A survey of commercial buildings served by the Cincinnati...

A survey of commercial buildings served by the Cincinnati Gas \& Electric Company asked what main heating fuel was used and what year the building was constructed. A partial crosstabulation of the findings follows. a. Complete the crosstabulation by showing the row totals and column totals. b. Show the frequency distributions for year constructed and for fuel type. c. Prepare a crosstabulation showing column percentages. d. Prepare a crosstabulation showing row percentages. e. Comment on the relationship between year constructed and fuel type.

A survey of commercial buildings served by the Cincinnati Gas \& Electric Company asked what main heating fuel was used and what year the building was constructed. A partial crosstabulation of the findings follows.
a. Complete the crosstabulation by showing the row totals and column totals.
b. Show the frequency distributions for year constructed and for fuel type.
c. Prepare a crosstabulation showing column percentages.
d. Prepare a crosstabulation showing row percentages.
e. Comment on the relationship between year constructed and fuel type.

Key Concepts

Crosstabulation

A crosstabulation is a statistical tool that displays the frequency distribution of variables in a matrix format, showing how the categories of one variable relate to the categories of another. It is used to analyze the pattern of relationships between categorical variables and can be extended to include summary statistics such as percentages along rows or columns.

Marginal Totals

Marginal totals refer to the sums obtained at the end of rows or columns in a crosstabulation. They provide the overall frequencies for each category of the variables, and are essential for understanding the distribution of each individual variable within the dataset.

Frequency Distribution

A frequency distribution is a summary that shows the number of observations within each category or interval of a variable. This distribution helps in identifying trends and patterns in the data by illustrating how frequently each category or group appears in the dataset.

Column Percentages

Column percentages are calculated by dividing the frequency count in each cell by the total frequency for its respective column and then multiplying by 100. This method allows for the comparison of how different categories of the row variable contribute to each category of the column variable, providing insight into the relationship from the column perspective.

Row Percentages

Row percentages are computed by dividing the frequency count in each cell by the total frequency for its respective row and then multiplying by 100. This approach helps in understanding how each category of the column variable is distributed within each category of the row variable, offering a row-wise perspective on the data distribution.

Association Analysis

Association analysis involves examining the crosstabulated data to determine if there is a relationship or dependency between the categorical variables. By comparing the frequency counts, the corresponding percentages (both row and column), and possibly employing statistical tests, one can assess whether the distribution of one variable is influenced by the other.

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