Statistics Day 4 Displaying Categorical Data

Do Now Act question ACT #9,10,13,14

Quick review Qualitative/Categorical vs Quantitative 1) Preferred TV show 2) Number of tried cases 3) Nationality 4) Height 5) Cost 6) Race number Categorical Quantitative Categorical

Agenda ALL ABOUT DISPLAYING CATEGORICAL DATA If you did your homework and read the chapter, you will not be lost Frequency tables and Relative Frequency Bar charts Pie Charts Contingency Tables Segmented Bar Charts

Different Categorical Displays Let’s take a look at our class data again… Which of the variables are categorical?

Displaying Categorical Data How many students are Mexican? How did you determine this? Is there an easier way to present this data to get at the information quicker?

Frequency Tables Frequency Table: Showing the frequency (how many times) a category is chosen Relative Frequency Table: Showing the category’s frequency in percentage (relative to the total) [Distribution: shows the variables and their frequencies (how the data is distributed)]

Frequency and Relative Frequency Tables

Contingency Tables Still measures frequency distribution or relative frequency It represents multiple categorical variables with the total

Marginal Distribution Marginal distributions: the sum totals in the table in a table with 2 variables looking at the totals (in the margins) of a single variable

Conditional Distribution Conditional Distribution: shows the distribution for a sub-population that has a characteristic you are interested in (it’s selective information in the middle)

Importance of Relativity 1) What percent of the class is male? 2) What percent of the class is conservative? 3) What percent of males is conservative? 4) What percent of all students in the class are males who are conservatives? 5) What percent of all females in the class are conservative? Liberal? Moderate? 6) What percent of all males in the class are conservative? Liberal? Moderate? 7) Are there more males or females who are liberal? Moderate? Conservative? Does this represent the data? Politics in Intro Stats LiberalModerateConservativeTotal Female Male Total BECAUSE THERE ARE NOT AN EVEN AMOUNT OF MALES to FEMALES, RELATIVE FREQUENCY IS IMPORTANT

Independence Independence: There is no association between the variables - they do not affect each other How can we tell? Use the relative contingency table Politics in Intro Stats LiberalModerateConservativeTotal Female Male Total Is gender independent of political orientation? If I were to put the names in a hat and pull one out, would the persons gender affect the likelihood of the person being a certain orientation?

Bar Charts, Relative Frequency Bar Chart, and Pie Charts A way to graphically show frequency and relative frequency

Segmented Bar Chart Shows multiple categorical variables

Issues with Graphs Area Principle- be careful not to misrepresent -the area should be proportional

Issues with Graphs Simpson’s Paradox: a misrepresentation of averages- when the combined average shows a different trend than the individualized groups of data TeacherTest 1 ScoreTest 2 ScoreTotal(%) (Mr Selan) /50= /200= (Ms Shein) /100= /20=

Activity A random sample of 16 Pritzker kids were surveyed on their likes and dislikes The data is provided In pairs, decide on what you want to compare/know/study about this sample Create two different displays of the provided data Frequency/relative frequency tables Pie charts Bar charts Contingency tables Segmented Bar charts

Displaying Categorical Data AgeGenderSportsVideo GamesDrawingDriving 14MYYNN 15FYYYN MYYNN MNYYN 16FNNNN 17FNNYY MYNNY 18FYNYY FNNNN MYYYY 17MNYNY MYYYN 14FYYYN FNNYN

Activity Smoking and Education

Homework Ch.3 #5-9,14,19,20,23,27