Glossary
Association
A relationship between two variables where the value of one variable tends to change with the value of the other variable.
Example:
If students who study more tend to get higher test scores, there is an association between study time and test scores.
Bar Graph
A visual display that uses rectangular bars to represent the frequencies or relative frequencies of different categories of categorical data.
Example:
A teacher might use a bar graph to show the number of students who prefer different types of snacks in the cafeteria, with each bar's height indicating the count for that snack.
Categorical Data
Data that represents characteristics or qualities, grouping observations into distinct categories rather than numerical values.
Example:
When surveying students about their favorite color, the responses like 'blue,' 'red,' or 'green' are examples of categorical data.
Conditional Distribution
The distribution of one variable for only those observations that satisfy a specific condition or category of another variable.
Example:
To find the conditional distribution of favorite sport among females, you would only look at the 'female' row in the contingency table and calculate proportions within that row.
Contingency Table
Also known as a two-way table, it organizes data for two or more categorical variables to show the distribution of observations across their combinations.
Example:
A researcher might create a contingency table to examine if there's a relationship between a person's gender and their preferred genre of movie.
Frequency
The count of how many times a particular category or value appears in a dataset.
Example:
If 15 students in a class chose 'pizza' as their favorite food, then 15 is the frequency for the 'pizza' category.
Frequency Table
A table that lists each category of a variable and the count (frequency) of observations that fall into that category.
Example:
A frequency table for types of cars in a parking lot might list 'Sedan: 30', 'SUV: 25', 'Truck: 15'.
Independent Variables
In the context of contingency tables, two categorical variables are considered independent if the distribution of one variable is not affected by the categories of the other variable.
Example:
If the proportion of people who own a dog is the same regardless of their hair color, then dog ownership and hair color would be considered independent variables.
Marginal Distribution
The distribution of one of the categorical variables in a contingency table, found by looking at the row or column totals.
Example:
In a table showing gender and favorite sport, the marginal distribution of gender would be the total number of males and the total number of females, regardless of their sport preference.
Misleading Graphs
Graphs that are designed or presented in a way that distorts the data, leading to incorrect interpretations or conclusions.
Example:
A company might use a misleading graph with a truncated y-axis to make a small increase in sales appear much larger than it actually is.
Pie Chart
A circular graph divided into slices, where each slice represents the proportion or percentage of a category relative to the whole dataset.
Example:
A pie chart could illustrate the breakdown of a household budget, showing what proportion of income is spent on housing, food, transportation, etc.
Proportion
A part, share, or number considered in comparative relation to a whole; often expressed as a fraction or decimal between 0 and 1.
Example:
If 20 out of 100 people surveyed prefer coffee, the proportion of coffee lovers is 0.20.
Relative Frequency
The proportion or percentage of observations that fall into a particular category, calculated by dividing the frequency of the category by the total number of observations.
Example:
If 15 out of 50 students chose 'pizza', the relative frequency for pizza would be 15/50 = 0.30 or 30%.
Relative Frequency Table
A table that lists each category of a variable and the proportion or percentage (relative frequency) of observations that fall into that category.
Example:
Building on the car example, a relative frequency table would show 'Sedan: 43%', 'SUV: 36%', 'Truck: 21%'.
Truncated Graphs
Bar graphs where the vertical axis (y-axis) does not start at zero, which can exaggerate differences between categories.
Example:
A news report showing a slight rise in unemployment might use a truncated graph to make the increase look like a dramatic spike, causing undue alarm.