Two-Way Table vs Frequency Table
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Two-way table
Graphs and displays
A two-way table displays counts for two categorical variables at once, with one variable's categories as rows and the other's as columns.
A two-way table, also called a contingency table, cross-classifies each individual by two categorical variables to show where the categories overlap. Row and column totals, called marginal totals, let you compute conditional and joint proportions to compare groups. For example, a table of 100 students by grade level in rows and whether they play a sport in columns reveals the sport rate within each grade. Such a table is the input to a chi-square test of independence or homogeneity, through its expected counts.
Frequency table
Graphs and displays
A frequency table lists the categories or value ranges of a variable alongside the count of observations in each.
A frequency table organizes raw data by showing how many observations fall into each category or class. For example, a table of favorite colors might show red 12, blue 8, and green 5. Adding a column that divides each count by the total turns it into relative frequencies. Here the total is , so red's relative frequency is .