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Author's title

Author

*Unverified author*

R Software Module

rwasp_boxcoxnorm.wasp

Title produced by software

Box-Cox Normality Plot

Date of computation

Thu, 09 Jul 2020 11:54:27 +0200

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/2020/Jul/10/t1594362824pprmqxbrb8bak6r.htm/, Retrieved Sat, 20 Apr 2024 11:32:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319194, Retrieved Sat, 20 Apr 2024 11:32:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

117

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

-       [Box-Cox Normality Plot] [] [2020-07-09 09:54:27] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

3,9
4,4
4,8
5,1
5,1
5,2
5,2
5,3
5,4
5,5
5,6
5,7
5,7
5,8
5,9
5,9
5,9
5,9
6,0
6,1
6,1
6,1
6,1
6,2
6,2
6,2
6,2
6,3
6,3
6,3
6,3
6,4
6,4
6,4
6,4
6,4
6,5
6,5
6,5
6,5
6,7
6,7
6,7
6,7
6,7
6,7
6,8
6,9
6,9
7,0
7,0
7,0
7,0
7,1
7,2
7,2
7,2
7,2
7,2
7,3
7,4
7,4
7,5
7,5
7,6
7,7
7,7
7,7
7,7
7,8
7,8
7,8
7,9
7,9
7,9
8,0
8,0
8,0
8,1
8,2
8,3
8,4
8,4
8,5
8,5
8,5
8,6
8,6
8,6
8,7
8,7
8,7
8,8
8,9
8,9
9,0
9,0
9,0
9,1
9,2
9,2
9,2
9,2
9,2
9,2
9,2
9,3
9,3
9,3
9,4
9,4
9,4
9,5
9,6
9,6
9,7
9,7
9,7
9,9
10,0
10,0
10,0
10,1
10,3
10,3
10,3
10,4
10,4
10,5
10,5
10,5
10,7
10,7
10,8
11,0
11,0
11,1
11,2
11,3
11,3
11,4
11,4
11,4
11,5
11,6
11,6
11,6
11,9
11,9
11,9
11,9
12,0
12,1
12,1
12,2
12,3
12,4
12,5
12,5
12,6
12,7
13,0
13,0
13,3
13,4
13,4
13,4
13,8
13,9
14,0
14,6
14,8
15,0
15,1
15,3
15,4
15,5
15,5
15,6
15,7
15,8
16,3
16,4
16,5
17,1
17,7
18,5
18,7
18,7
19,5
19,5
22,7
23,1
25,5
28,0
32,5
32,6
36,4
39,0

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319194&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319194&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319194&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Box-Cox Normality Plot
# observations x	199
maximum correlation	0.997876153103535
optimal lambda	-0.69
transformation formula	for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

\begin{tabular}{lllllllll}
\hline
Box-Cox Normality Plot \tabularnewline
# observations x & 199 \tabularnewline
maximum correlation & 0.997876153103535 \tabularnewline
optimal lambda & -0.69 \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=319194&T=1

[TABLE]
[ROW][C]Box-Cox Normality Plot[/C][/ROW]
[ROW][C]# observations x[/C][C]199[/C][/ROW]
[ROW][C]maximum correlation[/C][C]0.997876153103535[/C][/ROW]
[ROW][C]optimal lambda[/C][C]-0.69[/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=319194&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319194&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	199
maximum correlation	0.997876153103535
optimal lambda	-0.69
transformation formula	for all lambda <> 0 : T(Y) = (Y^lambda - 1) / lambda

Obs.	Original	Transformed
1	3.9	0.882623486970309
2	4.4	0.92787832092391
3	4.8	0.958260706134117
4	5.1	0.9783766663759
5	5.1	0.9783766663759
6	5.2	0.984643913232501
7	5.2	0.984643913232501
8	5.3	0.990710726461036
9	5.4	0.996587119705227
10	5.5	1.00228243285757
11	5.6	1.00780538864538
12	5.7	1.0131641435525
13	5.7	1.0131641435525
14	5.8	1.01836633373166
15	5.9	1.02341911647723
16	5.9	1.02341911647723
17	5.9	1.02341911647723
18	5.9	1.02341911647723
19	6	1.02832920775448
20	6.1	1.03310291621917
21	6.1	1.03310291621917
22	6.1	1.03310291621917
23	6.1	1.03310291621917
24	6.2	1.03774617410694
25	6.2	1.03774617410694
26	6.2	1.03774617410694
27	6.2	1.03774617410694
28	6.3	1.04226456532598
29	6.3	1.04226456532598
30	6.3	1.04226456532598
31	6.3	1.04226456532598
32	6.4	1.04666335104575
33	6.4	1.04666335104575
34	6.4	1.04666335104575
35	6.4	1.04666335104575
36	6.4	1.04666335104575
37	6.5	1.05094749304037
38	6.5	1.05094749304037
39	6.5	1.05094749304037
40	6.5	1.05094749304037
41	6.7	1.0591903221148
42	6.7	1.0591903221148
43	6.7	1.0591903221148
44	6.7	1.0591903221148
45	6.7	1.0591903221148
46	6.7	1.0591903221148
47	6.8	1.06315761880257
48	6.9	1.06702752525234
49	6.9	1.06702752525234
50	7	1.07080379241206
51	7	1.07080379241206
52	7	1.07080379241206
53	7	1.07080379241206
54	7.1	1.07448997585471
55	7.2	1.07808944853263
56	7.2	1.07808944853263
57	7.2	1.07808944853263
58	7.2	1.07808944853263
59	7.2	1.07808944853263
60	7.3	1.08160541253556
61	7.4	1.08504090994265
62	7.4	1.08504090994265
63	7.5	1.08839883284951
64	7.5	1.08839883284951
65	7.6	1.09168193264285
66	7.7	1.0948928285885
67	7.7	1.0948928285885
68	7.7	1.0948928285885
69	7.7	1.0948928285885
70	7.8	1.09803401579162
71	7.8	1.09803401579162
72	7.8	1.09803401579162
73	7.9	1.10110787258238
74	7.9	1.10110787258238
75	7.9	1.10110787258238
76	8	1.10411666737539
77	8	1.10411666737539
78	8	1.10411666737539
79	8.1	1.10706256504626
80	8.2	1.10994763286494
81	8.3	1.11277384602138
82	8.4	1.11554309277634
83	8.4	1.11554309277634
84	8.5	1.1182571792667
85	8.5	1.1182571792667
86	8.5	1.1182571792667
87	8.6	1.1209178339922
88	8.6	1.1209178339922
89	8.6	1.1209178339922
90	8.7	1.12352671200832
91	8.7	1.12352671200832
92	8.7	1.12352671200832
93	8.8	1.12608539884749
94	8.9	1.12859541418917
95	8.9	1.12859541418917
96	9	1.13105821529751
97	9	1.13105821529751
98	9	1.13105821529751
99	9.1	1.1334752002437
100	9.2	1.13584771092866
101	9.2	1.13584771092866
102	9.2	1.13584771092866
103	9.2	1.13584771092866
104	9.2	1.13584771092866
105	9.2	1.13584771092866
106	9.2	1.13584771092866
107	9.3	1.13817703592049
108	9.3	1.13817703592049
109	9.3	1.13817703592049
110	9.4	1.14046441311988
111	9.4	1.14046441311988
112	9.4	1.14046441311988
113	9.5	1.1427110322656
114	9.6	1.14491803729129
115	9.6	1.14491803729129
116	9.7	1.1470865285437
117	9.7	1.1470865285437
118	9.7	1.1470865285437
119	9.9	1.15131216559674
120	10	1.15337131236674
121	10	1.15337131236674
122	10	1.15337131236674
123	10.1	1.15539595091101
124	10.3	1.1593453164731
125	10.3	1.1593453164731
126	10.3	1.1593453164731
127	10.4	1.16127176978577
128	10.4	1.16127176978577
129	10.5	1.16316717033628
130	10.5	1.16316717033628
131	10.5	1.16316717033628
132	10.7	1.16686794268634
133	10.7	1.16686794268634
134	10.8	1.16867481229887
135	11	1.17220507408313
136	11	1.17220507408313
137	11.1	1.17392981746649
138	11.2	1.17562849949142
139	11.3	1.17730174141348
140	11.3	1.17730174141348
141	11.4	1.17895014435163
142	11.4	1.17895014435163
143	11.4	1.17895014435163
144	11.5	1.18057429011052
145	11.6	1.18217474196246
146	11.6	1.18217474196246
147	11.6	1.18217474196246
148	11.9	1.18683930418653
149	11.9	1.18683930418653
150	11.9	1.18683930418653
151	11.9	1.18683930418653
152	12	1.18835026778227
153	12.1	1.18984010066748
154	12.1	1.18984010066748
155	12.2	1.19130926935274
156	12.3	1.19275822633551
157	12.4	1.19418741063088
158	12.5	1.19559724827799
159	12.5	1.19559724827799
160	12.6	1.19698815282367
161	12.7	1.19836052578432
162	13	1.20237029899644
163	13	1.20237029899644
164	13.3	1.20622667659008
165	13.4	1.20747964833286
166	13.4	1.20747964833286
167	13.4	1.20747964833286
168	13.8	1.21233756887066
169	13.9	1.21351505058515
170	14	1.21467830260812
171	14.6	1.22137372842758
172	14.8	1.22350323472193
173	15	1.22558465616364
174	15.1	1.22660787127897
175	15.3	1.22862033738538
176	15.4	1.22960998442415
177	15.5	1.23058883028516
178	15.5	1.23058883028516
179	15.6	1.23155706140547
180	15.7	1.23251485983593
181	15.8	1.23346240337148
182	16.3	1.23805223800049
183	16.4	1.23894176281543
184	16.5	1.23982216814964
185	17.1	1.24492115051123
186	17.7	1.24972645433962
187	18.5	1.25572124387725
188	18.7	1.25715199017738
189	18.7	1.25715199017738
190	19.5	1.26262577784434
191	19.5	1.26262577784434
192	22.7	1.28120425251733
193	23.1	1.28321780579988
194	25.5	1.29416593843619
195	28	1.30385947166563
196	32.5	1.31807005881621
197	32.6	1.31834789550753
198	36.4	1.32793900448384
199	39	1.33357989878712

\begin{tabular}{lllllllll}
\hline
Obs. & Original & Transformed \tabularnewline
1 & 3.9 & 0.882623486970309 \tabularnewline
2 & 4.4 & 0.92787832092391 \tabularnewline
3 & 4.8 & 0.958260706134117 \tabularnewline
4 & 5.1 & 0.9783766663759 \tabularnewline
5 & 5.1 & 0.9783766663759 \tabularnewline
6 & 5.2 & 0.984643913232501 \tabularnewline
7 & 5.2 & 0.984643913232501 \tabularnewline
8 & 5.3 & 0.990710726461036 \tabularnewline
9 & 5.4 & 0.996587119705227 \tabularnewline
10 & 5.5 & 1.00228243285757 \tabularnewline
11 & 5.6 & 1.00780538864538 \tabularnewline
12 & 5.7 & 1.0131641435525 \tabularnewline
13 & 5.7 & 1.0131641435525 \tabularnewline
14 & 5.8 & 1.01836633373166 \tabularnewline
15 & 5.9 & 1.02341911647723 \tabularnewline
16 & 5.9 & 1.02341911647723 \tabularnewline
17 & 5.9 & 1.02341911647723 \tabularnewline
18 & 5.9 & 1.02341911647723 \tabularnewline
19 & 6 & 1.02832920775448 \tabularnewline
20 & 6.1 & 1.03310291621917 \tabularnewline
21 & 6.1 & 1.03310291621917 \tabularnewline
22 & 6.1 & 1.03310291621917 \tabularnewline
23 & 6.1 & 1.03310291621917 \tabularnewline
24 & 6.2 & 1.03774617410694 \tabularnewline
25 & 6.2 & 1.03774617410694 \tabularnewline
26 & 6.2 & 1.03774617410694 \tabularnewline
27 & 6.2 & 1.03774617410694 \tabularnewline
28 & 6.3 & 1.04226456532598 \tabularnewline
29 & 6.3 & 1.04226456532598 \tabularnewline
30 & 6.3 & 1.04226456532598 \tabularnewline
31 & 6.3 & 1.04226456532598 \tabularnewline
32 & 6.4 & 1.04666335104575 \tabularnewline
33 & 6.4 & 1.04666335104575 \tabularnewline
34 & 6.4 & 1.04666335104575 \tabularnewline
35 & 6.4 & 1.04666335104575 \tabularnewline
36 & 6.4 & 1.04666335104575 \tabularnewline
37 & 6.5 & 1.05094749304037 \tabularnewline
38 & 6.5 & 1.05094749304037 \tabularnewline
39 & 6.5 & 1.05094749304037 \tabularnewline
40 & 6.5 & 1.05094749304037 \tabularnewline
41 & 6.7 & 1.0591903221148 \tabularnewline
42 & 6.7 & 1.0591903221148 \tabularnewline
43 & 6.7 & 1.0591903221148 \tabularnewline
44 & 6.7 & 1.0591903221148 \tabularnewline
45 & 6.7 & 1.0591903221148 \tabularnewline
46 & 6.7 & 1.0591903221148 \tabularnewline
47 & 6.8 & 1.06315761880257 \tabularnewline
48 & 6.9 & 1.06702752525234 \tabularnewline
49 & 6.9 & 1.06702752525234 \tabularnewline
50 & 7 & 1.07080379241206 \tabularnewline
51 & 7 & 1.07080379241206 \tabularnewline
52 & 7 & 1.07080379241206 \tabularnewline
53 & 7 & 1.07080379241206 \tabularnewline
54 & 7.1 & 1.07448997585471 \tabularnewline
55 & 7.2 & 1.07808944853263 \tabularnewline
56 & 7.2 & 1.07808944853263 \tabularnewline
57 & 7.2 & 1.07808944853263 \tabularnewline
58 & 7.2 & 1.07808944853263 \tabularnewline
59 & 7.2 & 1.07808944853263 \tabularnewline
60 & 7.3 & 1.08160541253556 \tabularnewline
61 & 7.4 & 1.08504090994265 \tabularnewline
62 & 7.4 & 1.08504090994265 \tabularnewline
63 & 7.5 & 1.08839883284951 \tabularnewline
64 & 7.5 & 1.08839883284951 \tabularnewline
65 & 7.6 & 1.09168193264285 \tabularnewline
66 & 7.7 & 1.0948928285885 \tabularnewline
67 & 7.7 & 1.0948928285885 \tabularnewline
68 & 7.7 & 1.0948928285885 \tabularnewline
69 & 7.7 & 1.0948928285885 \tabularnewline
70 & 7.8 & 1.09803401579162 \tabularnewline
71 & 7.8 & 1.09803401579162 \tabularnewline
72 & 7.8 & 1.09803401579162 \tabularnewline
73 & 7.9 & 1.10110787258238 \tabularnewline
74 & 7.9 & 1.10110787258238 \tabularnewline
75 & 7.9 & 1.10110787258238 \tabularnewline
76 & 8 & 1.10411666737539 \tabularnewline
77 & 8 & 1.10411666737539 \tabularnewline
78 & 8 & 1.10411666737539 \tabularnewline
79 & 8.1 & 1.10706256504626 \tabularnewline
80 & 8.2 & 1.10994763286494 \tabularnewline
81 & 8.3 & 1.11277384602138 \tabularnewline
82 & 8.4 & 1.11554309277634 \tabularnewline
83 & 8.4 & 1.11554309277634 \tabularnewline
84 & 8.5 & 1.1182571792667 \tabularnewline
85 & 8.5 & 1.1182571792667 \tabularnewline
86 & 8.5 & 1.1182571792667 \tabularnewline
87 & 8.6 & 1.1209178339922 \tabularnewline
88 & 8.6 & 1.1209178339922 \tabularnewline
89 & 8.6 & 1.1209178339922 \tabularnewline
90 & 8.7 & 1.12352671200832 \tabularnewline
91 & 8.7 & 1.12352671200832 \tabularnewline
92 & 8.7 & 1.12352671200832 \tabularnewline
93 & 8.8 & 1.12608539884749 \tabularnewline
94 & 8.9 & 1.12859541418917 \tabularnewline
95 & 8.9 & 1.12859541418917 \tabularnewline
96 & 9 & 1.13105821529751 \tabularnewline
97 & 9 & 1.13105821529751 \tabularnewline
98 & 9 & 1.13105821529751 \tabularnewline
99 & 9.1 & 1.1334752002437 \tabularnewline
100 & 9.2 & 1.13584771092866 \tabularnewline
101 & 9.2 & 1.13584771092866 \tabularnewline
102 & 9.2 & 1.13584771092866 \tabularnewline
103 & 9.2 & 1.13584771092866 \tabularnewline
104 & 9.2 & 1.13584771092866 \tabularnewline
105 & 9.2 & 1.13584771092866 \tabularnewline
106 & 9.2 & 1.13584771092866 \tabularnewline
107 & 9.3 & 1.13817703592049 \tabularnewline
108 & 9.3 & 1.13817703592049 \tabularnewline
109 & 9.3 & 1.13817703592049 \tabularnewline
110 & 9.4 & 1.14046441311988 \tabularnewline
111 & 9.4 & 1.14046441311988 \tabularnewline
112 & 9.4 & 1.14046441311988 \tabularnewline
113 & 9.5 & 1.1427110322656 \tabularnewline
114 & 9.6 & 1.14491803729129 \tabularnewline
115 & 9.6 & 1.14491803729129 \tabularnewline
116 & 9.7 & 1.1470865285437 \tabularnewline
117 & 9.7 & 1.1470865285437 \tabularnewline
118 & 9.7 & 1.1470865285437 \tabularnewline
119 & 9.9 & 1.15131216559674 \tabularnewline
120 & 10 & 1.15337131236674 \tabularnewline
121 & 10 & 1.15337131236674 \tabularnewline
122 & 10 & 1.15337131236674 \tabularnewline
123 & 10.1 & 1.15539595091101 \tabularnewline
124 & 10.3 & 1.1593453164731 \tabularnewline
125 & 10.3 & 1.1593453164731 \tabularnewline
126 & 10.3 & 1.1593453164731 \tabularnewline
127 & 10.4 & 1.16127176978577 \tabularnewline
128 & 10.4 & 1.16127176978577 \tabularnewline
129 & 10.5 & 1.16316717033628 \tabularnewline
130 & 10.5 & 1.16316717033628 \tabularnewline
131 & 10.5 & 1.16316717033628 \tabularnewline
132 & 10.7 & 1.16686794268634 \tabularnewline
133 & 10.7 & 1.16686794268634 \tabularnewline
134 & 10.8 & 1.16867481229887 \tabularnewline
135 & 11 & 1.17220507408313 \tabularnewline
136 & 11 & 1.17220507408313 \tabularnewline
137 & 11.1 & 1.17392981746649 \tabularnewline
138 & 11.2 & 1.17562849949142 \tabularnewline
139 & 11.3 & 1.17730174141348 \tabularnewline
140 & 11.3 & 1.17730174141348 \tabularnewline
141 & 11.4 & 1.17895014435163 \tabularnewline
142 & 11.4 & 1.17895014435163 \tabularnewline
143 & 11.4 & 1.17895014435163 \tabularnewline
144 & 11.5 & 1.18057429011052 \tabularnewline
145 & 11.6 & 1.18217474196246 \tabularnewline
146 & 11.6 & 1.18217474196246 \tabularnewline
147 & 11.6 & 1.18217474196246 \tabularnewline
148 & 11.9 & 1.18683930418653 \tabularnewline
149 & 11.9 & 1.18683930418653 \tabularnewline
150 & 11.9 & 1.18683930418653 \tabularnewline
151 & 11.9 & 1.18683930418653 \tabularnewline
152 & 12 & 1.18835026778227 \tabularnewline
153 & 12.1 & 1.18984010066748 \tabularnewline
154 & 12.1 & 1.18984010066748 \tabularnewline
155 & 12.2 & 1.19130926935274 \tabularnewline
156 & 12.3 & 1.19275822633551 \tabularnewline
157 & 12.4 & 1.19418741063088 \tabularnewline
158 & 12.5 & 1.19559724827799 \tabularnewline
159 & 12.5 & 1.19559724827799 \tabularnewline
160 & 12.6 & 1.19698815282367 \tabularnewline
161 & 12.7 & 1.19836052578432 \tabularnewline
162 & 13 & 1.20237029899644 \tabularnewline
163 & 13 & 1.20237029899644 \tabularnewline
164 & 13.3 & 1.20622667659008 \tabularnewline
165 & 13.4 & 1.20747964833286 \tabularnewline
166 & 13.4 & 1.20747964833286 \tabularnewline
167 & 13.4 & 1.20747964833286 \tabularnewline
168 & 13.8 & 1.21233756887066 \tabularnewline
169 & 13.9 & 1.21351505058515 \tabularnewline
170 & 14 & 1.21467830260812 \tabularnewline
171 & 14.6 & 1.22137372842758 \tabularnewline
172 & 14.8 & 1.22350323472193 \tabularnewline
173 & 15 & 1.22558465616364 \tabularnewline
174 & 15.1 & 1.22660787127897 \tabularnewline
175 & 15.3 & 1.22862033738538 \tabularnewline
176 & 15.4 & 1.22960998442415 \tabularnewline
177 & 15.5 & 1.23058883028516 \tabularnewline
178 & 15.5 & 1.23058883028516 \tabularnewline
179 & 15.6 & 1.23155706140547 \tabularnewline
180 & 15.7 & 1.23251485983593 \tabularnewline
181 & 15.8 & 1.23346240337148 \tabularnewline
182 & 16.3 & 1.23805223800049 \tabularnewline
183 & 16.4 & 1.23894176281543 \tabularnewline
184 & 16.5 & 1.23982216814964 \tabularnewline
185 & 17.1 & 1.24492115051123 \tabularnewline
186 & 17.7 & 1.24972645433962 \tabularnewline
187 & 18.5 & 1.25572124387725 \tabularnewline
188 & 18.7 & 1.25715199017738 \tabularnewline
189 & 18.7 & 1.25715199017738 \tabularnewline
190 & 19.5 & 1.26262577784434 \tabularnewline
191 & 19.5 & 1.26262577784434 \tabularnewline
192 & 22.7 & 1.28120425251733 \tabularnewline
193 & 23.1 & 1.28321780579988 \tabularnewline
194 & 25.5 & 1.29416593843619 \tabularnewline
195 & 28 & 1.30385947166563 \tabularnewline
196 & 32.5 & 1.31807005881621 \tabularnewline
197 & 32.6 & 1.31834789550753 \tabularnewline
198 & 36.4 & 1.32793900448384 \tabularnewline
199 & 39 & 1.33357989878712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319194&T=2

[TABLE]
[ROW][C]Obs.[/C][C]Original[/C][C]Transformed[/C][/ROW]
[ROW][C]1[/C][C]3.9[/C][C]0.882623486970309[/C][/ROW]
[ROW][C]2[/C][C]4.4[/C][C]0.92787832092391[/C][/ROW]
[ROW][C]3[/C][C]4.8[/C][C]0.958260706134117[/C][/ROW]
[ROW][C]4[/C][C]5.1[/C][C]0.9783766663759[/C][/ROW]
[ROW][C]5[/C][C]5.1[/C][C]0.9783766663759[/C][/ROW]
[ROW][C]6[/C][C]5.2[/C][C]0.984643913232501[/C][/ROW]
[ROW][C]7[/C][C]5.2[/C][C]0.984643913232501[/C][/ROW]
[ROW][C]8[/C][C]5.3[/C][C]0.990710726461036[/C][/ROW]
[ROW][C]9[/C][C]5.4[/C][C]0.996587119705227[/C][/ROW]
[ROW][C]10[/C][C]5.5[/C][C]1.00228243285757[/C][/ROW]
[ROW][C]11[/C][C]5.6[/C][C]1.00780538864538[/C][/ROW]
[ROW][C]12[/C][C]5.7[/C][C]1.0131641435525[/C][/ROW]
[ROW][C]13[/C][C]5.7[/C][C]1.0131641435525[/C][/ROW]
[ROW][C]14[/C][C]5.8[/C][C]1.01836633373166[/C][/ROW]
[ROW][C]15[/C][C]5.9[/C][C]1.02341911647723[/C][/ROW]
[ROW][C]16[/C][C]5.9[/C][C]1.02341911647723[/C][/ROW]
[ROW][C]17[/C][C]5.9[/C][C]1.02341911647723[/C][/ROW]
[ROW][C]18[/C][C]5.9[/C][C]1.02341911647723[/C][/ROW]
[ROW][C]19[/C][C]6[/C][C]1.02832920775448[/C][/ROW]
[ROW][C]20[/C][C]6.1[/C][C]1.03310291621917[/C][/ROW]
[ROW][C]21[/C][C]6.1[/C][C]1.03310291621917[/C][/ROW]
[ROW][C]22[/C][C]6.1[/C][C]1.03310291621917[/C][/ROW]
[ROW][C]23[/C][C]6.1[/C][C]1.03310291621917[/C][/ROW]
[ROW][C]24[/C][C]6.2[/C][C]1.03774617410694[/C][/ROW]
[ROW][C]25[/C][C]6.2[/C][C]1.03774617410694[/C][/ROW]
[ROW][C]26[/C][C]6.2[/C][C]1.03774617410694[/C][/ROW]
[ROW][C]27[/C][C]6.2[/C][C]1.03774617410694[/C][/ROW]
[ROW][C]28[/C][C]6.3[/C][C]1.04226456532598[/C][/ROW]
[ROW][C]29[/C][C]6.3[/C][C]1.04226456532598[/C][/ROW]
[ROW][C]30[/C][C]6.3[/C][C]1.04226456532598[/C][/ROW]
[ROW][C]31[/C][C]6.3[/C][C]1.04226456532598[/C][/ROW]
[ROW][C]32[/C][C]6.4[/C][C]1.04666335104575[/C][/ROW]
[ROW][C]33[/C][C]6.4[/C][C]1.04666335104575[/C][/ROW]
[ROW][C]34[/C][C]6.4[/C][C]1.04666335104575[/C][/ROW]
[ROW][C]35[/C][C]6.4[/C][C]1.04666335104575[/C][/ROW]
[ROW][C]36[/C][C]6.4[/C][C]1.04666335104575[/C][/ROW]
[ROW][C]37[/C][C]6.5[/C][C]1.05094749304037[/C][/ROW]
[ROW][C]38[/C][C]6.5[/C][C]1.05094749304037[/C][/ROW]
[ROW][C]39[/C][C]6.5[/C][C]1.05094749304037[/C][/ROW]
[ROW][C]40[/C][C]6.5[/C][C]1.05094749304037[/C][/ROW]
[ROW][C]41[/C][C]6.7[/C][C]1.0591903221148[/C][/ROW]
[ROW][C]42[/C][C]6.7[/C][C]1.0591903221148[/C][/ROW]
[ROW][C]43[/C][C]6.7[/C][C]1.0591903221148[/C][/ROW]
[ROW][C]44[/C][C]6.7[/C][C]1.0591903221148[/C][/ROW]
[ROW][C]45[/C][C]6.7[/C][C]1.0591903221148[/C][/ROW]
[ROW][C]46[/C][C]6.7[/C][C]1.0591903221148[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]1.06315761880257[/C][/ROW]
[ROW][C]48[/C][C]6.9[/C][C]1.06702752525234[/C][/ROW]
[ROW][C]49[/C][C]6.9[/C][C]1.06702752525234[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]1.07080379241206[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]1.07080379241206[/C][/ROW]
[ROW][C]52[/C][C]7[/C][C]1.07080379241206[/C][/ROW]
[ROW][C]53[/C][C]7[/C][C]1.07080379241206[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]1.07448997585471[/C][/ROW]
[ROW][C]55[/C][C]7.2[/C][C]1.07808944853263[/C][/ROW]
[ROW][C]56[/C][C]7.2[/C][C]1.07808944853263[/C][/ROW]
[ROW][C]57[/C][C]7.2[/C][C]1.07808944853263[/C][/ROW]
[ROW][C]58[/C][C]7.2[/C][C]1.07808944853263[/C][/ROW]
[ROW][C]59[/C][C]7.2[/C][C]1.07808944853263[/C][/ROW]
[ROW][C]60[/C][C]7.3[/C][C]1.08160541253556[/C][/ROW]
[ROW][C]61[/C][C]7.4[/C][C]1.08504090994265[/C][/ROW]
[ROW][C]62[/C][C]7.4[/C][C]1.08504090994265[/C][/ROW]
[ROW][C]63[/C][C]7.5[/C][C]1.08839883284951[/C][/ROW]
[ROW][C]64[/C][C]7.5[/C][C]1.08839883284951[/C][/ROW]
[ROW][C]65[/C][C]7.6[/C][C]1.09168193264285[/C][/ROW]
[ROW][C]66[/C][C]7.7[/C][C]1.0948928285885[/C][/ROW]
[ROW][C]67[/C][C]7.7[/C][C]1.0948928285885[/C][/ROW]
[ROW][C]68[/C][C]7.7[/C][C]1.0948928285885[/C][/ROW]
[ROW][C]69[/C][C]7.7[/C][C]1.0948928285885[/C][/ROW]
[ROW][C]70[/C][C]7.8[/C][C]1.09803401579162[/C][/ROW]
[ROW][C]71[/C][C]7.8[/C][C]1.09803401579162[/C][/ROW]
[ROW][C]72[/C][C]7.8[/C][C]1.09803401579162[/C][/ROW]
[ROW][C]73[/C][C]7.9[/C][C]1.10110787258238[/C][/ROW]
[ROW][C]74[/C][C]7.9[/C][C]1.10110787258238[/C][/ROW]
[ROW][C]75[/C][C]7.9[/C][C]1.10110787258238[/C][/ROW]
[ROW][C]76[/C][C]8[/C][C]1.10411666737539[/C][/ROW]
[ROW][C]77[/C][C]8[/C][C]1.10411666737539[/C][/ROW]
[ROW][C]78[/C][C]8[/C][C]1.10411666737539[/C][/ROW]
[ROW][C]79[/C][C]8.1[/C][C]1.10706256504626[/C][/ROW]
[ROW][C]80[/C][C]8.2[/C][C]1.10994763286494[/C][/ROW]
[ROW][C]81[/C][C]8.3[/C][C]1.11277384602138[/C][/ROW]
[ROW][C]82[/C][C]8.4[/C][C]1.11554309277634[/C][/ROW]
[ROW][C]83[/C][C]8.4[/C][C]1.11554309277634[/C][/ROW]
[ROW][C]84[/C][C]8.5[/C][C]1.1182571792667[/C][/ROW]
[ROW][C]85[/C][C]8.5[/C][C]1.1182571792667[/C][/ROW]
[ROW][C]86[/C][C]8.5[/C][C]1.1182571792667[/C][/ROW]
[ROW][C]87[/C][C]8.6[/C][C]1.1209178339922[/C][/ROW]
[ROW][C]88[/C][C]8.6[/C][C]1.1209178339922[/C][/ROW]
[ROW][C]89[/C][C]8.6[/C][C]1.1209178339922[/C][/ROW]
[ROW][C]90[/C][C]8.7[/C][C]1.12352671200832[/C][/ROW]
[ROW][C]91[/C][C]8.7[/C][C]1.12352671200832[/C][/ROW]
[ROW][C]92[/C][C]8.7[/C][C]1.12352671200832[/C][/ROW]
[ROW][C]93[/C][C]8.8[/C][C]1.12608539884749[/C][/ROW]
[ROW][C]94[/C][C]8.9[/C][C]1.12859541418917[/C][/ROW]
[ROW][C]95[/C][C]8.9[/C][C]1.12859541418917[/C][/ROW]
[ROW][C]96[/C][C]9[/C][C]1.13105821529751[/C][/ROW]
[ROW][C]97[/C][C]9[/C][C]1.13105821529751[/C][/ROW]
[ROW][C]98[/C][C]9[/C][C]1.13105821529751[/C][/ROW]
[ROW][C]99[/C][C]9.1[/C][C]1.1334752002437[/C][/ROW]
[ROW][C]100[/C][C]9.2[/C][C]1.13584771092866[/C][/ROW]
[ROW][C]101[/C][C]9.2[/C][C]1.13584771092866[/C][/ROW]
[ROW][C]102[/C][C]9.2[/C][C]1.13584771092866[/C][/ROW]
[ROW][C]103[/C][C]9.2[/C][C]1.13584771092866[/C][/ROW]
[ROW][C]104[/C][C]9.2[/C][C]1.13584771092866[/C][/ROW]
[ROW][C]105[/C][C]9.2[/C][C]1.13584771092866[/C][/ROW]
[ROW][C]106[/C][C]9.2[/C][C]1.13584771092866[/C][/ROW]
[ROW][C]107[/C][C]9.3[/C][C]1.13817703592049[/C][/ROW]
[ROW][C]108[/C][C]9.3[/C][C]1.13817703592049[/C][/ROW]
[ROW][C]109[/C][C]9.3[/C][C]1.13817703592049[/C][/ROW]
[ROW][C]110[/C][C]9.4[/C][C]1.14046441311988[/C][/ROW]
[ROW][C]111[/C][C]9.4[/C][C]1.14046441311988[/C][/ROW]
[ROW][C]112[/C][C]9.4[/C][C]1.14046441311988[/C][/ROW]
[ROW][C]113[/C][C]9.5[/C][C]1.1427110322656[/C][/ROW]
[ROW][C]114[/C][C]9.6[/C][C]1.14491803729129[/C][/ROW]
[ROW][C]115[/C][C]9.6[/C][C]1.14491803729129[/C][/ROW]
[ROW][C]116[/C][C]9.7[/C][C]1.1470865285437[/C][/ROW]
[ROW][C]117[/C][C]9.7[/C][C]1.1470865285437[/C][/ROW]
[ROW][C]118[/C][C]9.7[/C][C]1.1470865285437[/C][/ROW]
[ROW][C]119[/C][C]9.9[/C][C]1.15131216559674[/C][/ROW]
[ROW][C]120[/C][C]10[/C][C]1.15337131236674[/C][/ROW]
[ROW][C]121[/C][C]10[/C][C]1.15337131236674[/C][/ROW]
[ROW][C]122[/C][C]10[/C][C]1.15337131236674[/C][/ROW]
[ROW][C]123[/C][C]10.1[/C][C]1.15539595091101[/C][/ROW]
[ROW][C]124[/C][C]10.3[/C][C]1.1593453164731[/C][/ROW]
[ROW][C]125[/C][C]10.3[/C][C]1.1593453164731[/C][/ROW]
[ROW][C]126[/C][C]10.3[/C][C]1.1593453164731[/C][/ROW]
[ROW][C]127[/C][C]10.4[/C][C]1.16127176978577[/C][/ROW]
[ROW][C]128[/C][C]10.4[/C][C]1.16127176978577[/C][/ROW]
[ROW][C]129[/C][C]10.5[/C][C]1.16316717033628[/C][/ROW]
[ROW][C]130[/C][C]10.5[/C][C]1.16316717033628[/C][/ROW]
[ROW][C]131[/C][C]10.5[/C][C]1.16316717033628[/C][/ROW]
[ROW][C]132[/C][C]10.7[/C][C]1.16686794268634[/C][/ROW]
[ROW][C]133[/C][C]10.7[/C][C]1.16686794268634[/C][/ROW]
[ROW][C]134[/C][C]10.8[/C][C]1.16867481229887[/C][/ROW]
[ROW][C]135[/C][C]11[/C][C]1.17220507408313[/C][/ROW]
[ROW][C]136[/C][C]11[/C][C]1.17220507408313[/C][/ROW]
[ROW][C]137[/C][C]11.1[/C][C]1.17392981746649[/C][/ROW]
[ROW][C]138[/C][C]11.2[/C][C]1.17562849949142[/C][/ROW]
[ROW][C]139[/C][C]11.3[/C][C]1.17730174141348[/C][/ROW]
[ROW][C]140[/C][C]11.3[/C][C]1.17730174141348[/C][/ROW]
[ROW][C]141[/C][C]11.4[/C][C]1.17895014435163[/C][/ROW]
[ROW][C]142[/C][C]11.4[/C][C]1.17895014435163[/C][/ROW]
[ROW][C]143[/C][C]11.4[/C][C]1.17895014435163[/C][/ROW]
[ROW][C]144[/C][C]11.5[/C][C]1.18057429011052[/C][/ROW]
[ROW][C]145[/C][C]11.6[/C][C]1.18217474196246[/C][/ROW]
[ROW][C]146[/C][C]11.6[/C][C]1.18217474196246[/C][/ROW]
[ROW][C]147[/C][C]11.6[/C][C]1.18217474196246[/C][/ROW]
[ROW][C]148[/C][C]11.9[/C][C]1.18683930418653[/C][/ROW]
[ROW][C]149[/C][C]11.9[/C][C]1.18683930418653[/C][/ROW]
[ROW][C]150[/C][C]11.9[/C][C]1.18683930418653[/C][/ROW]
[ROW][C]151[/C][C]11.9[/C][C]1.18683930418653[/C][/ROW]
[ROW][C]152[/C][C]12[/C][C]1.18835026778227[/C][/ROW]
[ROW][C]153[/C][C]12.1[/C][C]1.18984010066748[/C][/ROW]
[ROW][C]154[/C][C]12.1[/C][C]1.18984010066748[/C][/ROW]
[ROW][C]155[/C][C]12.2[/C][C]1.19130926935274[/C][/ROW]
[ROW][C]156[/C][C]12.3[/C][C]1.19275822633551[/C][/ROW]
[ROW][C]157[/C][C]12.4[/C][C]1.19418741063088[/C][/ROW]
[ROW][C]158[/C][C]12.5[/C][C]1.19559724827799[/C][/ROW]
[ROW][C]159[/C][C]12.5[/C][C]1.19559724827799[/C][/ROW]
[ROW][C]160[/C][C]12.6[/C][C]1.19698815282367[/C][/ROW]
[ROW][C]161[/C][C]12.7[/C][C]1.19836052578432[/C][/ROW]
[ROW][C]162[/C][C]13[/C][C]1.20237029899644[/C][/ROW]
[ROW][C]163[/C][C]13[/C][C]1.20237029899644[/C][/ROW]
[ROW][C]164[/C][C]13.3[/C][C]1.20622667659008[/C][/ROW]
[ROW][C]165[/C][C]13.4[/C][C]1.20747964833286[/C][/ROW]
[ROW][C]166[/C][C]13.4[/C][C]1.20747964833286[/C][/ROW]
[ROW][C]167[/C][C]13.4[/C][C]1.20747964833286[/C][/ROW]
[ROW][C]168[/C][C]13.8[/C][C]1.21233756887066[/C][/ROW]
[ROW][C]169[/C][C]13.9[/C][C]1.21351505058515[/C][/ROW]
[ROW][C]170[/C][C]14[/C][C]1.21467830260812[/C][/ROW]
[ROW][C]171[/C][C]14.6[/C][C]1.22137372842758[/C][/ROW]
[ROW][C]172[/C][C]14.8[/C][C]1.22350323472193[/C][/ROW]
[ROW][C]173[/C][C]15[/C][C]1.22558465616364[/C][/ROW]
[ROW][C]174[/C][C]15.1[/C][C]1.22660787127897[/C][/ROW]
[ROW][C]175[/C][C]15.3[/C][C]1.22862033738538[/C][/ROW]
[ROW][C]176[/C][C]15.4[/C][C]1.22960998442415[/C][/ROW]
[ROW][C]177[/C][C]15.5[/C][C]1.23058883028516[/C][/ROW]
[ROW][C]178[/C][C]15.5[/C][C]1.23058883028516[/C][/ROW]
[ROW][C]179[/C][C]15.6[/C][C]1.23155706140547[/C][/ROW]
[ROW][C]180[/C][C]15.7[/C][C]1.23251485983593[/C][/ROW]
[ROW][C]181[/C][C]15.8[/C][C]1.23346240337148[/C][/ROW]
[ROW][C]182[/C][C]16.3[/C][C]1.23805223800049[/C][/ROW]
[ROW][C]183[/C][C]16.4[/C][C]1.23894176281543[/C][/ROW]
[ROW][C]184[/C][C]16.5[/C][C]1.23982216814964[/C][/ROW]
[ROW][C]185[/C][C]17.1[/C][C]1.24492115051123[/C][/ROW]
[ROW][C]186[/C][C]17.7[/C][C]1.24972645433962[/C][/ROW]
[ROW][C]187[/C][C]18.5[/C][C]1.25572124387725[/C][/ROW]
[ROW][C]188[/C][C]18.7[/C][C]1.25715199017738[/C][/ROW]
[ROW][C]189[/C][C]18.7[/C][C]1.25715199017738[/C][/ROW]
[ROW][C]190[/C][C]19.5[/C][C]1.26262577784434[/C][/ROW]
[ROW][C]191[/C][C]19.5[/C][C]1.26262577784434[/C][/ROW]
[ROW][C]192[/C][C]22.7[/C][C]1.28120425251733[/C][/ROW]
[ROW][C]193[/C][C]23.1[/C][C]1.28321780579988[/C][/ROW]
[ROW][C]194[/C][C]25.5[/C][C]1.29416593843619[/C][/ROW]
[ROW][C]195[/C][C]28[/C][C]1.30385947166563[/C][/ROW]
[ROW][C]196[/C][C]32.5[/C][C]1.31807005881621[/C][/ROW]
[ROW][C]197[/C][C]32.6[/C][C]1.31834789550753[/C][/ROW]
[ROW][C]198[/C][C]36.4[/C][C]1.32793900448384[/C][/ROW]
[ROW][C]199[/C][C]39[/C][C]1.33357989878712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319194&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319194&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	3.9	0.882623486970309
2	4.4	0.92787832092391
3	4.8	0.958260706134117
4	5.1	0.9783766663759
5	5.1	0.9783766663759
6	5.2	0.984643913232501
7	5.2	0.984643913232501
8	5.3	0.990710726461036
9	5.4	0.996587119705227
10	5.5	1.00228243285757
11	5.6	1.00780538864538
12	5.7	1.0131641435525
13	5.7	1.0131641435525
14	5.8	1.01836633373166
15	5.9	1.02341911647723
16	5.9	1.02341911647723
17	5.9	1.02341911647723
18	5.9	1.02341911647723
19	6	1.02832920775448
20	6.1	1.03310291621917
21	6.1	1.03310291621917
22	6.1	1.03310291621917
23	6.1	1.03310291621917
24	6.2	1.03774617410694
25	6.2	1.03774617410694
26	6.2	1.03774617410694
27	6.2	1.03774617410694
28	6.3	1.04226456532598
29	6.3	1.04226456532598
30	6.3	1.04226456532598
31	6.3	1.04226456532598
32	6.4	1.04666335104575
33	6.4	1.04666335104575
34	6.4	1.04666335104575
35	6.4	1.04666335104575
36	6.4	1.04666335104575
37	6.5	1.05094749304037
38	6.5	1.05094749304037
39	6.5	1.05094749304037
40	6.5	1.05094749304037
41	6.7	1.0591903221148
42	6.7	1.0591903221148
43	6.7	1.0591903221148
44	6.7	1.0591903221148
45	6.7	1.0591903221148
46	6.7	1.0591903221148
47	6.8	1.06315761880257
48	6.9	1.06702752525234
49	6.9	1.06702752525234
50	7	1.07080379241206
51	7	1.07080379241206
52	7	1.07080379241206
53	7	1.07080379241206
54	7.1	1.07448997585471
55	7.2	1.07808944853263
56	7.2	1.07808944853263
57	7.2	1.07808944853263
58	7.2	1.07808944853263
59	7.2	1.07808944853263
60	7.3	1.08160541253556
61	7.4	1.08504090994265
62	7.4	1.08504090994265
63	7.5	1.08839883284951
64	7.5	1.08839883284951
65	7.6	1.09168193264285
66	7.7	1.0948928285885
67	7.7	1.0948928285885
68	7.7	1.0948928285885
69	7.7	1.0948928285885
70	7.8	1.09803401579162
71	7.8	1.09803401579162
72	7.8	1.09803401579162
73	7.9	1.10110787258238
74	7.9	1.10110787258238
75	7.9	1.10110787258238
76	8	1.10411666737539
77	8	1.10411666737539
78	8	1.10411666737539
79	8.1	1.10706256504626
80	8.2	1.10994763286494
81	8.3	1.11277384602138
82	8.4	1.11554309277634
83	8.4	1.11554309277634
84	8.5	1.1182571792667
85	8.5	1.1182571792667
86	8.5	1.1182571792667
87	8.6	1.1209178339922
88	8.6	1.1209178339922
89	8.6	1.1209178339922
90	8.7	1.12352671200832
91	8.7	1.12352671200832
92	8.7	1.12352671200832
93	8.8	1.12608539884749
94	8.9	1.12859541418917
95	8.9	1.12859541418917
96	9	1.13105821529751
97	9	1.13105821529751
98	9	1.13105821529751
99	9.1	1.1334752002437
100	9.2	1.13584771092866
101	9.2	1.13584771092866
102	9.2	1.13584771092866
103	9.2	1.13584771092866
104	9.2	1.13584771092866
105	9.2	1.13584771092866
106	9.2	1.13584771092866
107	9.3	1.13817703592049
108	9.3	1.13817703592049
109	9.3	1.13817703592049
110	9.4	1.14046441311988
111	9.4	1.14046441311988
112	9.4	1.14046441311988
113	9.5	1.1427110322656
114	9.6	1.14491803729129
115	9.6	1.14491803729129
116	9.7	1.1470865285437
117	9.7	1.1470865285437
118	9.7	1.1470865285437
119	9.9	1.15131216559674
120	10	1.15337131236674
121	10	1.15337131236674
122	10	1.15337131236674
123	10.1	1.15539595091101
124	10.3	1.1593453164731
125	10.3	1.1593453164731
126	10.3	1.1593453164731
127	10.4	1.16127176978577
128	10.4	1.16127176978577
129	10.5	1.16316717033628
130	10.5	1.16316717033628
131	10.5	1.16316717033628
132	10.7	1.16686794268634
133	10.7	1.16686794268634
134	10.8	1.16867481229887
135	11	1.17220507408313
136	11	1.17220507408313
137	11.1	1.17392981746649
138	11.2	1.17562849949142
139	11.3	1.17730174141348
140	11.3	1.17730174141348
141	11.4	1.17895014435163
142	11.4	1.17895014435163
143	11.4	1.17895014435163
144	11.5	1.18057429011052
145	11.6	1.18217474196246
146	11.6	1.18217474196246
147	11.6	1.18217474196246
148	11.9	1.18683930418653
149	11.9	1.18683930418653
150	11.9	1.18683930418653
151	11.9	1.18683930418653
152	12	1.18835026778227
153	12.1	1.18984010066748
154	12.1	1.18984010066748
155	12.2	1.19130926935274
156	12.3	1.19275822633551
157	12.4	1.19418741063088
158	12.5	1.19559724827799
159	12.5	1.19559724827799
160	12.6	1.19698815282367
161	12.7	1.19836052578432
162	13	1.20237029899644
163	13	1.20237029899644
164	13.3	1.20622667659008
165	13.4	1.20747964833286
166	13.4	1.20747964833286
167	13.4	1.20747964833286
168	13.8	1.21233756887066
169	13.9	1.21351505058515
170	14	1.21467830260812
171	14.6	1.22137372842758
172	14.8	1.22350323472193
173	15	1.22558465616364
174	15.1	1.22660787127897
175	15.3	1.22862033738538
176	15.4	1.22960998442415
177	15.5	1.23058883028516
178	15.5	1.23058883028516
179	15.6	1.23155706140547
180	15.7	1.23251485983593
181	15.8	1.23346240337148
182	16.3	1.23805223800049
183	16.4	1.23894176281543
184	16.5	1.23982216814964
185	17.1	1.24492115051123
186	17.7	1.24972645433962
187	18.5	1.25572124387725
188	18.7	1.25715199017738
189	18.7	1.25715199017738
190	19.5	1.26262577784434
191	19.5	1.26262577784434
192	22.7	1.28120425251733
193	23.1	1.28321780579988
194	25.5	1.29416593843619
195	28	1.30385947166563
196	32.5	1.31807005881621
197	32.6	1.31834789550753
198	36.4	1.32793900448384
199	39	1.33357989878712

Maximum Likelihood Estimation of Lambda

> summary(mypT)
bcPower Transformation to Normality 
  Est Power Rounded Pwr Wald Lwr Bnd Wald Upr Bnd
x   -0.6811        -0.5      -0.9768      -0.3853
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 22.25967  1 2.3816e-06
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 152.3224  1 < 2.22e-16

\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   -0.6811        -0.5      -0.9768      -0.3853
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 22.25967  1 2.3816e-06
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 152.3224  1 < 2.22e-16
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319194&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   -0.6811        -0.5      -0.9768      -0.3853
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 22.25967  1 2.3816e-06
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 152.3224  1 < 2.22e-16
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319194&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319194&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   -0.6811        -0.5      -0.9768      -0.3853
Likelihood ratio test that transformation parameter is equal to 0
 (log transformation)
                           LRT df       pval
LR test, lambda = (0) 22.25967  1 2.3816e-06
Likelihood ratio test that no transformation is needed
                           LRT df       pval
LR test, lambda = (1) 152.3224  1 < 2.22e-16

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):

par1 = Full Box-Cox transform ; par2 = -2 ; par3 = 2 ; par4 = 0 ; par5 = Yes ;

Parameters (R input):

par1 = Full Box-Cox transform ; par2 = -2 ; par3 = 2 ; 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
}
}
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code