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What are the differences between side-by-side bar graphs and segmented bar graphs?
Side-by-side: Separate bars for each category. | Segmented: Segments within a single bar representing different categories.
What are the differences between bar graphs and mosaic plots?
Bar Graphs: Use height to represent frequency or proportion. | Mosaic Plots: Use area to represent joint relative frequency.
What are the differences between counts and joint relative frequencies in two-way tables?
Counts: Show the number of data points in each category. | Joint Relative Frequencies: Show the proportion of the total sample in each category.
Explain the concept of association between two categorical variables.
Association means the variables are dependent or correlated. Significant differences in the heights/widths of segments across categories suggest an association.
Explain the purpose of using two-way tables.
Two-way tables organize data from two categorical variables, displaying how individuals are distributed across different categories.
Explain how joint relative frequencies are used in two-way tables.
They show the proportion of the total sample that falls into each combination of categories, making it easier to compare different groups.
Explain the key purpose of using side-by-side bar graphs.
Side-by-side bar graphs visually compare the proportions of data points in each category of one variable across the categories of the other variable.
Explain the key purpose of using segmented bar graphs.
Segmented bar graphs are used to compare proportions within each category of one variable across the categories of the other variable, displayed as segments within a single bar.
Explain how mosaic plots represent joint relative frequencies.
Mosaic plots divide the plot into rectangles, where the area of each rectangle is proportional to the joint relative frequency of each combination of categories.
What is the definition of a two-way table (contingency table)?
A grid that organizes data from two categorical variables, showing counts or percentages for each combination of categories.
What are joint relative frequencies?
Proportions of the total sample that fall into each combination of categories in a two-way table.
What is a side-by-side bar graph?
Two separate bar charts displayed next to each other, one for each categorical variable, allowing visual comparison of proportions.
What is a segmented bar graph?
A bar graph that displays proportions of data points as segments within a single bar, useful for comparing proportions within each category.
What is a mosaic plot?
A plot divided into rectangles, where the area of each rectangle is proportional to the joint relative frequency of each combination of categories.