Categorical Data! Frequency Table –Records the totals (counts or percentage of observations) for each category. If percentages are shown, it is a relative frequency table. Distribution –Shows the possible values of the variable and the relative frequency of each value

Types of Graphs Picture –Remember… Bar Chart – counts for comparison

Pie Chart – pieces for proportion

Segmented Bar Chart

Contingency Table Displays counts and sometimes percentages of individuals falling into named categories on two or more variables. Shows how individuals are distributed along each variable contingent on the value of another variable. –Marginal distribution: distribution of either variable by itself (last row or column) –Conditional Distribution: distribution of 1 variable for those individuals satisfying a condition on another variable. Considers a smaller group isolated from the whole.

Independence??? Independence…think impact! –Variables are independent (one variable does not influence the value of the other variable) if the conditional distribution of 1 variable is the same for each category of the other.

Python Eggs ColdNeutralHot Number of Eggs Number hatched )What percent of cold eggs hatched? 2)Neutral eggs hatched represent what percent of the total? 3)Are temperature and eggs hatched independent?

Smoking by Students & Parents Neither Parent Smokes One Parent Smokes Both Parents Smoke Student Does Not Smoke Student Smokes

Neither Parent Smokes One Parent Smokes Both Parents Smoke Student Does Not Smoke Student Smokes The Marginal Distribution

What percent of children have no parent that smokes? Students and both parents that smoke compose what percent of the total? Of 1 parent smokers, what is the percentage of children who smoke?

Is student smoking preference independent of parent choice? Neither Parent Smokes One Parent Smokes Both Parents Smoke Student Does Not Smoke % % % Student Smokes % % %

Year Response of families Both work full time full time, 1 part time full time, 1 work from home full time, 1 homemaker No Opinion51 Is there evidence of a change in working patterns in families???

Simpson’s Paradox When averages “pooled” together AND taken across different groups appear to be contradictory. Example: Baseball PlayerOverallvs LHPvs RHP A33/103 (.320)28/81 (.346)5/22 (.227) B45/151 (.298)12/32 (.375)33/119 (.277)

#14 StudentStaffTotals American European3312 Asian5547 Totals

#15 WhiteMinorityTotals 4-yr college yr college366 Military41 Employment143 Other163 Totals