Descriptive statistics: Outcome = categorical levels

These statistics are used for analyzing research results when the levels of the outcome variable are categorical (discrete, non-continuous). The main calculation is frequency of occurrence or observed frequencies, by category (counts by outcome level). Then, the frequencies are transformed into percentages for final presentation.

Contingency table

The first step in analyzing outcomes that are categorical (e.g., Yes vs. No, Low vs. Medium vs. High) is to enter the frequencies (counts) in a contingency table. A contingency table is a grid or matrix of cells, each one representing a value or level of each variable in the study. Example of a contingency table:

    Independent variable (predictor)
Dependent variable
(outcome)
Level 1 Level 2
Level 1
A B

C

D
E F
Level 2
Level 3

There can be as many rows and columns as you need. Each little box is called a cell. The independent or predictor variable is shown at the top, with the outcome along the side.

Letters (A, B, ....) = counts in respective categories

The following example shows the results of a poll of college (lower division vs. upper division) students' preferences for quarter versus semester terms.

Step 1. Create a table for the data. Being in the upper lefthand cell indicates a lower division student who prefers the quarter system.

The table is called a contingency table because being in a particular cell is contingent upon the levels of the independent and dependent variables.

Step 2. Enter the appropriate numbers in the cells. In this example, 11 of the lower division students prefer the quarter system (term), 3 prefer semester, etc.
Step 3. Sum all the rows and columns. These are called the marginal totals. The grand total (N) is 26.
Here is the table (or matrix) with the cells and margins labeled. In this example, N = 26, Lower division n = 14, Upper division n = 12 (use lower case to indicate sample size of the subgroups).
Percentages
 

Percentages are a good way to summarize the contingency table data. Change the counts to percents.

  1. 11/14 = .786 = 78.6%
  2. 4/12 = .333 = 33.3%
  3. 3/14 = .214 = 21.4%
  4. 8/12 = .667 = 66.7%

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