
61	2.5	1.83135409224422
62	2.5	1.83135409224422
63	2.5	1.83135409224422
64	2.4	1.69204340864528
65	2.1	1.28713786745724
66	2.1	1.28713786745724
67	2.3	1.55486445994355
68	2.3	1.55486445994355
69	2.3	1.55486445994355
70	2.9	2.40888055272437
71	2.8	2.26155183643942
72	2.9	2.40888055272437
73	3	2.55810133025798
74	3	2.55810133025798
75	2.9	2.40888055272437
76	2.6	1.97274236183518
77	2.8	2.26155183643942
78	2.9	2.40888055272437
79	3.1	2.70917417456483
80	2.8	2.26155183643942
81	2.4	1.69204340864528
82	1.6	0.65978179747346
83	1.5	0.542182380945475
84	1.7	0.780133866993087

\begin{tabular}{lllllllll}
\hline
Obs. & Original & Transformed \tabularnewline
1 & 1.4 & 0.427449977073897 \tabularnewline
2 & 1.5 & 0.542182380945475 \tabularnewline
3 & 1.8 & 0.903135337074741 \tabularnewline
4 & 1.8 & 0.903135337074741 \tabularnewline
5 & 1.8 & 0.903135337074741 \tabularnewline
6 & 1.7 & 0.780133866993087 \tabularnewline
7 & 1.5 & 0.542182380945475 \tabularnewline
8 & 1.1 & 0.101812654591103 \tabularnewline
9 & 1.3 & 0.31571211889867 \tabularnewline
10 & 1.6 & 0.65978179747346 \tabularnewline
11 & 1.9 & 1.02869241874922 \tabularnewline
12 & 1.9 & 1.02869241874922 \tabularnewline
13 & 2 & 1.15671946078466 \tabularnewline
14 & 2.2 & 1.41987520549572 \tabularnewline
15 & 2.2 & 1.41987520549572 \tabularnewline
16 & 2 & 1.15671946078466 \tabularnewline
17 & 2.3 & 1.55486445994355 \tabularnewline
18 & 2.6 & 1.97274236183518 \tabularnewline
19 & 3.2 & 2.8620612079205 \tabularnewline
20 & 3.2 & 2.8620612079205 \tabularnewline
21 & 3.1 & 2.70917417456483 \tabularnewline
22 & 2.8 & 2.26155183643942 \tabularnewline
23 & 2.3 & 1.55486445994355 \tabularnewline
24 & 1.9 & 1.02869241874922 \tabularnewline
25 & 1.9 & 1.02869241874922 \tabularnewline
26 & 2 & 1.15671946078466 \tabularnewline
27 & 2 & 1.15671946078466 \tabularnewline
28 & 1.8 & 0.903135337074741 \tabularnewline
29 & 1.6 & 0.65978179747346 \tabularnewline
30 & 1.4 & 0.427449977073897 \tabularnewline
31 & 0.2 & -0.649446533048873 \tabularnewline
32 & 0.3 & -0.589666452695153 \tabularnewline
33 & 0.4 & -0.521908669882174 \tabularnewline
34 & 0.7 & -0.282147980962377 \tabularnewline
35 & 1 & 0 \tabularnewline
36 & 1.1 & 0.101812654591103 \tabularnewline
37 & 0.8 & -0.192260832928292 \tabularnewline
38 & 0.8 & -0.192260832928292 \tabularnewline
39 & 1 & 0 \tabularnewline
40 & 1.1 & 0.101812654591103 \tabularnewline
41 & 1 & 0 \tabularnewline
42 & 0.8 & -0.192260832928292 \tabularnewline
43 & 1.6 & 0.65978179747346 \tabularnewline
44 & 1.5 & 0.542182380945475 \tabularnewline
45 & 1.6 & 0.65978179747346 \tabularnewline
46 & 1.6 & 0.65978179747346 \tabularnewline
47 & 1.6 & 0.65978179747346 \tabularnewline
48 & 1.9 & 1.02869241874922 \tabularnewline
49 & 2 & 1.15671946078466 \tabularnewline
50 & 1.9 & 1.02869241874922 \tabularnewline
51 & 2 & 1.15671946078466 \tabularnewline
52 & 2.1 & 1.28713786745724 \tabularnewline
53 & 2.3 & 1.55486445994355 \tabularnewline
54 & 2.3 & 1.55486445994355 \tabularnewline
55 & 2.6 & 1.97274236183518 \tabularnewline
56 & 2.6 & 1.97274236183518 \tabularnewline
57 & 2.7 & 2.11615749031873 \tabularnewline
58 & 2.6 & 1.97274236183518 \tabularnewline
59 & 2.6 & 1.97274236183518 \tabularnewline
60 & 2.4 & 1.69204340864528 \tabularnewline
61 & 2.5 & 1.83135409224422 \tabularnewline
62 & 2.5 & 1.83135409224422 \tabularnewline
63 & 2.5 & 1.83135409224422 \tabularnewline
64 & 2.4 & 1.69204340864528 \tabularnewline
65 & 2.1 & 1.28713786745724 \tabularnewline
66 & 2.1 & 1.28713786745724 \tabularnewline
67 & 2.3 & 1.55486445994355 \tabularnewline
68 & 2.3 & 1.55486445994355 \tabularnewline
69 & 2.3 & 1.55486445994355 \tabularnewline
70 & 2.9 & 2.40888055272437 \tabularnewline
71 & 2.8 & 2.26155183643942 \tabularnewline
72 & 2.9 & 2.40888055272437 \tabularnewline
73 & 3 & 2.55810133025798 \tabularnewline
74 & 3 & 2.55810133025798 \tabularnewline
75 & 2.9 & 2.40888055272437 \tabularnewline
76 & 2.6 & 1.97274236183518 \tabularnewline
77 & 2.8 & 2.26155183643942 \tabularnewline
78 & 2.9 & 2.40888055272437 \tabularnewline
79 & 3.1 & 2.70917417456483 \tabularnewline
80 & 2.8 & 2.26155183643942 \tabularnewline
81 & 2.4 & 1.69204340864528 \tabularnewline
82 & 1.6 & 0.65978179747346 \tabularnewline
83 & 1.5 & 0.542182380945475 \tabularnewline
84 & 1.7 & 0.780133866993087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286040&T=2

[TABLE]
[ROW][C]Obs.[/C][C]Original[/C][C]Transformed[/C][/ROW]
[ROW][C]1[/C][C]1.4[/C][C]0.427449977073897[/C][/ROW]
[ROW][C]2[/C][C]1.5[/C][C]0.542182380945475[/C][/ROW]
[ROW][C]3[/C][C]1.8[/C][C]0.903135337074741[/C][/ROW]
[ROW][C]4[/C][C]1.8[/C][C]0.903135337074741[/C][/ROW]
[ROW][C]5[/C][C]1.8[/C][C]0.903135337074741[/C][/ROW]
[ROW][C]6[/C][C]1.7[/C][C]0.780133866993087[/C][/ROW]
[ROW][C]7[/C][C]1.5[/C][C]0.542182380945475[/C][/ROW]
[ROW][C]8[/C][C]1.1[/C][C]0.101812654591103[/C][/ROW]
[ROW][C]9[/C][C]1.3[/C][C]0.31571211889867[/C][/ROW]
[ROW][C]10[/C][C]1.6[/C][C]0.65978179747346[/C][/ROW]
[ROW][C]11[/C][C]1.9[/C][C]1.02869241874922[/C][/ROW]
[ROW][C]12[/C][C]1.9[/C][C]1.02869241874922[/C][/ROW]
[ROW][C]13[/C][C]2[/C][C]1.15671946078466[/C][/ROW]
[ROW][C]14[/C][C]2.2[/C][C]1.41987520549572[/C][/ROW]
[ROW][C]15[/C][C]2.2[/C][C]1.41987520549572[/C][/ROW]
[ROW][C]16[/C][C]2[/C][C]1.15671946078466[/C][/ROW]
[ROW][C]17[/C][C]2.3[/C][C]1.55486445994355[/C][/ROW]
[ROW][C]18[/C][C]2.6[/C][C]1.97274236183518[/C][/ROW]
[ROW][C]19[/C][C]3.2[/C][C]2.8620612079205[/C][/ROW]
[ROW][C]20[/C][C]3.2[/C][C]2.8620612079205[/C][/ROW]
[ROW][C]21[/C][C]3.1[/C][C]2.70917417456483[/C][/ROW]
[ROW][C]22[/C][C]2.8[/C][C]2.26155183643942[/C][/ROW]
[ROW][C]23[/C][C]2.3[/C][C]1.55486445994355[/C][/ROW]
[ROW][C]24[/C][C]1.9[/C][C]1.02869241874922[/C][/ROW]
[ROW][C]25[/C][C]1.9[/C][C]1.02869241874922[/C][/ROW]
[ROW][C]26[/C][C]2[/C][C]1.15671946078466[/C][/ROW]
[ROW][C]27[/C][C]2[/C][C]1.15671946078466[/C][/ROW]
[ROW][C]28[/C][C]1.8[/C][C]0.903135337074741[/C][/ROW]
[ROW][C]29[/C][C]1.6[/C][C]0.65978179747346[/C][/ROW]
[ROW][C]30[/C][C]1.4[/C][C]0.427449977073897[/C][/ROW]
[ROW][C]31[/C][C]0.2[/C][C]-0.649446533048873[/C][/ROW]
[ROW][C]32[/C][C]0.3[/C][C]-0.589666452695153[/C][/ROW]
[ROW][C]33[/C][C]0.4[/C][C]-0.521908669882174[/C][/ROW]
[ROW][C]34[/C][C]0.7[/C][C]-0.282147980962377[/C][/ROW]
[ROW][C]35[/C][C]1[/C][C]0[/C][/ROW]
[ROW][C]36[/C][C]1.1[/C][C]0.101812654591103[/C][/ROW]
[ROW][C]37[/C][C]0.8[/C][C]-0.192260832928292[/C][/ROW]
[ROW][C]38[/C][C]0.8[/C][C]-0.192260832928292[/C][/ROW]
[ROW][C]39[/C][C]1[/C][C]0[/C][/ROW]
[ROW][C]40[/C][C]1.1[/C][C]0.101812654591103[/C][/ROW]
[ROW][C]41[/C][C]1[/C][C]0[/C][/ROW]
[ROW][C]42[/C][C]0.8[/C][C]-0.192260832928292[/C][/ROW]
[ROW][C]43[/C][C]1.6[/C][C]0.65978179747346[/C][/ROW]
[ROW][C]44[/C][C]1.5[/C][C]0.542182380945475[/C][/ROW]
[ROW][C]45[/C][C]1.6[/C][C]0.65978179747346[/C][/ROW]
[ROW][C]46[/C][C]1.6[/C][C]0.65978179747346[/C][/ROW]
[ROW][C]47[/C][C]1.6[/C][C]0.65978179747346[/C][/ROW]
[ROW][C]48[/C][C]1.9[/C][C]1.02869241874922[/C][/ROW]
[ROW][C]49[/C][C]2[/C][C]1.15671946078466[/C][/ROW]
[ROW][C]50[/C][C]1.9[/C][C]1.02869241874922[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]1.15671946078466[/C][/ROW]
[ROW][C]52[/C][C]2.1[/C][C]1.28713786745724[/C][/ROW]
[ROW][C]53[/C][C]2.3[/C][C]1.55486445994355[/C][/ROW]
[ROW][C]54[/C][C]2.3[/C][C]1.55486445994355[/C][/ROW]
[ROW][C]55[/C][C]2.6[/C][C]1.97274236183518[/C][/ROW]
[ROW][C]56[/C][C]2.6[/C][C]1.97274236183518[/C][/ROW]
[ROW][C]57[/C][C]2.7[/C][C]2.11615749031873[/C][/ROW]
[ROW][C]58[/C][C]2.6[/C][C]1.97274236183518[/C][/ROW]
[ROW][C]59[/C][C]2.6[/C][C]1.97274236183518[/C][/ROW]
[ROW][C]60[/C][C]2.4[/C][C]1.69204340864528[/C][/ROW]
[ROW][C]61[/C][C]2.5[/C][C]1.83135409224422[/C][/ROW]
[ROW][C]62[/C][C]2.5[/C][C]1.83135409224422[/C][/ROW]
[ROW][C]63[/C][C]2.5[/C][C]1.83135409224422[/C][/ROW]
[ROW][C]64[/C][C]2.4[/C][C]1.69204340864528[/C][/ROW]
[ROW][C]65[/C][C]2.1[/C][C]1.28713786745724[/C][/ROW]
[ROW][C]66[/C][C]2.1[/C][C]1.28713786745724[/C][/ROW]
[ROW][C]67[/C][C]2.3[/C][C]1.55486445994355[/C][/ROW]
[ROW][C]68[/C][C]2.3[/C][C]1.55486445994355[/C][/ROW]
[ROW][C]69[/C][C]2.3[/C][C]1.55486445994355[/C][/ROW]
[ROW][C]70[/C][C]2.9[/C][C]2.40888055272437[/C][/ROW]
[ROW][C]71[/C][C]2.8[/C][C]2.26155183643942[/C][/ROW]
[ROW][C]72[/C][C]2.9[/C][C]2.40888055272437[/C][/ROW]
[ROW][C]73[/C][C]3[/C][C]2.55810133025798[/C][/ROW]
[ROW][C]74[/C][C]3[/C][C]2.55810133025798[/C][/ROW]
[ROW][C]75[/C][C]2.9[/C][C]2.40888055272437[/C][/ROW]
[ROW][C]76[/C][C]2.6[/C][C]1.97274236183518[/C][/ROW]
[ROW][C]77[/C][C]2.8[/C][C]2.26155183643942[/C][/ROW]
[ROW][C]78[/C][C]2.9[/C][C]2.40888055272437[/C][/ROW]
[ROW][C]79[/C][C]3.1[/C][C]2.70917417456483[/C][/ROW]
[ROW][C]80[/C][C]2.8[/C][C]2.26155183643942[/C][/ROW]
[ROW][C]81[/C][C]2.4[/C][C]1.69204340864528[/C][/ROW]
[ROW][C]82[/C][C]1.6[/C][C]0.65978179747346[/C][/ROW]
[ROW][C]83[/C][C]1.5[/C][C]0.542182380945475[/C][/ROW]
[ROW][C]84[/C][C]1.7[/C][C]0.780133866993087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286040&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286040&T=2

As an alternative you can also use a QR Code:

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

Obs.	Original	Transformed
1	1.4	0.427449977073897
2	1.5	0.542182380945475
3	1.8	0.903135337074741
4	1.8	0.903135337074741
5	1.8	0.903135337074741
6	1.7	0.780133866993087
7	1.5	0.542182380945475
8	1.1	0.101812654591103
9	1.3	0.31571211889867
10	1.6	0.65978179747346
11	1.9	1.02869241874922
12	1.9	1.02869241874922
13	2	1.15671946078466
14	2.2	1.41987520549572
15	2.2	1.41987520549572
16	2	1.15671946078466
17	2.3	1.55486445994355
18	2.6	1.97274236183518
19	3.2	2.8620612079205
20	3.2	2.8620612079205
21	3.1	2.70917417456483
22	2.8	2.26155183643942
23	2.3	1.55486445994355
24	1.9	1.02869241874922
25	1.9	1.02869241874922
26	2	1.15671946078466
27	2	1.15671946078466
28	1.8	0.903135337074741
29	1.6	0.65978179747346
30	1.4	0.427449977073897
31	0.2	-0.649446533048873
32	0.3	-0.589666452695153
33	0.4	-0.521908669882174
34	0.7	-0.282147980962377
35	1	0
36	1.1	0.101812654591103
37	0.8	-0.192260832928292
38	0.8	-0.192260832928292
39	1	0
40	1.1	0.101812654591103
41	1	0
42	0.8	-0.192260832928292
43	1.6	0.65978179747346
44	1.5	0.542182380945475
45	1.6	0.65978179747346
46	1.6	0.65978179747346
47	1.6	0.65978179747346
48	1.9	1.02869241874922
49	2	1.15671946078466
50	1.9	1.02869241874922
51	2	1.15671946078466
52	2.1	1.28713786745724
53	2.3	1.55486445994355
54	2.3	1.55486445994355
55	2.6	1.97274236183518
56	2.6	1.97274236183518
57	2.7	2.11615749031873
58	2.6	1.97274236183518
59	2.6	1.97274236183518
60	2.4	1.69204340864528
61	2.5	1.83135409224422
62	2.5	1.83135409224422
63	2.5	1.83135409224422
64	2.4	1.69204340864528
65	2.1	1.28713786745724
66	2.1	1.28713786745724
67	2.3	1.55486445994355
68	2.3	1.55486445994355
69	2.3	1.55486445994355
70	2.9	2.40888055272437
71	2.8	2.26155183643942
72	2.9	2.40888055272437
73	3	2.55810133025798
74	3	2.55810133025798
75	2.9	2.40888055272437
76	2.6	1.97274236183518
77	2.8	2.26155183643942
78	2.9	2.40888055272437
79	3.1	2.70917417456483
80	2.8	2.26155183643942
81	2.4	1.69204340864528
82	1.6	0.65978179747346
83	1.5	0.542182380945475
84	1.7	0.780133866993087

Maximum Likelihood Estimation of Lambda

> summary(mypT)
bcPower Transformation to Normality 
  Est.Power Std.Err. Wald Lower Bound Wald Upper Bound
x    1.2483   0.2299           0.7977           1.6988
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 43.569629  1 4.091394e-11
LR test, lambda = (1)  1.251589  1 2.632493e-01

\begin{tabular}{lllllllll}
\hline
Maximum Likelihood Estimation of Lambda \tabularnewline
> summary(mypT)
bcPower Transformation to Normality 
  Est.Power Std.Err. Wald Lower Bound Wald Upper Bound
x    1.2483   0.2299           0.7977           1.6988
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 43.569629  1 4.091394e-11
LR test, lambda = (1)  1.251589  1 2.632493e-01
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286040&T=3

[TABLE]
[ROW][C]Maximum Likelihood Estimation of Lambda[/C][/ROW]
[ROW][C]> summary(mypT)
bcPower Transformation to Normality 
  Est.Power Std.Err. Wald Lower Bound Wald Upper Bound
x    1.2483   0.2299           0.7977           1.6988
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 43.569629  1 4.091394e-11
LR test, lambda = (1)  1.251589  1 2.632493e-01
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286040&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286040&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 Std.Err. Wald Lower Bound Wald Upper Bound
x    1.2483   0.2299           0.7977           1.6988
Likelihood ratio tests about transformation parameters
                            LRT df         pval
LR test, lambda = (0) 43.569629  1 4.091394e-11
LR test, lambda = (1)  1.251589  1 2.632493e-01

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = Full Box-Cox transform ; par2 = -8 ; par3 = 8 ; par4 = 0 ; 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
}
}
c
mx
mxli
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code