# Contingency Test

### Example Homework Problem:

When polled about a proposition on an upcoming ballot, the responses of men and women were as follows:

Agree | Undecided | Disagree | |

Men: | 70 | 25 | 40 |

Women: | 30 | 20 | 25 |

Do men and women differ in their attitudes towards this issue (alpha = .05)?

If you would like help with the hand-written work for this problem, click here.

In *Stats Homework* pull down the **Analyze** menu, choose **Analysis of Frequency or Proportion**, and then choose **Contingency Table**.

#### Manually Entering Frequency Data

In the first dialog, enter the names of both variables, and the number of levels of each. Then click all the output options and click **Next Step**.

Next, you will enter the column and row headings. When finished, click **Next Step**.

Finally, you will enter the frequencies for each cell in your contingency table. When finished, click the **Compute** button.

#### Basic Output

**Contingency Table**. This table summarizes all of the observed and expected frequencies, including the row and column totals.

**Cell Statistics**. This table lists the observed and expected frequencies for each cell. In addition, this table presents each cell’s contribution to the Chi Square statistic, and the total Chi Square statistic.

**Inferential Statistics**. This table presents the Chi Square statistic (3.13), its *df* (2), and the *p* value for the obtained value of Chi Square (.21).

#### Optional Output

**Effect Size Statistics**. This table includes the effect size statistic, Cramer’s V (.12) and Cohen’s w (.12). If you analyze a 2 X 2 contingency table, the Phi coefficient will be displayed instead of Cramer’s V.

**Critical Values**. These are the values from a statistical table of critical values for the Chi Square test. In our case, we are conducting a test with alpha = .05. So, we would compare the value of our obtained Chi Square (3.13) to 5.991.

**Supplemental Statistics**. This table lists the contribution that each cell made toward the Chi-Squared statistic. This can be used to double-check your hand-written solution to this problem.

**Bar Chart**. This chart graphically illustrates the frequencies analyzed in the contingency test. It can display frequencies and relative frequencies, and it includes a number of options for reversing the variables and changing the appearance of the chart.

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