The "In the eye of the beholder" graphic shows two circle...

The "In the eye of the beholder" graphic shows two circle graphs, each with four sections. This same information could be represented in the form of a $2 \times 4$ contingency table of two qualitative variables. a. Identify the population and name the two variables. b. Construct the contingency table using entries of percentages based on row totals.

The "In the eye of the beholder" graphic shows two circle graphs, each with four sections. This same information could be represented in the form of a $2 \times 4$ contingency table of two qualitative variables.
a. Identify the population and name the two variables.
b. Construct the contingency table using entries of percentages based on row totals.

Key Concepts

Row Percentages

Row percentages refer to the calculation where each entry in a row of a contingency table is expressed as a percentage of the total for that row. This method of normalization allows for easier comparison of the distribution of categories within each subgroup of the data.

Circle Graphs (Pie Charts)

Circle graphs, or pie charts, are visual representations that show parts of a whole as slices of a circle. They are often used to display the percentage or proportion of each category within a total, and the information from these charts can be re-organized into a contingency table format.

Population

The population in a study is the entire set of subjects or items that are being investigated. It forms the basis from which samples may be drawn or data collected, and in the context of constructing a contingency table, the population consists of all individuals for whom the categorical data is collected.

Qualitative Variables

Qualitative variables are non-numeric, categorical variables that describe qualities, characteristics, or attributes. They are used to classify subjects into distinct groups and are essential in creating the rows and columns of a contingency table, such as when comparing different groups based on non-numeric attributes.

Contingency Table

A contingency table is a two-dimensional table used to display the frequency distribution of two qualitative variables. It is a useful tool for summarizing categorical data, allowing analysts to examine the relationships or associations between the variables by organizing data into rows and columns.

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