• Know how to summarize categorical data using contingency tables
• Understand how contingency tables answers different questions about the data
• Develop an understanding of different ways on visualizing categorical data
• Activity: Interpret row and column proportions

For Numerical Variables

• Measures of Central Tendency
  • Mean (Average), Median, and Mode
• Measures of Dispersion (Spread)
  • Range, Variance, Standard Deviation, Interquartile Range (IQR)

For Categorical Variables

• Frequency
• Relative Frequency (Proportion)
• Percentage

The Titanic Data Matrix

The number of observations in the data set is \(2207\) passengers.

Contingency Table:

To answer this question we examine the row proportions:

• Survived 1st class passengers: \(\frac{201}{711} = 0.283\)
• Survived 2nd class passengers: \(\frac{118}{711} = 0.166\)
• Survived 3rd class passengers: \(\frac{181}{711} = 0.255\)
• Survived crew: \(\frac{211}{711} = 0.297\)

There appears to be almost equal proportion of passenger class who survived. Note that this is only considering cases who survived.

Contingency Table:

To answer this question we examine the column proportions:

• 1st class passengers who survived: \(\frac{201}{324} = 0.620\)
• 2nd class passengers who survived: \(\frac{118}{284} = 0.415\)
• 3rd class passengers who survived: \(\frac{181}{709} = 0.255\)
• Crew who survived: \(\frac{211}{890} = 0.237\)

The disproportionate survival of 1st class passengers suggests a relationship between class and survival.

• Bar Plots: Show distributions of categorical variables
  • Categories can be arranged in any order
  • Useful for nominal and ordinal data
• Histograms: Show distributions of numerical variables
  • The x-axis is a number line, so the order is fixed
  • Used for continuous or discrete numerical data

Features:

• Represents discrete categories
• Bar height corresponds to frequency or value
• Can be vertical or horizontal

Types of Bar Plots:

• Stacked bar plot: Graphical display of contingency table information, for counts.

• Side-by-side bar plot: Displays the same information by placing bars next to, instead of on top of, each other.

• Standardized stacked bar plot: Graphical display of contingency table information, for proportions.

Features:

• Each tile represents a combination of categories from two or more categorical variables.
• The area of each tile is proportional to the frequency or probability of that combination.
• Provides an intuitive way to analyze relationships, such as independence or associations between categorical variables.

Features:

• Each slice represents a category’s proportion relative to the whole dataset.
• The total sum of all slices equals 100%.
• Useful for showing part-to-whole relationships.