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Example 13.2: Domain Analysis

Suppose that you are studying profiles of the 800 top-performing companies to provide information on their impact on the economy. You are also interested in the company profiles within each market type. A sample of 66 companies is selected with unequal probability across market types. However, market type is not included in the sample design. Thus, the number of companies within each market type is a random variable in your sample. To obtain statistics within each market type, you should use domain analysis. The data of the 66 companies are saved in the following data set:

   data Company; 
      length Type $14;
      input Type$ Asset Sale Value Profit Employee Weight;
      datalines; 
   Other            2764.0  1828.0  1850.3   144.0   18.7   9.6 
   Energy          13246.2  4633.5  4387.7   462.9   24.3  42.6 
   Finance          3597.7   377.8    93.0    14.0    1.1  12.2 
   Transportation   6646.1  6414.2  2377.5   348.2   47.1  21.8 
   HiTech           1068.4  1689.8  1430.2    72.9    4.6   4.3 
   Manufacturing    1125.0  1719.4  1057.5    98.1   20.4   4.5 
   Other            1459.0  1241.4   452.7    24.5   20.1   5.5 
   Finance          2672.3   262.5   296.2    23.1    2.2   9.3 
   Finance           311.0   566.2   932.0    52.8    2.7   1.9 
   Energy           1148.6  1014.6   485.1    60.6    4.0   4.5 
   Finance          5327.0   572.4   372.9    25.2    4.2  17.7 
   Energy           1602.7   678.4   653.0    75.6    2.8   6.0 
   Energy           5808.8  1288.4  2007.0   318.8    5.9  19.2 
   Medical           268.8   204.4   820.9    45.6    3.7   1.8 
   Transportation   5222.6  2627.8  1910.0   245.6   22.8  17.4 
   Other             872.7  1419.4   939.3    69.7   12.2   3.7 
   Retail           4461.7  8946.8  4662.7   289.0  132.1  15.0 
   HiTech           6719.2  6942.0  8240.2   381.3   85.8  22.1 
   Retail            833.4  1538.8  1090.3    64.9   15.4   3.5 
   Finance           415.9   167.3  1126.8    56.8    0.7   2.2 
   HiTech            442.4  1139.9  1039.9    57.6   22.7   2.3 
   Other             801.5  1157.0   664.2    56.9   15.5   3.4 
   Finance          4954.8   468.8   366.4    41.7    3.0  16.5 
   Finance          2661.9   257.9   181.1    21.2    2.1   9.3 
   Finance          5345.8   530.1   337.4    36.4    4.3  17.8 
   Energy           3334.3  1644.7  1407.8   157.6    6.4  11.4 
   Manufacturing    1826.6  2671.7   483.2    71.3   25.3   6.7 
   Retail            618.8  2354.7   767.7    58.6   19.0   2.9 
   Retail           1529.1  6534.0   826.3    58.3   65.8   5.7 
   Manufacturing    4458.4  4824.5  3132.1    28.9   67.0  15.0 
   HiTech           5831.7  6611.1  9464.7   459.6   86.7  19.3 
   Medical          6468.3  4199.2  3170.4   270.1   59.5  21.3 
   Energy           1720.7   473.1   811.1    86.6    1.6   6.3 
   Energy           1679.7  1379.9   721.1    91.8    4.5   6.2 
   Retail           4018.2 16823.4  2038.3   178.1  162.0  13.6 
   Other             227.1   575.8  1083.8    62.6    1.9   1.6 
   Finance          3872.8   362.0   209.3    27.6    2.4  13.1 
   Retail           3359.3  4844.7  2651.4   224.1   75.6  11.5 
   Energy           1295.6   356.9   180.8   162.3    0.6   5.0 
   Energy           1658.0   626.6   688.0   126.0    3.5   6.1 
   Finance         12156.7  1345.5   680.7   106.6    9.4  39.2 
   HiTech           3982.6  4196.0  3946.8   313.9   64.3  13.5 
   Finance          8760.7   886.4  1006.9    90.0    7.5  28.5 
   Manufacturing    2362.2  3153.3  1080.0   137.0   25.2   8.4 
   Transportation   2499.9  3419.0   992.6    47.2   25.3   8.8 
   Energy           1430.4  1610.0   664.3    77.7    3.5   5.4 
   Energy          13666.5 15465.4  2736.7   411.4   26.6  43.9 
   Manufacturing    4069.3  4174.7  2907.6   289.2   38.2  13.7 
   Energy           2924.7   711.9  1067.8   146.7    3.4  10.1 
   Transportation   1262.1  1716.0   364.3    71.2   14.5   4.9 
   Medical           684.4   672.9   287.4    61.8    6.0   3.1 
   Energy           3069.3  1719.0  1439.0   196.4    4.9  10.6 
   Medical           246.5   318.8   924.1    43.8    3.1   1.7 
   Finance         11562.2  1128.5   580.4    64.2    6.7  37.3 
   Finance          9316.0  1059.4   816.5    95.9    8.0  30.2 
   Retail           1094.3  3848.0   563.3    29.4   44.7   4.4 
   Retail           1102.1  4878.3   932.4    65.2   47.3   4.4 
   HiTech            466.4   675.8   845.7    64.5    5.2   2.4 
   Manufacturing   10839.4  5468.7  1895.4   232.8   47.8  35.0 
   Manufacturing     733.5  2135.3    96.6    10.9    2.7   3.2 
   Manufacturing   10354.2 14477.4  5607.2   321.9  188.5  33.5 
   Energy           1902.1  2697.9   329.3    34.2    2.2   6.9 
   Other            2245.2  2132.2  2230.4   198.9    8.0   8.0 
   Transportation    949.4  1248.3   298.9    35.4   10.4   3.9 
   Retail           2834.4  2884.6   458.2    41.2   49.8   9.8 
   Retail           2621.1  6173.8  1992.7   183.7  115.1   9.2 
   ;

For each company in your sample,

• The variable Type identifies the type of market for the company.
• The variable Asset contains the company's assets in millions of dollars.
• The variable Sale contains sales in millions of dollars.
• The variable Value contains the market value of the company in millions of dollars.
• The variable Profit contains the profit in millions of dollars.
• The variable Employee stores the number of employees in thousands.
• The variable Weight contains the sampling weight.

The following SAS statements use PROC SURVEYMEANS to perform the domain analysis, estimating means and other statistics for the overall population and also for the subpopulations (or domain) defined by market type. The DOMAIN statement specifies Type as the domain variable:

   title1 'Top Companies Profile Study';
   proc surveymeans data=Company total=800 mean sum;     
      var Asset Sale Value Profit Employee; 
      weight Weight;
      domain Type;
   run;

The "Statistics" table in Output 13.2.1 displays the estimates of the mean and total for all analysis variables for the entire 800 companies, while Output 13.2.2 shows the mean and total estimates for each company type.

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