Chapter 3 Chapter03 Presentation 1213 Displaying and Describing Categorical Data Copyright 2009 Pearson Education Inc 1 Types of Univariate Categorical Displays Frequency and Relative Frequency Table Bar Chart Pareto Chart Pie Chart Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 2 Frequency Tables The name of each category and the number of observations in each category Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 3 Relative Frequency Tables Similar but gives the percentages instead of counts for each category Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 4 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 Frequency Relative Frequency First Second 325 285 0 1477 0 1295 14 77 12 95 Third Crew Total 706 885 2201 0 3208 0 4021 1 000 32 08 40 21 100 0 Class Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 5 Frequency Bar Chart A graphical display of the data in a frequency table Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 6 Relative Frequency Bar Chart A graphical display of the data in a relative frequency table Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 7 Output from JMP Software It is possible to get JMP software to display the frequency or the relative frequency bar chart Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 8 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 Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 9 Example Pareto Chart 168 Late Arrivals to Work http en wikipedia org wiki Pareto chart Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 10 Pie Charts Another common method of displaying categorical data Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 11 Pie Charts from JMP Both frequency and relative frequency pie charts can be generated JMPs pie charts are designed to be presented in color i e which slice is which category is difficult to determine in black and white Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 12 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 Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 13 Types of Bivariate Categorical Data Displays Contingency Tables Side by Side Pie Charts Segmented Bar Charts Mosaic Plot Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 14 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 Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 15 Contingency Tables cont Each cell of the table gives the count for a combination of values of the two variables Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 16 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 Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 17 Contingency Tables cont The marginal distribution of Class is Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 18 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 Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 19 Conditional Distributions cont The following is the conditional distribution of ticket Class conditional on having survived 28 6 Chapter03 Presentation 1213 16 6 Copyright 2009 Pearson Education Inc 25 0 29 8 100 20 Conditional Distributions cont The following is the conditional distribution of ticket Class conditional on having died 8 2 Chapter03 Presentation 1213 11 2 Copyright 2009 Pearson Education Inc 35 4 45 2 100 21 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 shown with pie charts of the two distributions Chapter03 Presentation 1213 Third Crew Third Crew Second First Copyright 2009 Pearson Education Inc First 22 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 Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 23 Segmented Bar Charts A segmented bar chart displays the same information as a pie chart but in the form of bars instead of circles First First Second Second Third Third Crew Crew Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 24 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 education level and smoking Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 25 Class Activity Smoker Nonsmoker Total High school 32 61 93 2 yr college 5 17 22 4 yr college 13 72 85 Total 50 150 200 To help you answer the question on the previous page make segmented bar charts of smokers vs non smokers on your own Chapter03 Presentation 1213 Copyright 2009 Pearson Education Inc 26 Class Activity After you have finished compare your bar charts with your teammate s If they look
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