S1600 #2Data Presentation #1

January 14, 2016

Data Presentation #1

Outline

1 Data Presentation #1Statistics and DataVariable TypesSummarizing Categorical Data

(WMU) S1600 #2 S1600, Lecture 2 2 / 14

Data Presentation #1

Statistics and Data

StatisticsBroader sense: collection of techniques/procedures for analyzingdata, i.e., Statistics = Data AnalysisNarrower sense: statistics = numbers derived from data

Data = table/spreadsheet like collection of measurements madeon a number of subjects

row = subject or case or observationcolumn = measurement or variableCLASS DATA EXAMPLE: there are 10 subjects (students) and sixvariables: Sex, (Class) Level, GPA, Hours Taken, Transport, andSleep Hours Last Night. Note: the column ‘Student’ is forobservation labels.

(WMU) S1600 #2 S1600, Lecture 2 3 / 14

Data Presentation #1

Statistics and Data

StatisticsBroader sense: collection of techniques/procedures for analyzingdata, i.e., Statistics = Data AnalysisNarrower sense: statistics = numbers derived from data

Data = table/spreadsheet like collection of measurements madeon a number of subjects

row = subject or case or observationcolumn = measurement or variableCLASS DATA EXAMPLE: there are 10 subjects (students) and sixvariables: Sex, (Class) Level, GPA, Hours Taken, Transport, andSleep Hours Last Night. Note: the column ‘Student’ is forobservation labels.

(WMU) S1600 #2 S1600, Lecture 2 3 / 14

Data Presentation #1

Statistics and Data

StatisticsBroader sense: collection of techniques/procedures for analyzingdata, i.e., Statistics = Data AnalysisNarrower sense: statistics = numbers derived from data

Data = table/spreadsheet like collection of measurements madeon a number of subjects

row = subject or case or observationcolumn = measurement or variableCLASS DATA EXAMPLE: there are 10 subjects (students) and sixvariables: Sex, (Class) Level, GPA, Hours Taken, Transport, andSleep Hours Last Night. Note: the column ‘Student’ is forobservation labels.

(WMU) S1600 #2 S1600, Lecture 2 3 / 14

Data Presentation #1

Statistics and Data

StatisticsBroader sense: collection of techniques/procedures for analyzingdata, i.e., Statistics = Data AnalysisNarrower sense: statistics = numbers derived from data

Data = table/spreadsheet like collection of measurements madeon a number of subjects

row = subject or case or observationcolumn = measurement or variableCLASS DATA EXAMPLE: there are 10 subjects (students) and sixvariables: Sex, (Class) Level, GPA, Hours Taken, Transport, andSleep Hours Last Night. Note: the column ‘Student’ is forobservation labels.

(WMU) S1600 #2 S1600, Lecture 2 3 / 14

Data Presentation #1

Statistics and Data

StatisticsBroader sense: collection of techniques/procedures for analyzingdata, i.e., Statistics = Data AnalysisNarrower sense: statistics = numbers derived from data

Data = table/spreadsheet like collection of measurements madeon a number of subjects

row = subject or case or observationcolumn = measurement or variableCLASS DATA EXAMPLE: there are 10 subjects (students) and sixvariables: Sex, (Class) Level, GPA, Hours Taken, Transport, andSleep Hours Last Night. Note: the column ‘Student’ is forobservation labels.

(WMU) S1600 #2 S1600, Lecture 2 3 / 14

Data Presentation #1

Statistics and Data

StatisticsBroader sense: collection of techniques/procedures for analyzingdata, i.e., Statistics = Data AnalysisNarrower sense: statistics = numbers derived from data

Data = table/spreadsheet like collection of measurements madeon a number of subjects

row = subject or case or observationcolumn = measurement or variableCLASS DATA EXAMPLE: there are 10 subjects (students) and sixvariables: Sex, (Class) Level, GPA, Hours Taken, Transport, andSleep Hours Last Night. Note: the column ‘Student’ is forobservation labels.

(WMU) S1600 #2 S1600, Lecture 2 3 / 14

Data Presentation #1

Statistics and Data

StatisticsBroader sense: collection of techniques/procedures for analyzingdata, i.e., Statistics = Data AnalysisNarrower sense: statistics = numbers derived from data

Data = table/spreadsheet like collection of measurements madeon a number of subjects

row = subject or case or observationcolumn = measurement or variableCLASS DATA EXAMPLE: there are 10 subjects (students) and sixvariables: Sex, (Class) Level, GPA, Hours Taken, Transport, andSleep Hours Last Night. Note: the column ‘Student’ is forobservation labels.

(WMU) S1600 #2 S1600, Lecture 2 3 / 14

Data Presentation #1

Statistics and Data

StatisticsBroader sense: collection of techniques/procedures for analyzingdata, i.e., Statistics = Data AnalysisNarrower sense: statistics = numbers derived from data

Data = table/spreadsheet like collection of measurements madeon a number of subjects

row = subject or case or observationcolumn = measurement or variableCLASS DATA EXAMPLE: there are 10 subjects (students) and sixvariables: Sex, (Class) Level, GPA, Hours Taken, Transport, andSleep Hours Last Night. Note: the column ‘Student’ is forobservation labels.

(WMU) S1600 #2 S1600, Lecture 2 3 / 14

Data Presentation #1

Levels of Measurementin increasing order of complexity

nominal: pure labeling, no orderingordinal: ordering exists, but not distanceinterval: distance exists, but not ratios, zero is arbitraryratio: ratios exist, zero indicates the absence of suchmeasurement

(WMU) S1600 #2 S1600, Lecture 2 4 / 14

Data Presentation #1

Levels of Measurementin increasing order of complexity

nominal: pure labeling, no orderingordinal: ordering exists, but not distanceinterval: distance exists, but not ratios, zero is arbitraryratio: ratios exist, zero indicates the absence of suchmeasurement

(WMU) S1600 #2 S1600, Lecture 2 4 / 14

Data Presentation #1

Levels of Measurementin increasing order of complexity

nominal: pure labeling, no orderingordinal: ordering exists, but not distanceinterval: distance exists, but not ratios, zero is arbitraryratio: ratios exist, zero indicates the absence of suchmeasurement

(WMU) S1600 #2 S1600, Lecture 2 4 / 14

Data Presentation #1

Levels of Measurementin increasing order of complexity

nominal: pure labeling, no orderingordinal: ordering exists, but not distanceinterval: distance exists, but not ratios, zero is arbitraryratio: ratios exist, zero indicates the absence of suchmeasurement

(WMU) S1600 #2 S1600, Lecture 2 4 / 14

Data Presentation #1

Levels of Measurementin increasing order of complexity

nominal: pure labeling, no orderingordinal: ordering exists, but not distanceinterval: distance exists, but not ratios, zero is arbitraryratio: ratios exist, zero indicates the absence of suchmeasurement

(WMU) S1600 #2 S1600, Lecture 2 4 / 14

Data Presentation #1

CLASS DATA EXAMPLE

Sex Level GPA Hours Transport Sleep Hrs.Taken Last Night

M Sophomore 3.10 32 Car 7.0M Junior 3.20 66 Car 8.0F Senior 3.49 94 Bus 8.0M Senior 2.68 89 Walk 10.0F Junior 3.73 69 Bicycle 8.0: : : : : :M Senior 3.10 96 Walk 3.0

nominal: Sex, Transport Ordinal: Levelinterval: GPA ratio: Hours Taken, Sleep Hrs. Last Night

(WMU) S1600 #2 S1600, Lecture 2 5 / 14

Data Presentation #1

CLASS DATA EXAMPLE

Sex Level GPA Hours Transport Sleep Hrs.Taken Last Night

M Sophomore 3.10 32 Car 7.0M Junior 3.20 66 Car 8.0F Senior 3.49 94 Bus 8.0M Senior 2.68 89 Walk 10.0F Junior 3.73 69 Bicycle 8.0: : : : : :M Senior 3.10 96 Walk 3.0

nominal: Sex, Transport

Ordinal: Levelinterval: GPA ratio: Hours Taken, Sleep Hrs. Last Night

(WMU) S1600 #2 S1600, Lecture 2 5 / 14

Data Presentation #1

CLASS DATA EXAMPLE

Sex Level GPA Hours Transport Sleep Hrs.Taken Last Night

M Sophomore 3.10 32 Car 7.0M Junior 3.20 66 Car 8.0F Senior 3.49 94 Bus 8.0M Senior 2.68 89 Walk 10.0F Junior 3.73 69 Bicycle 8.0: : : : : :M Senior 3.10 96 Walk 3.0

nominal: Sex, Transport Ordinal: Level

interval: GPA ratio: Hours Taken, Sleep Hrs. Last Night

(WMU) S1600 #2 S1600, Lecture 2 5 / 14

Data Presentation #1

CLASS DATA EXAMPLE

Sex Level GPA Hours Transport Sleep Hrs.Taken Last Night

M Sophomore 3.10 32 Car 7.0M Junior 3.20 66 Car 8.0F Senior 3.49 94 Bus 8.0M Senior 2.68 89 Walk 10.0F Junior 3.73 69 Bicycle 8.0: : : : : :M Senior 3.10 96 Walk 3.0

nominal: Sex, Transport Ordinal: Levelinterval: GPA

ratio: Hours Taken, Sleep Hrs. Last Night

(WMU) S1600 #2 S1600, Lecture 2 5 / 14

Data Presentation #1

CLASS DATA EXAMPLE

Sex Level GPA Hours Transport Sleep Hrs.Taken Last Night

M Sophomore 3.10 32 Car 7.0M Junior 3.20 66 Car 8.0F Senior 3.49 94 Bus 8.0M Senior 2.68 89 Walk 10.0F Junior 3.73 69 Bicycle 8.0: : : : : :M Senior 3.10 96 Walk 3.0

nominal: Sex, Transport Ordinal: Levelinterval: GPA ratio: Hours Taken, Sleep Hrs. Last Night

(WMU) S1600 #2 S1600, Lecture 2 5 / 14

Data Presentation #1

Numerical Versus Categorical Variables

Categorical: nominal & ordinalQuantitative (or numerical): interval & ratio

Categorical 6= non-numerical. E.g., SSN

(WMU) S1600 #2 S1600, Lecture 2 6 / 14

Data Presentation #1

iClicker Question 2.1

Which of the following is nominal?1 Final exam score2 Student’s Gender3 Class level (Freshman, Sofomore, ...)4 Student’s height5 Student’s high school GPA

(WMU) S1600 #2 S1600, Lecture 2 7 / 14

Data Presentation #1

iClicker Question 2.2

For each of the following variables, identify the type of variable(categorical, numerical).I. Temperature (in Fahrenheit) of office buildingII. Duration (in minutes) of flight between two locations.

1 I. Numeric, and II. Categorical2 I. Categorical, and II. Numeric3 There is no correct match4 I. Categorical, and II. Categorical5 I. Numeric, and II. Numeric

(WMU) S1600 #2 S1600, Lecture 2 8 / 14

Data Presentation #1

Dependent Versus Independent Variablesterms used in cause-and-effect studies

independent variable: a probable causedependent variable: outcome being affected or caused

For the vaccine-autism study, the amount of mercury in thepreservative in vaccine is the independent variable, whereas the 42measures of brain function are dependent variables.Note: Likert items & Likert scale.

(WMU) S1600 #2 S1600, Lecture 2 9 / 14

Data Presentation #1

Relative Frequency TableAmerican Community Survey Data

Payment Type is nominal which can be summarized by a relativefrequency table:

-------------------------Type Frequency Rel. Freq. (%)-------------------------Mortgage 44 57.9

= (44/76) × 100%

Rent 20 26.3None 12 15.8-------------------------Total 76 100.0

Frequency = count

Rel. Freq.(%) = (Frequency / Total) × 100%

(WMU) S1600 #2 S1600, Lecture 2 10 / 14

Data Presentation #1

Relative Frequency TableAmerican Community Survey Data

Payment Type is nominal which can be summarized by a relativefrequency table:

-------------------------Type Frequency Rel. Freq. (%)-------------------------Mortgage 44 57.9 = (44/76) × 100%Rent 20 26.3None 12 15.8-------------------------Total 76 100.0

Frequency = countRel. Freq.(%) = (Frequency / Total) × 100%

(WMU) S1600 #2 S1600, Lecture 2 10 / 14

Data Presentation #1

Bar Charta plot of frequencies/relative frequencies

bar height = frequency (or rel. freq)

Mortgage Rent None

Monthly Payment Type

Fre

quen

cy

010

2030

40

Rel

. Fre

q. (

%)

015

3045

60(WMU) S1600 #2 S1600, Lecture 2 11 / 14

Data Presentation #1

Pie Chart

Mortgage

NoneRent

a bad graphical tool

(WMU) S1600 #2 S1600, Lecture 2 12 / 14

Data Presentation #1

Pie Chart

Mortgage

NoneRent

Mortgage

NoneRent

57.9%

26.3%15.8%

a bad graphical tool

(WMU) S1600 #2 S1600, Lecture 2 12 / 14

Data Presentation #1

Pie Chart

Mortgage

NoneRent

Mortgage

NoneRent

57.9%

26.3%15.8%

a bad graphical tool

(WMU) S1600 #2 S1600, Lecture 2 12 / 14

Data Presentation #1

Pie Chart, continued

A

B

C

impossible to discern the orderof wedges’ sizes

untill adding actual rel. freq.a simple (sorted) relativefrequency table will do:

Category rel. freq.A 36%C 33%B 31%

(WMU) S1600 #2 S1600, Lecture 2 13 / 14

Data Presentation #1

Pie Chart, continued

A

B

C

A

B

C

36%

33%31%

impossible to discern the orderof wedges’ sizesuntill adding actual rel. freq.

a simple (sorted) relativefrequency table will do:

Category rel. freq.A 36%C 33%B 31%

(WMU) S1600 #2 S1600, Lecture 2 13 / 14

Data Presentation #1

Pie Chart, continued

A

B

C

A

B

C

36%

33%31%

impossible to discern the orderof wedges’ sizesuntill adding actual rel. freq.a simple (sorted) relativefrequency table will do:

Category rel. freq.A 36%C 33%B 31%

(WMU) S1600 #2 S1600, Lecture 2 13 / 14

Data Presentation #1

iClicker Question 2.3

In a frequency/relative frequency table, the total of the relativefrequencies is

1 50%2 75%3 100%4 150%5 Cannot determine

(WMU) S1600 #2 S1600, Lecture 2 14 / 14