Supplementary exercise 9.50 of IPS7e
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Data: performance assessments (partial, usual, continuous; see text for
further explanation) of employees in two age groups (under and above 40
years).

Minitab commands and output:

MTB > WOpen "H:\VHM\VHM801\Datasets\Minitab\Chapter 9\ex09_050.mtw".
Retrieving worksheet from file: 'H:\VHM\VHM801\Datasets\Minitab\Chapter
9\ex09_050.mtw'
Worksheet was saved on 24/10/2014

MTB > XTabs 'perf' 'over40';
SUBC>   Layout 1 1;
SUBC>   Frequencies 'count';
SUBC>   Counts;
SUBC>   ColPercents;
SUBC>   ChiSquare;
SUBC>   Expected;
SUBC>   XResiduals;
SUBC>   DMissing 'perf' 'over40'.
Tabulated Statistics: perf, over40 
Using frequencies in count

Rows: perf   Columns: over40

               n       y     All

contin        63      32      95
           12.55    4.20    7.52
            37.8    57.2
          16.872  11.130

part          82     237     319
           16.33   31.14   25.26
           126.8   192.2
          15.824  10.438

usual        357     492     849
           71.12   64.65   67.22
           337.4   511.6
           1.133   0.747

All          502     761    1263
          100.00  100.00  100.00

Cell Contents:      Count
                    % of Column
                    Expected count
                    Contribution to Chi-square

Pearson Chi-Square = 56.144, DF = 2, P-Value = 0.000
(Likelihood Ratio Chi-Square = 56.969, DF = 2, P-Value = 0.000)

Minitab technical note: in order to avoid reordering af rows and
columns by their labels, one can set the value ordering of variables in
the "Editor-Column properties-Value order" menu (available only when the 
worksheet is the active window, or by right-clicking a highlighted
column of interest).

Comments:
--------
Only little information is given about how the data were collected. It
seems most natural that two samples of employees were taken, one for
each age group. Then age group is not a response variable (it is instead 
an explanatory variable). Performance is a response variable. Thus, the 
appropriate model is two independent multinomial distributions, one for 
each column in the table (age group). We assume multinomial settings 
within each age group.

Parameter estimates are the sample proportions within each group, as
listed in the above table. The values are quite close for the middle
outcome ("usually") but differ considerably for the other outcomes. The 
above 40 age group shows a higher proportion of performance assessments
as "partial", and conversely the under 40 age group shows a higher
proportion of "continually" performances.

Null hypothesis H0: same proportions in the two groups, two-sided 
alternative hypothesis Ha: different proportions in the two groups.

Test statistic: X^2 = 56.1, df = (3-1)*(2-1) = 2, P-value < 0.0005.
All cells have large expected values, so the chi-square distribution 
may be considered a valid reference distribution.

Conclusion: the P-value is strongly significant and gives clear evidence
of different performances in the groups of employees below and above 40 
years of age. The under 40 group received more assessments indicating
continual exceedance of expectations than the above 40 group, and the over
40 group received more assessments indicating (only) expectations to be met 
than the younger group.