Lesson 2: Working with Categorical Data

side-by-side bar chart

bar chart that groups the bars of two or more conditional distributions side by side

contingency table

table showing counts and sometimes percentages of individuals falling into named categories on two or more variables

contingency tables are used to…

reveal possible patterns in one variable that may be contingent on the category of the other

categorical variable

variable that names categories

categories can be named using…

words or numbers

mosaic plot

special kind of segmented bar chart whose bars’ widths display the marginal distribution of the variable represented by the bars

Simpson’s Paradox

averages that are taken across different groups can appear to contradict the overall averages

the distribution of a variable gives…

the possible values of the variable and the relative frequency of each value

conditional distribution

distribution of a variable restricting the who in order to consider only a smaller group of individuals

categorical data condition

condition that data used to create frequency tables, relative frequency tables, bar charts, pie charts, contingency tables, segmented bar charts, side-by-side bar charts, and mosaic plots must be non-overlapping categorical data

frequency table

table that lists the categories of a categorical variable and gives the number of observations in each category

simulation

random re-enactment of data collection under one or more assumptions

if real data look very different from simulated data, then…

the assumptions are called into question

variables are said to be independent if…

the conditional distribution of one variable is the same for all categories of another variable

if the variables are independent…

there is no association between them

if the variables are not independent…

there is an association between the variables

bar chart

graph consisting of bars whose area represents the count of observations for each category of a categorical variable

a bar chart should always have…

gaps separating the bars

relative frequency table

table that lists the categories of a categorical variable and gives the relative frequency of each category

area principle

principle which states that the area occupied by a part of a graph should correspond to the amount of data it represents

pie chart

circle sliced into pieces whose sizes are proportional to the fraction of the whole in each category

relative frequency

ratio of the number of observations in a category to the total number of observations

a relative frequency is represented as…

a fraction or a percentage

segmented bar chart

bar chart whose bars are stacked on top of one another in a vertical graph or are lined up side by side in a horizontal graph

a segmented bar chart usually shows…

relative frequencies so that the distribution of the categorical variable can be more easily compared between different groups

marginal distribution

distribution of values for individual variables in a contingency table

for a two-way table, the counts or percentages are the…

totals found in the margins (last row of the column) of the table