Chapter 2 Displaying and Describing Categorical Data Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 1 2 1 Summarizing and Displaying a Single Categorical Variable Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 2 Types of Univariate Categorical Displays Frequency and Relative Frequency Table Bar Chart Pareto Chart Pie Chart Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 3 Frequency Tables The name of each category and the number of observations in each category Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 4 Relative Frequency Tables Similar but gives the percentages instead of counts for each category Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 5 Relative Frequency vs Percentage The table on the previous page may be called a relative frequency table but it is displaying percentages not relative frequencies Percentages will range from 0 to 100 Relative frequencies will range from 0 to 1 00 Class First Second Third Crew Total Chapter02 Presentation 0115 Frequency Relative Frequency 325 285 706 885 2201 0 1477 0 1295 0 3208 0 4021 1 000 14 77 12 95 32 08 40 21 100 0 Copyright 2014 2012 2009 Pearson Education Inc 6 Frequency Bar Chart A graphical display of the data in a frequency table Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 7 Relative Frequency Bar Chart A graphical display of the data in a relative frequency table Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 8 Column Charts from Excel Excel can easily display both frequency and relative frequency bar charts See the file Ch03 Titanic Passengers xlsx Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 9 Pareto Chart A bar chart with the bars put in order from the most frequently occurring category on the left to least frequently occurring category on the right is called a Pareto Chart Typically a Pareto Chart has a frequency scale on the left and a relative frequency scale on the right Sometimes a Pareto Chart contains a line above the bars indicating cumulative frequency and cumulative relative frequency Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 10 Example Pareto Chart 168 Late Arrivals to Work Chapter02 Presentation 0115 http en wikipedia org wiki Pareto chart Copyright 2014 2012 2009 Pearson Education Inc 11 Pie Charts Another common method of displaying categorical data Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 12 Pie Charts from Excel Both frequency and relative frequency pie charts can be generated If your audience is colorblind these images will be difficult to make sense of Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 13 What s Wrong Here This pie chart of the percentage of high school students who engage in specified dangerous behaviors has a problem Can you see it Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 14 2 2 Exploring the Relationship Between Two Categorical Variables Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 15 Types of Bivariate Categorical Data Displays Contingency Tables Side by Side Pie Charts Segmented Bar Charts Mosaic Plot Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 16 Contingency Tables A contingency table allows us to look at two categorical variables together Example we can examine the class of ticket and whether a person survived the Titanic Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 17 Contingency Tables cont Each cell of the table gives the count for a combination of values of the two variables Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 18 Contingency Tables cont The margins of the table both on the right and on the bottom give totals and the frequency distributions for each of the variables Each frequency distribution is called a marginal distribution of its respective variable The marginal distribution of Survival is Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 19 Contingency Tables cont The marginal distribution of Class is Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 20 Conditional Distributions A conditional distribution shows the distribution of one variable for just the individuals who satisfy some condition on another variable The following is the conditional distribution of Survival conditional on having been a crew member 24 76 100 Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 21 Conditional Distributions cont The following is the conditional distribution of ticket Class conditional on having survived 28 6 Chapter02 Presentation 0115 16 6 25 0 Copyright 2014 2012 2009 Pearson Education Inc 29 8 100 22 Conditional Distributions cont The following is the conditional distribution of ticket Class conditional on having died 8 2 Chapter02 Presentation 0115 11 2 35 4 Copyright 2014 2012 2009 Pearson Education Inc 45 2 100 23 Conditional Distributions cont These last two conditional distributions tell us that there is a difference in class for those who survived and those who perished This can be Third shown with pie charts ofSecond the two distributions Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc Crew on d First Third Se c Crew First 24 Conditional Distributions cont We see that the distribution of Class for the survivors is different from that of the nonsurvivors This leads us to believe that Class and Survival are associated that they are not independent The variables would be considered independent when the distribution of one variable in a contingency table is the same for all categories of the other variable Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 25 Segmented Bar Charts A segmented bar chart displays the same First information as a pie chart but in the form of bars Second First instead of circles Second Third Third Crew Crew Chapter02 Presentation 0115 Copyright 2014 2012 2009 Pearson Education Inc 26 Class Activity Groups of 2 or 3 200 adults shopping at a supermarket were asked about the highest level of education they had completed and whether or not they smoke cigarettes Results are summarized in the table on the next page Is there an association between
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