Question

In Data 2.1 on page \(48,\) we introduce a study in which people were asked whether they agreed or disagreed with the statement that there is only one true love for each person. Is the level of a person's education related to the answer given, and if so, how? Table 2.8 gives a two-way table showing the results for these two variables. A person's education is categorized as HS (high school degree or less), Some (some college), or College (college graduate or higher). (a) Create a new two-way table with row and column totals added. (b) Find the percent who agree that there is only one true love, for each education level. Does there seem to be an association between education level and agreement with the statement? If so, in what direction? (c) What percent of people participating in the survey have a college degree or higher? (d) What percent of the people who disagree with the statement have a high school degree or less? $$\begin{array}{lccc} \hline & \text { HS } & \text { Some } & \text { College } \\\\\hline \text { Agree } & 363 & 176 & 196 \\ \text { Disagree } & 557 & 466 & 789 \\\\\text { Don't know } & 20 & 26 & 32 \\\ \hline\end{array}$$

Short answer

The two-way table with totals reveals a total of 940 individuals with HS, 668 with Some college, and 1017 with College degrees. The percent of agreement on 'one true love' is 38.7%, 26.35% and 19.28% for HS, Some College and College respectively. The percent of college graduates was 50.79%. The percent of people with HS degree or less who disagree is 37.93%.

Step-by-step solution

Create a Two-Way Table with Totals

First, calcualte the total for each category (HS, Some, College) as well as the total of people who agree, disagree, and don't know. This can be done by summing all the values in a row for categories and all the values in a column for agreement or disagreement.

Calculate Percent of Agreement for Each Education Level

Next, find the percentage of people who agree at each education level. This is done by dividing the count of people who agree at a certain education level by the total at that same level, and multiplying by 100 to get a percentage. Do this for all categories: HS, Some, College.

Calculate Percent of College Graduates

The percentage of people with a college degree or higher is found by summing the number of college graduates who agree, disagree and don't know their stance, then dividing by the total number of participants. Multiply by 100 to get the percentange.

Calculate Percent of High School Degree or Less who Disagree

Find the number of people who disagree with a high school degree or less by dividing the number of HS who disagree by the total number of people who disagree, and then multiplying by 100.

Key concepts

Education Level Association

When examining the relationship between education level and opinions, such as agreement with a statement, we look for an education level association. An association between two categorical variables exists if the distribution of one variable differs for various categories of the other. For example, In the given exercise, an association might reveal itself through differing agreement rates with the notion of 'one true love' among those with varying education levels (high school, some college, college graduate or higher).

By creating a two-way table with totals and computing the percentage of agreement at each education level, as seen in steps 1 and 2 of the solution, it's possible to notice patterns. If the percent who agree varies notably by education level, this suggests an association. Should the percentages be similar across education levels, this would imply a weaker or non-existent association. Understanding these patterns is pivotal for education policy makers, marketers, or sociologists interested in how educational attainment influences beliefs and attitudes.

Categorical Data Analysis

Categorical data, such as education level or survey responses, can be analyzed through various methods, one of which is by constructing a two-way table. This type of table is a matrix that displays the frequency of categories intersecting — in this case, the level of education and whether individuals agree that there is only one true love for each person.

The process of analyzing this table involves calculating row and column totals along with conversion of these frequencies into percentages to facilitate comparison (steps 1 and 2). By calculating the percentage of individuals in each category who agree or disagree with the statement, we can discern patterns and potential relationships between variables. Categorical data analysis helps turn raw data into informative results, thus allowing us to draw conclusions from numerical summaries rather than raw numbers that can be difficult to interpret.

Statistical Significance

In the realm of statistics, statistical significance is a critical concept that helps determine whether any observed association in the data is likely to be genuine or if it could be attributed to random chance. In steps (b) and (d), while calculating percentages gives us a good visual of potential trends, it doesn't confirm if the difference in agreement rates between education levels is significant.

To establish statistical significance, a hypothesis test could be conducted, such as the chi-square test for independence. This test compares the observed counts against expected counts if there were no association, and a low p-value (typically less than 0.05) suggests that the results are statistically significant. Although the example problem does not go this far, understanding statistical significance is crucial when interpreting data and making informed decisions.