Revisions to Positive skewness: what to do when transformations don't help?

added 2446 characters in body

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edited Jun 2, 2016 at 15:42

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Response: 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.3; 0.5; 0.5; 0.5; 0.5; 0.5; 0.8; 0.8; 1.0; 1.0; 1.0; 1.0; 1.0; 1.0; 1.2; 1.3; 1.5; 1.6; 1.8; 2.0; 2.0; 2.0; 2.0; 2.0; 2.5; 3.0; 3.0; 3.0; 3.0; 3.0; 3.0; 3.4; 3.4; 3.5; 3.5; 3.8; 4.0; 4.0; 4.2; 4.3; 4.5; 5.0; 5.0; 5.3; 5.8; 6.0; 6.0; 6.5; 7.0; 7.2; 7.5; 7.7; 8.0; 8.7; 9.3; 9.5; 10.0; 10.0; 10.5; 11.0; 11.6; 12.5; 13.0; 14.0; 14.5; 14.7; 15.0; 15.0; 15.0; 15.0; 16.0; 18.0; 18.0; 25.0

NumPredictor: 0.9; 2.6; 3.2; 6.6; 80.1; 41.4; 22.3; 29.8; 14.5; 9.9; 5.7; 6.7; 9.9; 19.0; 23.0; 0.3; 23.0; 1.0; 5.7; 7.4; 14.5; 14.5; 22.3; 7.0; 29.8; 9.6; 9.6; 12.0; 4.5; 5.8; 7.6; 7.6; 23.0; 23.0; 3.2; 5.1; 7.0; 7.3; 6.6; 23.0; 5.5; 0.4; 3.6; 12.0; 22.3; 7.6; 12.4; 0.9; 0.0; 1.0; 6.4; 11.0; 22.3; 2.2; 4.9; 22.3; 4.7; 5.2; 2.1; 14.5; 0.9; 8.3; 4.9; 22.3; 4.5; 3.3; 5.1; 9.9; 46.3; 1.1; 21.0; 3.6; 5.8; 0.8; 22.3; 0.2; 0.4; 3.6; 4.9; 11.0; 7.9; 9.6; 0.1

CatPredictor: A; A; A; A; A; AT; T; T; T; A; A; A; AT; T; T; A; T; A; A; A; T; T; T; A; T; A; AT; A; A; A; A; A; T; T; A; A; A; A; AT; T; A; A; A; A; T; A; T; A; A; A; A; AT; T; A; T; T; A; A; A; T; A; A; T; T; A; A; A; A; AT; A; A; A; A; A; T; A; A; A; T; T; A; A; A

identifier CatPredictor NumPredictor Response 
    1  A                  .9           0
    2  A                 2.6           0
    3  A                 3.2           0
    4  A                 6.6           0
    5  A                80.1           0
    6  AT               41.4           0
    7  T                22.3           0
    8  T                29.8           0
    9  T                14.5           0
   10  A                 9.9          .3
   11  A                 5.7          .5
   12  A                 6.7          .5
   13  AT                9.9          .5
   14  T                  19          .5
   15  T                  23          .5
   16  A                  .3          .8
   17  T                  23          .8
   18  A                   1           1
   19  A                 5.7           1
   20  A                 7.4           1
   21  T                14.5           1
   22  T                14.5           1
   23  T                22.3           1
   24  A                   7         1.2
   25  T                29.8         1.3
   26  A                 9.6         1.5
   27  AT                9.6         1.6
   28  A                  12         1.8
   29  A                 4.5           2
   30  A                 5.8           2
   31  A                 7.6           2
   32  A                 7.6           2
   33  T                  23           2
   34  T                  23         2.5
   35  A                 3.2           3
   36  A                 5.1           3
   37  A                   7           3
   38  A                 7.3           3
   39  AT                6.6           3
   40  T                  23           3
   41  A                 5.5         3.4
   42  A                  .4         3.4
   43  A                 3.6         3.5
   44  A                  12         3.5
   45  T                22.3         3.8
   46  A                 7.6           4
   47  T                12.4           4
   48  A                  .9         4.2
   49  A                   0         4.3
   50  A                   1         4.5
   51  A                 6.4           5
   52  AT                 11           5
   53  T                22.3         5.3
   54  A                 2.2         5.8
   55  T                 4.9           6
   56  T                22.3           6
   57  A                 4.7         6.5
   58  A                 5.2           7
   59  A                 2.1         7.2
   60  T                14.5         7.5
   61  A                  .9         7.7
   62  A                 8.3           8
   63  T                 4.9         8.7
   64  T                22.3         9.3
   65  A                 4.5         9.5
   66  A                 3.3          10
   67  A                 5.1          10
   68  A                 9.9        10.5
   69  AT               46.3          11
   70  A                 1.1        11.6
   71  A                  21        12.5
   72  A                 3.6          13
   73  A                 5.8          14
   74  A                  .8        14.5
   75  T                22.3        14.7
   76  A                  .2          15
   77  A                  .4          15
   78  A                 3.6          15
   79  T                 4.9          15
   80  T                  11          16
   81  A                 7.9          18
   82  A                 9.6          18
   83  A                  .1          25

Response: 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.3; 0.5; 0.5; 0.5; 0.5; 0.5; 0.8; 0.8; 1.0; 1.0; 1.0; 1.0; 1.0; 1.0; 1.2; 1.3; 1.5; 1.6; 1.8; 2.0; 2.0; 2.0; 2.0; 2.0; 2.5; 3.0; 3.0; 3.0; 3.0; 3.0; 3.0; 3.4; 3.4; 3.5; 3.5; 3.8; 4.0; 4.0; 4.2; 4.3; 4.5; 5.0; 5.0; 5.3; 5.8; 6.0; 6.0; 6.5; 7.0; 7.2; 7.5; 7.7; 8.0; 8.7; 9.3; 9.5; 10.0; 10.0; 10.5; 11.0; 11.6; 12.5; 13.0; 14.0; 14.5; 14.7; 15.0; 15.0; 15.0; 15.0; 16.0; 18.0; 18.0; 25.0

NumPredictor: 0.9; 2.6; 3.2; 6.6; 80.1; 41.4; 22.3; 29.8; 14.5; 9.9; 5.7; 6.7; 9.9; 19.0; 23.0; 0.3; 23.0; 1.0; 5.7; 7.4; 14.5; 14.5; 22.3; 7.0; 29.8; 9.6; 9.6; 12.0; 4.5; 5.8; 7.6; 7.6; 23.0; 23.0; 3.2; 5.1; 7.0; 7.3; 6.6; 23.0; 5.5; 0.4; 3.6; 12.0; 22.3; 7.6; 12.4; 0.9; 0.0; 1.0; 6.4; 11.0; 22.3; 2.2; 4.9; 22.3; 4.7; 5.2; 2.1; 14.5; 0.9; 8.3; 4.9; 22.3; 4.5; 3.3; 5.1; 9.9; 46.3; 1.1; 21.0; 3.6; 5.8; 0.8; 22.3; 0.2; 0.4; 3.6; 4.9; 11.0; 7.9; 9.6; 0.1

CatPredictor: A; A; A; A; A; AT; T; T; T; A; A; A; AT; T; T; A; T; A; A; A; T; T; T; A; T; A; AT; A; A; A; A; A; T; T; A; A; A; A; AT; T; A; A; A; A; T; A; T; A; A; A; A; AT; T; A; T; T; A; A; A; T; A; A; T; T; A; A; A; A; AT; A; A; A; A; A; T; A; A; A; T; T; A; A; A

identifier CatPredictor NumPredictor Response 
    1  A                  .9           0
    2  A                 2.6           0
    3  A                 3.2           0
    4  A                 6.6           0
    5  A                80.1           0
    6  AT               41.4           0
    7  T                22.3           0
    8  T                29.8           0
    9  T                14.5           0
   10  A                 9.9          .3
   11  A                 5.7          .5
   12  A                 6.7          .5
   13  AT                9.9          .5
   14  T                  19          .5
   15  T                  23          .5
   16  A                  .3          .8
   17  T                  23          .8
   18  A                   1           1
   19  A                 5.7           1
   20  A                 7.4           1
   21  T                14.5           1
   22  T                14.5           1
   23  T                22.3           1
   24  A                   7         1.2
   25  T                29.8         1.3
   26  A                 9.6         1.5
   27  AT                9.6         1.6
   28  A                  12         1.8
   29  A                 4.5           2
   30  A                 5.8           2
   31  A                 7.6           2
   32  A                 7.6           2
   33  T                  23           2
   34  T                  23         2.5
   35  A                 3.2           3
   36  A                 5.1           3
   37  A                   7           3
   38  A                 7.3           3
   39  AT                6.6           3
   40  T                  23           3
   41  A                 5.5         3.4
   42  A                  .4         3.4
   43  A                 3.6         3.5
   44  A                  12         3.5
   45  T                22.3         3.8
   46  A                 7.6           4
   47  T                12.4           4
   48  A                  .9         4.2
   49  A                   0         4.3
   50  A                   1         4.5
   51  A                 6.4           5
   52  AT                 11           5
   53  T                22.3         5.3
   54  A                 2.2         5.8
   55  T                 4.9           6
   56  T                22.3           6
   57  A                 4.7         6.5
   58  A                 5.2           7
   59  A                 2.1         7.2
   60  T                14.5         7.5
   61  A                  .9         7.7
   62  A                 8.3           8
   63  T                 4.9         8.7
   64  T                22.3         9.3
   65  A                 4.5         9.5
   66  A                 3.3          10
   67  A                 5.1          10
   68  A                 9.9        10.5
   69  AT               46.3          11
   70  A                 1.1        11.6
   71  A                  21        12.5
   72  A                 3.6          13
   73  A                 5.8          14
   74  A                  .8        14.5
   75  T                22.3        14.7
   76  A                  .2          15
   77  A                  .4          15
   78  A                 3.6          15
   79  T                 4.9          15
   80  T                  11          16
   81  A                 7.9          18
   82  A                 9.6          18
   83  A                  .1          25

added 235 characters in body

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edited Jun 2, 2016 at 14:50

biologist

23
5

Response: 0. 0, 0.0; 0, 0.0; 0, 0.0; 0, 0.0; 0, 0.0; 0, 0.0; 0, 0.0; 0, 0.0; 0, 0.3, 0.5, 0.5, 0.5, 0.5, 0.5, 0.8, 00; 0.8, 13; 0.5; 0, 1.5; 0, 1.5; 0, 1.5; 0, 1.5; 0, 1.8; 0, 1.2, 18; 1.3, 10; 1.5, 10; 1.6, 10; 1.8, 20; 1.0, 20; 1.0, 20; 1.0, 22; 1.0, 23; 1.0, 25; 1.5, 36; 1.0, 38; 2.0, 30; 2.0, 30; 2.0, 30; 2.0, 30; 2.0, 30; 2.4, 35; 3.4, 30; 3.5, 30; 3.5, 30; 3.8, 40; 3.0, 40; 3.0, 40; 3.2, 44; 3.4; 3, 4.5, 55; 3.0, 55; 3.0, 58; 4.3, 50; 4.8, 60; 4.0, 62; 4.0, 63; 4.5; 5, 7.0, 70; 5.2, 70; 5.3; 5, 7.8; 6.0; 6.0; 6.5; 7, 8.0, 80; 7.2; 7, 9.3, 95; 7.5, 107; 8.0, 100; 8.0, 107; 9.5, 113; 9.0, 115; 10.6, 120; 10.5, 130; 10.0, 145; 11.0, 140; 11.5, 146; 12.7, 155; 13.0, 150; 14.0, 150; 14.0, 155; 14.0, 167; 15.0, 180; 15.0, 180; 15.0, 250; 15.0; 16.0; 18.0; 18.0; 25.0

Numeric predictorNumPredictor: 0.9, 2.6, 3 0.9; 2, 6.6; 3.2; 6, 80.1, 416; 80.4, 221; 41.3, 294; 22.8, 143; 29.5, 98; 14.5; 9, 5.7, 69; 5.7, 97; 6.7; 9, 19.0, 239; 19.0; 23.0; 0, 0.3, 233; 23.0, 10; 1.0, 50; 5.7; 7, 7.4, 144; 14.5, 145; 14.5, 225; 22.3, 73; 7.0, 290; 29.8, 98; 9.6, 96; 9.6, 126; 12.0, 40; 4.5; 5, 5.8, 7.6, 78; 7.6, 236; 7.0, 236; 23.0, 30; 23.2, 50; 3.1, 72; 5.0, 71; 7.3, 60; 7.3; 6, 23.0, 56; 23.0; 5, 0.4, 3.6, 12.5; 0, 22.4; 3, 7.6, 126; 12.4, 00; 22.9, 03; 7.6; 12.4; 0, 1.9; 0, 6.4, 110; 1.0, 220; 6.3, 24; 11.0; 22.3; 2, 4.9, 222; 4.3, 49; 22.7, 53; 4.7; 5.2; 2, 2.1, 141; 14.5, 05; 0.9, 89; 8.3, 43; 4.9, 229; 22.3; 4.5; 3, 4.3; 5, 3.3, 51; 9.9; 46.3; 1, 9.9, 461; 21.0; 3, 1.1, 216; 5.8; 0, 3.6, 58; 22.8, 03; 0.8, 222; 0.4; 3, 0.2, 0.6; 4, 3.6, 4.9, 119; 11.0, 70; 7.9; 9, 9.6, 06; 0.1

Categorical predictorCatPredictor: A, A, A, A, A, AT, T, T, T, A, A, A, AT, T, T, A, T, A, A, A, T, T, T, A, T, A, AT, A, A, A, A, A, T, T, A, A, A, A, AT, T, A, A, A, A, T, A, T, A, A, A, A, AT, T, A, T, T, A, A, A, T, A, AT, T, A, A, A, A, AT, A, A, A, A, A, T, A, A, A, T, T, A, A, A A; A; A; A; A; AT; T; T; T; A; A; A; AT; T; T; A; T; A; A; A; T; T; T; A; T; A; AT; A; A; A; A; A; T; T; A; A; A; A; AT; T; A; A; A; A; T; A; T; A; A; A; A; AT; T; A; T; T; A; A; A; T; A; A; T; T; A; A; A; A; AT; A; A; A; A; A; T; A; A; A; T; T; A; A; A

Response: 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.3, 0.5, 0.5, 0.5, 0.5, 0.5, 0.8, 0.8, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.0, 2.0, 2.0, 2.0, 2.5, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.4, 3.4, 3.5, 3.5, 3.8, 4.0, 4.0, 4.2, 4.3, 4.5, 5.0, 5.0, 5.3, 5.8, 6.0, 6.0, 6.5, 7.0, 7.2, 7.5, 7.7, 8.0, 8.7, 9.3, 9.5, 10.0, 10.0, 10.5, 11.0, 11.6, 12.5, 13.0, 14.0, 14.5, 14.7, 15.0, 15.0, 15.0, 15.0, 16.0, 18.0, 18.0, 25.0

Numeric predictor: 0.9, 2.6, 3.2, 6.6, 80.1, 41.4, 22.3, 29.8, 14.5, 9.9, 5.7, 6.7, 9.9, 19.0, 23.0, 0.3, 23.0, 1.0, 5.7, 7.4, 14.5, 14.5, 22.3, 7.0, 29.8, 9.6, 9.6, 12.0, 4.5, 5.8, 7.6, 7.6, 23.0, 23.0, 3.2, 5.1, 7.0, 7.3, 6.6, 23.0, 5.5, 0.4, 3.6, 12.0, 22.3, 7.6, 12.4, 0.9, 0.0, 1.0, 6.4, 11.0, 22.3, 2.2, 4.9, 22.3, 4.7, 5.2, 2.1, 14.5, 0.9, 8.3, 4.9, 22.3, 4.5, 3.3, 5.1, 9.9, 46.3, 1.1, 21.0, 3.6, 5.8, 0.8, 22.3, 0.2, 0.4, 3.6, 4.9, 11.0, 7.9, 9.6, 0.1

Categorical predictor: A, A, A, A, A, AT, T, T, T, A, A, A, AT, T, T, A, T, A, A, A, T, T, T, A, T, A, AT, A, A, A, A, A, T, T, A, A, A, A, AT, T, A, A, A, A, T, A, T, A, A, A, A, AT, T, A, T, T, A, A, A, T, A, AT, T, A, A, A, A, AT, A, A, A, A, A, T, A, A, A, T, T, A, A, A

Response: 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.3; 0.5; 0.5; 0.5; 0.5; 0.5; 0.8; 0.8; 1.0; 1.0; 1.0; 1.0; 1.0; 1.0; 1.2; 1.3; 1.5; 1.6; 1.8; 2.0; 2.0; 2.0; 2.0; 2.0; 2.5; 3.0; 3.0; 3.0; 3.0; 3.0; 3.0; 3.4; 3.4; 3.5; 3.5; 3.8; 4.0; 4.0; 4.2; 4.3; 4.5; 5.0; 5.0; 5.3; 5.8; 6.0; 6.0; 6.5; 7.0; 7.2; 7.5; 7.7; 8.0; 8.7; 9.3; 9.5; 10.0; 10.0; 10.5; 11.0; 11.6; 12.5; 13.0; 14.0; 14.5; 14.7; 15.0; 15.0; 15.0; 15.0; 16.0; 18.0; 18.0; 25.0

NumPredictor: 0.9; 2.6; 3.2; 6.6; 80.1; 41.4; 22.3; 29.8; 14.5; 9.9; 5.7; 6.7; 9.9; 19.0; 23.0; 0.3; 23.0; 1.0; 5.7; 7.4; 14.5; 14.5; 22.3; 7.0; 29.8; 9.6; 9.6; 12.0; 4.5; 5.8; 7.6; 7.6; 23.0; 23.0; 3.2; 5.1; 7.0; 7.3; 6.6; 23.0; 5.5; 0.4; 3.6; 12.0; 22.3; 7.6; 12.4; 0.9; 0.0; 1.0; 6.4; 11.0; 22.3; 2.2; 4.9; 22.3; 4.7; 5.2; 2.1; 14.5; 0.9; 8.3; 4.9; 22.3; 4.5; 3.3; 5.1; 9.9; 46.3; 1.1; 21.0; 3.6; 5.8; 0.8; 22.3; 0.2; 0.4; 3.6; 4.9; 11.0; 7.9; 9.6; 0.1

CatPredictor: A; A; A; A; A; AT; T; T; T; A; A; A; AT; T; T; A; T; A; A; A; T; T; T; A; T; A; AT; A; A; A; A; A; T; T; A; A; A; A; AT; T; A; A; A; A; T; A; T; A; A; A; A; AT; T; A; T; T; A; A; A; T; A; A; T; T; A; A; A; A; AT; A; A; A; A; A; T; A; A; A; T; T; A; A; A

added 1208 characters in body

Source Link

edited Jun 2, 2016 at 11:26

biologist

23
5

I would like to perform General Linear Model with one response variable and two predictor variables (1 numeric, 1 categorical). The response variable is positively skewed and transformations don't seem to bring it closer to normality. I tried sqrt, logarithmic, inverse and Box Cox transformations (performed by SPSS). Is there any other way to transform it? Can Generalized Linear Model work with such skewed data (I'm not very familiar with it)? Here are the data:

Response: 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.3, 0.5, 0.5, 0.5, 0.5, 0.5, 0.8, 0.8, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.0, 2.0, 2.0, 2.0, 2.5, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.4, 3.4, 3.5, 3.5, 3.8, 4.0, 4.0, 4.2, 4.3, 4.5, 5.0, 5.0, 5.3, 5.8, 6.0, 6.0, 6.5, 7.0, 7.2, 7.5, 7.7, 8.0, 8.7, 9.3, 9.5, 10.0, 10.0, 10.5, 11.0, 11.6, 12.5, 13.0, 14.0, 14.5, 14.7, 15.0, 15.0, 15.0, 15.0, 16.0, 18.0, 18.0, 25.0

Numeric predictor: 0.9, 2.6, 3.2, 6.6, 80.1, 41.4, 22.3, 29.8, 14.5, 9.9, 5.7, 6.7, 9.9, 19.0, 23.0, 0.3, 23.0, 1.0, 5.7, 7.4, 14.5, 14.5, 22.3, 7.0, 29.8, 9.6, 9.6, 12.0, 4.5, 5.8, 7.6, 7.6, 23.0, 23.0, 3.2, 5.1, 7.0, 7.3, 6.6, 23.0, 5.5, 0.4, 3.6, 12.0, 22.3, 7.6, 12.4, 0.9, 0.0, 1.0, 6.4, 11.0, 22.3, 2.2, 4.9, 22.3, 4.7, 5.2, 2.1, 14.5, 0.9, 8.3, 4.9, 22.3, 4.5, 3.3, 5.1, 9.9, 46.3, 1.1, 21.0, 3.6, 5.8, 0.8, 22.3, 0.2, 0.4, 3.6, 4.9, 11.0, 7.9, 9.6, 0.1

Categorical predictor: A, A, A, A, A, AT, T, T, T, A, A, A, AT, T, T, A, T, A, A, A, T, T, T, A, T, A, AT, A, A, A, A, A, T, T, A, A, A, A, AT, T, A, A, A, A, T, A, T, A, A, A, A, AT, T, A, T, T, A, A, A, T, A, AT, T, A, A, A, A, AT, A, A, A, A, A, T, A, A, A, T, T, A, A, A

Here are two examples of my distributions :

I would like to perform General Linear Model with one response variable and two predictor variables (1 numeric, 1 categorical). The response variable is positively skewed and transformations don't seem to bring it closer to normality. I tried sqrt, logarithmic, inverse and Box Cox transformations (performed by SPSS). Is there any other way to transform it? Can Generalized Linear Model work with such skewed data (I'm not very familiar with it)? Here are two examples of my distributions

I would like to perform General Linear Model with one response variable and two predictor variables (1 numeric, 1 categorical). The response variable is positively skewed and transformations don't seem to bring it closer to normality. I tried sqrt, logarithmic, inverse and Box Cox transformations (performed by SPSS). Is there any other way to transform it? Can Generalized Linear Model work with such skewed data (I'm not very familiar with it)? Here are the data:

Response: 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.3, 0.5, 0.5, 0.5, 0.5, 0.5, 0.8, 0.8, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.0, 2.0, 2.0, 2.0, 2.5, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.4, 3.4, 3.5, 3.5, 3.8, 4.0, 4.0, 4.2, 4.3, 4.5, 5.0, 5.0, 5.3, 5.8, 6.0, 6.0, 6.5, 7.0, 7.2, 7.5, 7.7, 8.0, 8.7, 9.3, 9.5, 10.0, 10.0, 10.5, 11.0, 11.6, 12.5, 13.0, 14.0, 14.5, 14.7, 15.0, 15.0, 15.0, 15.0, 16.0, 18.0, 18.0, 25.0

Numeric predictor: 0.9, 2.6, 3.2, 6.6, 80.1, 41.4, 22.3, 29.8, 14.5, 9.9, 5.7, 6.7, 9.9, 19.0, 23.0, 0.3, 23.0, 1.0, 5.7, 7.4, 14.5, 14.5, 22.3, 7.0, 29.8, 9.6, 9.6, 12.0, 4.5, 5.8, 7.6, 7.6, 23.0, 23.0, 3.2, 5.1, 7.0, 7.3, 6.6, 23.0, 5.5, 0.4, 3.6, 12.0, 22.3, 7.6, 12.4, 0.9, 0.0, 1.0, 6.4, 11.0, 22.3, 2.2, 4.9, 22.3, 4.7, 5.2, 2.1, 14.5, 0.9, 8.3, 4.9, 22.3, 4.5, 3.3, 5.1, 9.9, 46.3, 1.1, 21.0, 3.6, 5.8, 0.8, 22.3, 0.2, 0.4, 3.6, 4.9, 11.0, 7.9, 9.6, 0.1

Categorical predictor: A, A, A, A, A, AT, T, T, T, A, A, A, AT, T, T, A, T, A, A, A, T, T, T, A, T, A, AT, A, A, A, A, A, T, T, A, A, A, A, AT, T, A, A, A, A, T, A, T, A, A, A, A, AT, T, A, T, T, A, A, A, T, A, AT, T, A, A, A, A, AT, A, A, A, A, A, T, A, A, A, T, T, A, A, A

Here are two examples of my distributions:

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edited May 31, 2016 at 13:52

Nick Cox

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asked May 31, 2016 at 13:35

biologist

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