# The CORRESP Procedure

### Displayed Output

The display options control the amount of displayed output. By default, the following information is displayed:

• an inertia and chi-square decomposition table including the total inertia, the principal inertias of each dimension (eigenvalues), the singular values (square roots of the eigenvalues), each dimension’s percentage of inertia, a horizontal bar chart of the percentages, and the total chi-square with its degrees of freedom and decomposition. The chi-square statistics and degrees of freedom are valid only when the constructed table is an ordinary two-way contingency table.

• the coordinates of the rows and columns on the dimensions

• the mass, relative contribution to the total inertia, and quality of representation in the DIMENS=n dimensional display of each row and column

• the squared cosines of the angles between each axis and a vector from the origin to the point

• the partial contributions of each point to each dimension’s inertia

• the table of indicators of which points best explain the inertia of each dimension

Specific display options and combinations of options display output as follows.

If you specify the OBSERVED or ALL option and you do not specify PRINT=PERCENT, PROC CORRESP displays the following:

• the contingency table, including the row and column marginal frequencies; or with BINARY, the binary table; or the Burt table in MCA

• the supplementary rows

• the supplementary columns

If you specify the OBSERVED or ALL option, with the PRINT=PERCENT or PRINT=BOTH option, PROC CORRESP displays the following:

• the contingency table or Burt table in MCA, scaled to percentages, including the row and column marginal percentages

• the supplementary rows, scaled to percentages

• the supplementary columns, scaled to percentages

If you specify the EXPECTED or ALL option and you do not specify PRINT=PERCENT, PROC CORRESP displays the product of the row marginals and the column marginals divided by the grand frequency of the observed frequency table. For ordinary two-way contingency tables, these are the expected frequencies under the hypothesis of row and column independence.

If you specify the EXPECTED or ALL option with the PRINT=PERCENT or PRINT=BOTH option, PROC CORRESP displays the product of the row marginals and the column marginals divided by the grand frequency of the observed percentages table. For ordinary two-way contingency tables, these are the expected percentages under the hypothesis of row and column independence.

If you specify the DEVIATION or ALL option and you do not specify PRINT=PERCENT, PROC CORRESP displays the observed minus expected frequencies. For ordinary two-way contingency tables, these are the expected frequencies under the hypothesis of row and column independence.

If you specify the DEVIATION or ALL option with the PRINT=PERCENT or PRINT=BOTH option, PROC CORRESP displays the observed minus expected percentages. For ordinary two-way contingency tables, these are the expected percentages under the hypothesis of row and column independence.

If you specify the CELLCHI2 or ALL option and you do not specify PRINT=PERCENT, PROC CORRESP displays contributions to the total chi-square test statistic, including the row and column marginals. The intersection of the marginals contains the total chi-square statistic.

If you specify the CELLCHI2 or ALL option with the PRINT=PERCENT or the PRINT=BOTH option, PROC CORRESP displays contributions to the total chi-square, scaled to percentages, including the row and column marginals.

If you specify the RP or ALL option and you do not specify PRINT=PERCENT, PROC CORRESP displays the row profiles and the supplementary row profiles.

If you specify the RP or ALL option with the PRINT=PERCENT or the PRINT=BOTH option, PROC CORRESP displays the row profiles (scaled to percentages) and the supplementary row profiles (scaled to percentages).

If you specify the CP or ALL option and you do not specify PRINT=PERCENT, PROC CORRESP displays the column profiles and the supplementary column profiles.

If you specify the CP or ALL option with the PRINT=PERCENT or PRINT=BOTH option, PROC CORRESP displays the column profiles (scaled to percentages) and the supplementary column profiles (scaled to percentages).

If you do not specify the NOPRINT option, PROC CORRESP displays the inertia and chi-square decomposition table. This includes the nonzero singular values of the contingency table (or, in MCA, the binary matrix used to create the Burt table), the nonzero principal inertias (or eigenvalues) for each dimension, the total inertia, the total chi-square, the decomposition of chi-square, the chi-square degrees of freedom (appropriate only when the table is an ordinary two-way contingency table), the percentage of the total chi-square and inertia for each dimension, and a bar chart of the percentages.

If you specify the MCA option and you do not specify the NOPRINT option, PROC CORRESP displays the adjusted inertias. This includes the nonzero adjusted inertias, percentages, cumulative percentages, and a bar chart of the percentages.

If you do not specify the NOROW, NOPRINT, or MCA option, PROC CORRESP displays the row coordinates and the supplementary row coordinates (displayed when there are supplementary row points).

If you do not specify the NOROW, NOPRINT, MCA, or SHORT option, PROC CORRESP displays the following:

• the summary statistics for the row points, including the quality of representation of the row points in the n-dimensional display, the mass, and the relative contributions to inertia

• the quality of representation of the supplementary row points in the n-dimensional display (displayed when there are supplementary row points)

• the partial contributions to inertia for the row points

• the table of indicators of which row points best explain the inertia of each dimension

• the squared cosines for the row points

• the squared cosines for the supplementary row points (displayed when there are supplementary row points)

If you do not specify the NOCOLUMN or NOPRINT option, PROC CORRESP displays the column coordinates and the supplementary column coordinates (displayed when there are supplementary column points).

If you do not specify the NOCOLUMN, NOPRINT, or SHORT option, PROC CORRESP displays the following:

• the summary statistics for the column points, including the quality of representation of the column points in the n-dimensional display, the mass, and the relative contributions to inertia for the supplementary column points

• the quality of representation of the supplementary column points in the n-dimensional display (displayed when there are supplementary column points)

• the partial contributions to inertia for the column points

• the table of indicators of which column points best explain the inertia of each dimension

• the squared cosines for the column points

• the squared cosines for the supplementary column points