Question

The results of a survey show that the 518 respondents may be categorized as 0 0 Protestant - Republicans Protestant - Democrats Protestant - Independents Catholic - Republicans Catholic - Democrats Catholic-Independents Jewish - Republicans Jewish - Democrat Jewish - Independents \begin{tabular}{c} 126 \\ 71 \\ 19 \\ 61 \\ 93 \\ 14 \\ 38 \\ 69 \\ 27 \\ \hline \end{tabular} 38 6 Given this data construct a contingency table.

Short answer

The contingency table for the given data is: | | Republican | Democrat | Independent | Total | |----------------|------------|----------|-------------|-------| | Protestant | 126 | 71 | 19 | 216 | | Catholic | 61 | 93 | 14 | 168 | | Jewish | 38 | 69 | 27 | 134 | | **Total** | 225 | 233 | 60 | **518**|

Step-by-step solution

Create a Contingency Table

A contingency table is a table that displays the frequencies of data in different categories. In this case, the categories are the different religions and political affiliations. We can create a contingency table by writing the given data in the format of a table with rows representing religions and columns representing political affiliations.

Label Rows and Columns

Our table will have 3 rows for the religions (Protestant, Catholic, and Jewish) and 3 columns for the political affiliations (Republican, Democrat, and Independent), plus an additional row and column for the totals.

Fill in the Table with Given Data

Now that we have our rows and columns labeled, we can fill in the table with the data provided in the survey results: - Protestant - Republican: 126 - Protestant - Democrat: 71 - Protestant - Independent: 19 - Catholic - Republican: 61 - Catholic - Democrat: 93 - Catholic - Independent: 14 - Jewish - Republican: 38 - Jewish - Democrat: 69 - Jewish - Independent: 27 We then add the totals for each row and column in the last row and column. Here is the completed contingency table: | | Republican | Democrat | Independent | Total | |----------------|------------|----------|-------------|-------| | Protestant | 126 | 71 | 19 | 216 | | Catholic | 61 | 93 | 14 | 168 | | Jewish | 38 | 69 | 27 | 134 | | **Total** | 225 | 233 | 60 | **518**|

Key concepts

Survey Data Analysis

Survey data analysis is an essential process for extracting meaningful insights from responses collected during surveys. These insights can inform decision-making and understanding of specific populations or phenomena. The survey data, often comprising multiple choice or categorical responses, needs to be organized for clarity and comprehensibility.

When analyzing survey data, researchers often begin by summarizing the gathered information using various descriptive statistics, like frequencies and percentages. One common technique is to organize the data into a contingency table, which helps detect patterns and relationships between different categorical variables. For example, survey results showing preferences or characteristics of respondents, like the exercise on religious and political affiliations, can be cross-tabulated to reveal how these affiliations interact.

Improving comprehension of survey analysis can involve simplifying complex data into visual formats like graphs or tables, ensuring that important trends and comparisons are made clear. Clear labels and a logical structure can significantly aid interpretation, making it easier for students to grasp the underlying patterns and conclusions.

Categorical Data Representation

Categorical data representation refers to the methods used to visualize or summarize data that can be divided into groups or categories. Unlike numerical data, categorical data represent characteristics such as religion, gender, or political preference—and are not inherently numerical. Methods of representation include tables, charts, and graphs that aid in summarizing and analyzing the data.

In the context of our exercise, the categorical data includes the respondents' religious and political affiliations. To effectively represent this data, one would organize it in a way that allows comparisons and pattern recognition. A contingency table serves this very purpose; it arranges categorical data into rows and columns, facilitating an understanding of the relationship between variables.

A clear explanation and appropriate labeling of these categories are crucial when developing instructional content. Including visual aids such as pie charts or bar graphs along with the contingency table can further improve understanding by providing a visual summary of the data's distribution.

Cross Tabulation

Cross tabulation, commonly referred to as 'crosstab', is a statistical tool used to analyze the relationship between multiple categorical variables. It displays the frequency distribution of variables simultaneously and can highlight significant interactions between them. This method is invaluable for survey data analysis, where it's essential to explore how different categories (like religious beliefs and political affiliations) relate to each other.

For the survey results in the exercise, cross tabulation is used to organize the data into a contingency table where one axis represents religious categories, and the other represents political affiliations. By filling in the number of respondents who fall into each intersection of these categories, patterns may emerge that provide valuable insights. For example, the crosstab might reveal a higher number of Protestant Republicans than Protestant Democrats, indicating a possible trend.

To enhance understanding, explanations of crosstab outcomes should focus on meaningful conclusions derived from the data. Highlighting significant results and providing interpretations can make the information more accessible, enabling students to quickly understand the practical implications of the findings.