5/2/20131STA291Statistical MethodsLecture 3Why do we (usually) provide graphs?Recall: Categorical or Qualitative Datao Nominal variables have a scale of unordered categorieso Nominal examples : gender, nationality, hair color, state of residenceo For ordinal variables, one case may have more of a certain property than does another caseo Ordinal examples: Disease status, company rating, grade in STA 2915/2/20132Numerical Summary of Categorical DataoWith one variable, nothing to do (for now) but count:Highest Degree Frequency (Number of Responses)Grade School 15High School 200Bachelor’s 185Master’s 55Doctorate 70Other 25Total 550Called a frequency distribution:list of possible values, or classes, and their frequencies, or countsBar Graph (Categorical Data)Features:o The bars are usually separated to emphasize that the variable is categorical rather than quantitativeo For nominal variables (no natural ordering), order the bars by frequency, except possibly for a category “other” that is always last5We could display this data in a bar chart…050100150200250Grade School High Scho ol Bachelor’s Master’s Do ctorate Other Bar Graph: If the data are ordinal, classes arepresented in the natural ordering.65/2/20133Pie Chart (Categorical Data)o First Step: Create a relative frequency distributionHighest Degree Frequency (Number of Responses)Relative FrequencyGrade School 15High School 200Bachelor’s 185Master’s 55Doctorate 70Other 25Total 5507Pie ChartHighest Degree Relative Frequency Angle ( = Rel. Freq. * 360◦Grade School.027 ( = 15/550 ) 9.72High School.364 131.04Bachelor’s.336 120.96Master’s.100 36.0Doctorate.127 45.72Other.045 16.2o Pie Chart: Pie is divided into slices; The area of each slice is proportional to the frequency of each class.8Pie Chart95/2/20134A contingency table is a table in which frequencies correspond to two variables. (One variable is used to categorize rows, and a second variable is used to categorize columns.)Contingency tables have at least two rows and at least two columns.Contingency TableCase-Control Study of Flu VaccineDoes whether the patient developed the flu seem to depend on whether they received the vaccine?Developed FluYe s N oVaccine Treatment 14 1056Placebo 95 437Case-Control Study of Flu VaccineDoes whether the patient developed the flu seem to depend on whether they received the vaccine?FluYesNoTota lYes NoVaccine Treatment Count 14 1056 1070% within VaccPlac 1.3% 98.7% 100.0%% within FluYesNo 12.8% 70.7% 66.8%% of Total .9% 65.9% 66.8%Placebo Count 95 437 532% within VaccPlac 17.9% 82.1% 100.0%% within FluYesNo 87.2% 29.3% 33.2%% of Total 5.9% 27.3% 33.2%Count 109 1493 1602% within VaccPlac 6.8% 93.2% 100.0%% within FluYesNo 100.0% 100.0% 100.0%% of Total 6.8% 93.2% 100.0%5/2/20135Be careful!Airline To Point Barrow Elsewhere OverallAlaska Onemoretime 50/75 22/25Juneau Whereyouregoing 15/25 60/75On‐Time PercentageWe’re going to compare two airlines’ performances:Looking backo Summary of categorical datao Numerical: frequency distributiono Graphic: bar graph or pie charto Two-dimensional:contingency