Supplementary Exercises 1.16 and 1.65 of IPS7e
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1.16
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Not all statistical software programs produce back-to-back stemplots; Minitab 
and Stata don't offer this option. We will therefore produce separate stemplots
for the control and experimental groups. In Minitab, we can use the
numerical group variable (labeled g) or split the data into separate
columns using the Data-Unstack Columns. It is also possible to manually
copy the values from the combined (wgain) column into separate columns,
but such manual editing in the worksheet is not generally recommended 
because the editing is not documented in the history. 

This solution uses the first of these three approaches. A dotplot is another
good option to display and compare the two groups.

 WOpen "R:\Chapter 1\ex01_016.mtw".

 Stem-and-Leaf 'wgain';
   By 'g'.

Stem-and-Leaf Display: wgain 

Stem-and-leaf of wgain  g = 1    N  = 20
Leaf Unit = 10

 1   2  7
 2   2  8
 3   3  1
 5   3  22
 10  3  44555
 10  3  66
 8   3  889
 5   4  01
 3   4  3
 2   4  5
 1   4  6


Stem-and-leaf of wgain  g = 2    N  = 20
Leaf Unit = 10

 1   3  1
 3   3  23
 3   3
 5   3  67
 7   3  99
(5)  4  00001
 8   4  22233
 3   4  4
 2   4  67

 Dotplot ( 'wgain' ) * 'group'.

Dotplot of wgain 


Comments:
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The default stemplots in Minitab use stems for 20's and leaves for
10's. The plots look fairly good, and there is no urgent need to
change the stem and leaf definitions. The dotplot gives another, and
simpler, picture of the distribution.

Both distributions appear to be unimodal with midpoints around 350 and
410 g for the control and experimental groups, respectively. These values
correspond reasonably well to the means and medians computed from
descriptive statistics (below). It therefore appears that chicks in
the experimental group grow faster than in the control group. One would
need to carry a formal statistical analysis to determine whether this
finding could have occurred by chance alone. None of the two groups
appear to have outliers.


1.65
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(a) 
We use the descriptive statistics menu to compute the mean and
standard deviation, as well as other statistics.

 Describe 'wgain';
   By 'group'.

Descriptive Statistics: wgain 

Variable  group          N  N*    Mean  SE Mean  StDev  Minimum      Q1  Median      Q3
wgain     Control       20   0   366.3     11.4   50.8    272.0   333.0   358.0   401.3
          Experimental  20   0  402.95     9.55  42.73   318.00  379.25  406.50  429.25

Variable  group         Maximum
wgain     Control         462.0
          Experimental   477.00

(b) 
Unimodal and roughly symmetrical distributions are best summarized
by the sample mean and sample standard deviation. Both distributions 
meet this requirement to a reasonable degree.