Supplementary Exercise 9.62 of IPS7e
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Sketch of solution only (most detail for cats).

A case-control design. Cases are cats brought to an animal shelter and controls 
are cats still in a private home. Cases and controls are selected randomly from
the respective populations, and information is obtained about the source of the
cat. For controls this must mean the source of the cat when it arrived in the private 
home (private/breeder, pet store, other). The only response variable is source of cat.
The classification into cases and controls is an explanatory variable because it
is fixed in advance of the study (it has been decided to sample a certain number
of cats from the two populations). 

Model: 2 independent samples from multinomial distributions. We compare
the distribution of sources within the random samples among cases and
controls, respectively.

Note that according to IPS terminology, the classification of explanatory and 
response variables would have been reversed because a relationship source ->
present location (shelter/private) is anticipated. In my view (and not mine
alone) this is misleading and confusing, and it may easily lead one to the wrong
model for the data. There is no question that considering the data as 3
independent samples corresponding to the sources (columns) is wrong and 
meaningless!

MTB > WOpen "H:\VHM\VHM801\Datasets\Minitab\Chapter 9\ex09_062.mtw".
Retrieving worksheet from file: 'H:\VHM\VHM801\Datasets\Minitab\Chapter
9\ex09_062.mtw'
Worksheet was saved on 24/10/2014

MTB > XTabs 'cc' 'source' 'animal';
SUBC>   Layout 1 1;
SUBC>   Frequencies 'count';
SUBC>   Counts;
SUBC>   RowPercents;
SUBC>   ChiSquare;
SUBC>   Expected;
SUBC>   DMissing 'cc' 'source' 'animal'.
Tabulated Statistics: cc, source, animal 
Using frequencies in count
 
Results for animal = cat 

Rows: cc   Columns: source

             other  petstore    priv     All

cases           76        16     124     216
             35.19      7.41   57.41  100.00
             91.03     13.05  111.92

controls       203        24     219     446
             45.52      5.38   49.10  100.00
            187.97     26.95  231.08

All            279        40     343     662
             42.15      6.04   51.81  100.00

Cell Contents:      Count
                    % of Row
                    Expected count

Pearson Chi-Square = 6.611, DF = 2, P-Value = 0.037
(Likelihood Ratio Chi-Square = 6.663, DF = 2, P-Value = 0.036)

Comments and answers to questions:
----------------------------------
a)
Estimation: the sample row proportions (proportions within each row) are given 
in the table above. We must use the row proportions because only the column
variable is a response variable. The largest difference between the two samples 
is for the proportion of cats from other sources (35% among cases and 46% among
controls), but also the proportion of cats from private sources differ
considerably (57% among cases and 49% among controls).

Hypothesis: H0: no difference in the source proportions for the cases and
controls. Ha: some difference...

Test: chi-square statistic X^2 = 6.61, df = (2-1)*(3-1) = 2,
      P-value = 0.037.

Conclusion: we have some (weak) evidence to reject H0 - there is some difference 
in the proportions, the most notable ones described above. In words, less cats
relinquished to animals shelter are from other sources and more from privates
than in the overall population. This implies that a cat being from a private
source is a risk factor for relinquishment, and being from other sources is a 
protective factor. It seems difficult to make sense of this finding; you may
look up the paper to see a discussion of it.

b) Minitab listing for dogs:

Results for animal = dog 

Rows: cc   Columns: source

             other  petstore    priv     All

cases           90         7     188     285
             31.58      2.46   65.96  100.00
             65.27     21.10  198.63

controls       142        68     518     728
             19.51      9.34   71.15  100.00
            166.73     53.90  507.37

All            232        75     706    1013
             22.90      7.40   69.69  100.00

Cell Contents:      Count
                    % of Row
                    Expected count

Pearson Chi-Square = 26.939, DF = 2, P-Value = 0.000
(Likelihood Ratio Chi-Square = 29.190, DF = 2, P-Value = 0.000)

Comments:
---------
The X^2 test is clearly significant. There is not the same distribution
of the sources of dogs in shelters than in the control population. Dogs
in shelters are more like to come from Other sources (including stray
dogs, born in shelter, and born in home). It seems natural that such
dogs could be more difficult to deal with or be less wanted by their
owners than dogs from private or pet store sources.