Analysis of contingency for Simple Correspondence Analysis

Find definitions and interpretation for every statistic that is provided in the analysis of contingency table for simple correspondence analysis.

Axis

Minitab calculates each principle axis, which is also called a principal component. Minitab orders the principal components by how much they account for the total inertia. The first principal component (axis) accounts for the most inertia. The second principal component (axis) accounts for most of the remaining inertia, and so on.

Interpretation

Use the principle axes to evaluate which components account for most of the variability in the data.

Analysis of Contingency Table Axis Inertia Proportion Cumulative 1 0.0391 0.4720 0.4720 2 0.0304 0.3666 0.8385 3 0.0109 0.1311 0.9697 4 0.0025 0.0303 1.0000 Total 0.0829

This table summarizes the decomposition of a 10 x 5 contingency table into 4 principal axes, or components. The total inertia explained by the four components is 0.0829. Of the total inertia, the first component accounts for 47.2% of the inertia, the second component accounts for 36.66% of the inertia, and so on. Ideally, the first one, two, or three components account for most of the total inertia.

Inertia

Cell inertia is the chi-squared value in the cell divided by the total frequency for the contingency table. The row inertia is the sum of the cell inertias for the row. The column inertia is the sum of the cell inertias for the column. The sum of all the cell inertias is the total inertia, or simply the inertia.

Interpretation

Use inertia to assess associations between categories and contributions to variation in the data. Higher values generally indicate a stronger association and greater variation. You can also use inertia to determine which principal components account for most of the deviation from the expected values in the data.

Analysis of Contingency Table Axis Inertia Proportion Cumulative 1 0.0391 0.4720 0.4720 2 0.0304 0.3666 0.8385 3 0.0109 0.1311 0.9697 4 0.0025 0.0303 1.0000 Total 0.0829

The Analysis of Contingency table shows the decomposition of the total inertia. The column labeled Inertia contains the chi-squared / n value accounted for by each principal component, also called a principal axis. These results show the decomposition of a 10 x 5 contingency table into 4 components. The total inertia explained by the four components is 0.0829. Of the total inertia, the first component accounts for 47.2% of the inertia, the second component accounts for 36.66% of the inertia, and so on. Ideally, the first one, two, or three components account for most of the total inertia.

Proportion, Cumulative, and Histogram

The proportion indicates the proportion of the total inertia (the inertia explained by all the components) that each principal component (axis) explains. Minitab displays the components in order of their proportions, from greatest to least. Each proportion is visually represented in the histogram.

The cumulative proportion indicates the cumulative sum of the proportions as components (axes) are added.

Interpretation

Use the proportion and cumulative proportion to help determine how many components are sufficient to explain most of the total inertia. Ideally, two or three components account for most of the total inertia and are more important than the other components.

Analysis of Contingency Table Axis Inertia Proportion Cumulative 1 0.0391 0.4720 0.4720 2 0.0304 0.3666 0.8385 3 0.0109 0.1311 0.9697 4 0.0025 0.0303 1.0000 Total 0.0829

The Analysis of Contingency table shows the decomposition of the total inertia. The column labeled Inertia contains the chi-squared / n value accounted for by each principal component, also called a principal axis. These results show the decomposition of a 10 x 5 contingency table into 4 components. The total inertia explained by the four components is 0.0829. Of the total inertia, the first component accounts for 47.2% of the inertia, the second component accounts for 36.66% of the inertia, and so on.

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