Displaying & Describing Categorical Data Chapter 3

Objective Look at different types of data and checking a condition before plugging ahead. Writing clear explanations in context. Independence and the importance to statistics. Simpson’s Paradox: think deeply or be mislead!!

Frequency Tables Number 1 Rule of Data Analysis? Draw a picture!!! Frequency Table: records totals and categories names!!

Frequency Tables Counts are useful but sometimes we want to know the fraction or proportion of data in each category. These counts are expressed as percentages. Relative Frequency Table: displays percentages rather than counts

Frequency Tables Both these types of tables describe the distribution across categories.

Area Principle The area principle says that the area occupied by a part of the graph should correspond to the magnitude of the value it represents. Violations of this principle are a common way to lie with statistics.

Bar Charts A bar chart displays the distribution of a categorical variable, showing the counts for each category next to each other for easy comparison.

Bar Charts If we are interested in the relative proportion we could replace the counts with percentages and use a relative frequency bar chart.

Pie Charts Pie Charts show the whole group of cases as a circle. They slice the circle into pieces whose sizes are proportional to the fraction of the whole in each category.

What should you pick!! Think before you draw!! Always check the categorical condition. If you want to make a relative frequency bar chart or a pie chart, make sure the categories do not overlap. If they overlap you can still make the chart but your percentages will not add up to 100.

Contingency Tables To look at two categorical variables together, we often arrange the counts in a two-way table. A contingency table displays counts and, sometimes percentages of individuals falling into named categories on two or more variables. The table categorizes the individuals on all variables at once to reveal possible patterns in one variable that may be contingent on the category of the other.

Contingency Tables In a contingency table, the distribution of either variable alone is called the marginal distribution. The counts or percentages are the totals found in the margins (last row or column) of the table.

Example In Jan 2007, a Gallup poll asked 1008 Americans age 18 and over whether they planned to watch the upcoming Super Bowl. The pollster also asked those who planned to watch whether they were looking forward more to seeing the football game or the commercials. The results are summarized in the table

Example What’s the marginal distribution of the responses? MaleFemaleTotal Game Commercials Won’t Watch Total

Conditional Distributions The distribution of a variable restricting the “Who” to consider only a smaller group of individuals is called a conditional distribution. In a contingency table, when the distribution of one variable is the same for all categories of another, we say that the variables are independent.

Conditional Distributions How do the conditional distributions of interest in the commercials differ for men and women?

Example Does it seem that there’s an association between interest in Super Bowl TV coverage and a person’s sex?

Segmented Bar Charts Segmented Bar Charts treat each bar as the “whole” and divides it proportionally into segments corresponding to the percentage in each group.

Simpson’s Paradox When averages are taken across different groups, they can appear to contradict the overall averages.

Example It’s the last inning of the important game. Your team is a run down with bases loaded and two outs. The pitcher is due up, so you’ll be sending in a pinch hitter. There are 2 batters available on the bench. Whom should you send to bat? PlayerOverallVs LHPVs RHP Wade33 for for 815 for 22 Lee45 for for 3233 for 119