Key Concepts Study Tool: Chapter 12

Key Concepts Study Tool: Chapter 12

Click on each concept below to check your understanding.

1. Analysis with Two Nominal Variables

  • Contingency tables, or cross-tabulations, are a first step to organizing data.

contingency table

2. The Chi-Square Test of Statistical Significance (X2)

  • The chi-square test is useful for determining whether a relationship exists between variables.
  • It measures the discrepancy between observed and expected values.
  • Suitable for all levels of measurement.
  • Measured with the following equation: where fo is the observed frequency of the cell, and fe is the expected frequency of the cell.)

chi-square

3. Calculating Chi-Square

  1. Compute row and column totals, or marginals.
  2. For each cell, multiply the row and column marginal, then divide by the total number of people in the sample (n) to determine the distribution of highest probability. These are the expected values.

    expected frequency

  3. Subtract expected cell frequencies from observed cell frequencies. (fo – fe)
  4. Square that number and divide it by the expected frequency.

    expected frequency

  5. Sum the product of these calculations. This is your observed chi-square value.

    expected frequency

  6. Assess the statistical significance using the chi-square chart; df = (r – 1)(c – 1).

4. Measures of Association for Nominal Data

  • Chi-square indicates whether a relationship is statistically significant, but it doesn’t indicate anything about the strength of the association. Measures of association provide information regarding the strength of a relationship between variables.
  • The level of measurement of a variable determines which measure of association is appropriate.
  • For nominal level variables, the commonly used measures of association include phi (used for 2×2 tables), Cramer’s V (used for tables larger than 2×2), and lambda (used to determine how much our ability to predict one variable [y] is improved by taking another variable [x] into account).

5. How to Calculate Phi and Cramer’s V

  1. Calculate the observed chi-square value.
  2. For phi, divide chi-square by the number of observations. Then take the square root.

    phi

  3. For Cramer’s V, divide chi-square by the number of observations, multiplied by either the number of rows minus 1 or by the number of columns minus 1 (use the smaller of the two values). Then take the square root.

    cramer's v

    phi association

6. How to Calculate Lambda

  1. Predict the mode for the whole sample. Subtract n from the amount of observations in the modal categories for the dependent variable. The lowest number gives you E1.
  2. For each category of the independent variable, predict the mode. Subtract n from the amount of observations in the modal category for each category of the independent variable. Sum these amounts. This is E2.
  3. Calculate lambda as:

    phi association

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