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Explain the concept of using relative frequencies to analyze two-way tables.
Relative frequencies (joint, marginal, conditional) help reveal patterns and relationships between categorical variables in a two-way table.
Explain how marginal and conditional relative frequencies are used to determine association.
Compare conditional relative frequencies to see if they differ significantly across categories. If they do, the variables are associated; if they are roughly equal, they are independent.
Explain the purpose of side-by-side bar graphs for categorical data.
Side-by-side bar graphs visually compare the distributions of a categorical variable across different groups or categories of another variable.
Explain the purpose of segmented bar graphs for categorical data.
Segmented bar graphs show the distribution of a categorical variable within each group or category of another variable, displayed as segments within a single bar.
Explain the purpose of mosaic plots for categorical data.
Mosaic plots visualize the relationship between two categorical variables, where the area of each rectangle is proportional to the joint relative frequency of the categories.
How do you calculate Marginal Relative Frequency?
\(\frac{\text{Row or Column Total}}{\text{Grand Total}}\)
How do you calculate Conditional Relative Frequency?
\(\frac{\text{Frequency of Intersection}}{\text{Total Frequency of Given Category}}\)
What is Joint Relative Frequency?
The proportion of observations falling into a specific combination of categories.
Define Marginal Relative Frequency.
The proportion of observations falling into a specific category, regardless of other categories.
What is Conditional Relative Frequency?
The proportion of observations falling into a specific category, given that they are already in another category.
Define Association (in categorical data).
Two variables are associated if conditional relative frequencies for one variable differ across categories of the other variable.
Define Independence (in categorical data).
Two variables are independent if conditional relative frequencies for one variable are the same across all categories of the other variable.