Getting Started

Data are available containing the numbers of Ph.Ds awarded in the United States during the years 1973 through 1978 (U.S. Bureau of the Census 1979). The table has six rows, one for each of six academic disciplines, and six columns for the six years . The following DATA step reads the complete table into a SAS data set, and PROC CORRESP displays correspondence analysis results including the inertia decomposition and coordinates. The concept of inertia in correspondence analysis is analogous to the concept of variance in principal component analysis, and it is proportional to the chi-square information. The %PLOTIT macro creates a graphical scatterplot of the results. See Appendix B, Using the %PLOTIT Macro, for more information on the % PLOTIT macro.

  title "Number of Ph.Ds Awarded from 1973 to 1978";   data PhD;   input Science $ 1-19 y1973-y1978;   label y1973 = '1973'   y1974 = '1974'   y1975 = '1975'   y1976 = '1976'   y1977 = '1977'   y1978 = '1978';   datalines;   Life Sciences       4489 4303 4402 4350 4266 4361   Physical Sciences   4101 3800 3749 3572 3410 3234   Social Sciences     3354 3286 3344 3278 3137 3008   Behavioral Sciences 2444 2587 2749 2878 2960 3049   Engineering         3338 3144 2959 2791 2641 2432   Mathematics         1222 1196 1149 1003  959  959   ;   proc corresp data=PhD out=Results short;   var y1973-y1978;   id Science;   run;   %plotit(data=Results, datatype=corresp, plotvars=Dim1 Dim2)  

  Number of Ph.D's Awarded from 1973 to 1978   The CORRESP Procedure   Inertia and Chi-Square Decomposition   Singular  Principal     Chi-           Cumulative   Value    Inertia   Square  Percent     Percent     19   38   57   76   95   ----+----+----+----+----+---   0.05845    0.00342  368.653    96.04       96.04  *************************   0.00861    0.00007    7.995     2.08       98.12  *   0.00694    0.00005    5.197     1.35       99.48   0.00414    0.00002    1.852     0.48       99.96   0.00122    0.00000    0.160     0.04      100.00   Total    0.00356  383.856   100.00   Degrees of Freedom = 25  

Figure 24.1: Inertia and Chi-Square Decomposition

The total chi-square statistic, which is a measure of the association between the rows and columns in the full five dimensions of the (centered) table, is 383.856. The maximum number of dimensions (or axes) is the minimum of the number of rows and columns, minus one. Over 96% of the total chi-square and inertia is explained by the first dimension, indicating that the association between the row and column categories is essentially one dimensional. The plot shows how the number of doctorates in the different areas changes over time. The plot shows that the number of doctorates in the behavioral sciences is associated with later years, and the number of doctorates in mathematics and engineering is associated with earlier years. This is consistent with the data which shows that number of doctorates in the behavioral sciences is increasing, the number of doctorates in every other discipline is decreasing , and the rate of decrease is greatest for mathematics and engineering.

Figure 24.2: Plot of Dimension 1 versus Dimension 2 for Ph.D. Data