1.1 ANALYZING CATEGORICAL DATA

FREQUENCY TABLE VS. RELATIVE FREQUENCY TABLE

Frequency Table  Table that displays the count (frequency) of observations in each category or class Relative Frequency Table  Table that shows the percents (relative frequencies) of observations in each category or class FREQUENCY TABLE VS. RELATIVE FREQUENCY TABLE

 The counts should add up to the total in the frequency table  In a relative frequency table all of the counts should at up to 1 or 100%.  So what happened in the previous example? ROUND OFF ERROR

 Charts take a long time to read so bar graphs or pie graphs are used to display the distribution of a categorical variable.  In a bar graph, you want to make sure that all of the widths are the same.  You also want to make sure you label both axes  In a pie graph all of the percents need to be related. BAR GRAPHS VS. PIE GRAPHS

FAVORITE COLOR

 Where two categorical variables are described TWO- WAY TABLE

 One of the categorical variables in a two-way table of counts is the distribution of values of that variable among all individuals described by the table. MARGINAL DISTRIBUTION

MARGINAL DISTRIBUTIONS FOR OPINION

CHECK YOUR UNDERSTANDING

 Describes the values of that variable among individuals who have a specific value of another variable  There is a separate conditional distribution for each value of the other variables CONDITIONAL DISTRIBUTION

Conditional distribution of opinion among women

FractionPercent Almost no chance Some chance A good chance Almost certain CONDITIONAL DISTRIBUTION OF OPINION AMONG MEN

FractionPercent Almost no chance98/ % Some chance286/ % / % A good chance758/ % Almost certain597/ % CONDITIONAL DISTRIBUTION OF OPINION AMONG MEN

 Graph used to compare the distribution of a categorical variable in each or several groups  For each group, there is a single bar with “segments” that correspond to the different values of the categorical variable  The height of each segment is determined by the percent of individuals in the group with that value.  Each bar has a total height of 100%. SEGMENTED BAR GRAPH

 Graph used to compare the distribution of a categorical variable in each of several groups.  For each value of the categorical variable, there is a bar corresponding to each group  The height of each bar is determined by the count or percent of individuals in the group with that value. SIDE-BY-SIDE GRAPH

 We say that there is an association between two variables if knowing the value of one variable helps predict the value of the other. If knowing the value of one variable does not help you predict the value of the other, then there is no association between the variables. ASSOCIATION