3. describing & presenting data

Describing*&*Presen-ng*Data*

Nooriah*Mohamed*Salleh*MBBS(Malaya),*MPH(Tulane),*DrPH(Tulane)*

Recap:*Variables*&*Data* Variables*are*labels.*The*value*of*variables*can*vary**

* Example:**

age,** Gender* Occupa-on* Ethnicity**

*

Data*is*the*value*you*get*from*observa-on*thru*measuring,*coun-ng*etc.*

* Example:****#*of*pa-ent****weight*of*baby*(kg)****#*of*doctors******

Recap:*Variables*&*Data*

Variable Data

Age (of mother) 23 years old

Weight (of baby) 3.0 kg

Gender male

Ethnic group Malay

Occupation of mother

Housewife

Types*of*Data*

Data

Categorical Data

Numerical Data

Nominal Data

Ordinal Data

Discrete Data

Continuous Data

Nominal*categorical*data*

It*can*be*allocated*into*one*of*a*number*of*categories.*

Has*no*meaningful*order* Example:*

Blood*type*(A,B,*AB,O),*sex*(M,*F)*

Ordinal*categorical*data*

It*can*be*allocated*to*one*of*a*number*of*categories*arranged*in*a*meaningful*order.*

Example:*Very*sa-sed,*sa-sed,*neutral,*unsa-sed,*very*unsa-sed.**

Grade*I,*Grade*II,*Grade*III*(Tumor*Grading)*Moderate,*Severe,*Very*Severe*(Pain)*

Discrete*numerical*data*

Countable*variables.* Integer*form*(discrete)* Numbers*of*things* Example:*

number*of*pregnancies*Number*of*pa-ents*Number*of*teeth***

Con-nuous*numerical*data*

Measurable*variables.* Round*to*the*nearest*integer* Example:*

Weight*(Kg)*Height*(metre)*BP*(mmHg)*Age*(years)*Dura-on*of*surgery*(hour)*

Describing*data*with*tables*

1)*frequency*table** 2)*rela-ve*and*cumula-ve*frequency* 3)*grouped*frequency* 4)*open[*ended*groups* 5)*cross[tabula-on**

1.*Frequency*table*

A*picture*of*the*frequency*distribu-ons*

Mortality (%) Tally No. of ICU patients

11.2-15.1 1, 1, 1, 1, 1, 1, 1, 1, 1 9

15.2-20.1 1, 1, 1, 1, 1, 1, 1, 1 8

20.2-25.1 1, 1, 1, 1, 1 5

25.2-30.1 1, 1, 1 3

30.2-35.1 1, 1

variables frequency

2.*Rela-ve*frequency,*cumula-ve*frequency*

Rela-ve*frequency:*percentage*of*the*total*Cumula-ve*frequency:**

parity No.of women Percentage (relative frequency)

Cumulative percentage

0 5 12.5 12.5

1 6 15 27.5

2 14 35 62.5

3 10 25 87.5

4 3 7.5 95

7 1 2.5 97.5

8 1 25 100

3.*Grouped*frequency* Grouped*frequency:*for*con-nuous*metric*data*

Birthweight No. of infants 2700-2999 2 3000-3299 3 3300-3599 9 3600-3899 9 3900-4199 4 4200-4499 3

A group width of

300g

The class lower limit

The class upper limit

Table*for*display*of*Data*

Type of data Table

Ordinal numerical Discrete

Frequency table

Continuous numerical data

Grouped Frequency

4.*Open[ended*group*

One*or*two*values*which*are*called*outliers,*are*a*long*way*from*the*general*mass*of*the*data.*

Use**or***

5)*Cross[tabula-on*

2 or fewer children

Breast lump diagnosis

Totals

Malignant Benign

Yes 4 21 25

No 4 11 15

Totals 8 32 40

Association between breast lump and parity

3.*Describing*data*with*charts*

1.Nominal*data:* (1)*the*pie*chart* (2)*the*simple*bar*chart* (3)*the*cluster*bar*chart* (4)*the*stacked*bar*chart*

2.*Ordinal*data:* (1)*the*pie*chart* (2)*the*bar*chart* (3)*the*dotplot***3.*Discrete*numerical*data*

4.*Con-nuous*numerical*data*[*histogram*

*5.*Cumula-ve*ordinal*or*discrete*

data*[*step*chart**6.*Cumula-ve*con-nuous*data*[*

cumula-ve*frequency*or*ogive**7.*Time*based*data:*-meseries*

chart**

1.1.*Pie*chart*

Pie chart: Hair color of children reciving d-phenothrin

blonde, 18, 18%

brown, 55, 57%

red, 4, 4%

dark , 21, 21%

blonde brown red dark

4[5*categories* Describe*1*variable* Start*at*0*in*the*same*order*as*the*table*

1.2*Simple*bar*chart*

Bar Chart: Hair colar of the chidren receiving d-phenothrin

18

55

4

21

0

10

20

30

40

50

60

blonde brown red dark

Same*widths,*equal*spaces*between*bars*

PharmacistsNursesDoctorsDentists

6000

5000

4000

3000

2000

1000

0

Profession

Num

ber

of w

orke

rs

Bar chart for number of health professionals 1.3**Clustered*bar*chart*

Cluster percetage bar chart of the hair color receiving Malathion and d-

phenothrin

16 18

5256

4 4

2822

0

10

20

30

40

50

60

malathion d-penothrin

blondebrownreddark

PrivatePublic

Dentists Doctors Nurses Pharmacists

0

1000

2000

3000

4000

Profession

Num

ber

of w

orke

rsClustered bar chart for number of health professionals


Private Public

0

1000

2000

3000

4000

Sector

Num

ber o

f wor

kers

Clustered bar charts of number of health professionals

Plotting by sector rather than by profession Look at the data from a different angle Highlight different aspects of the data

1.4*Stacked*bar*chart*

stacked bar chart

0%

20%

40%

60%

80%

100%

Breast-fed Bottle-fed

Non-smokersFomer smokersSmokers

PrivatePublic


6000

5000

4000

3000

2000

1000

0

Profession

Num

ber o

f wor

kers

Stacked bar chart for number of health professionals

Variation of the basic bar chart


PublicPrivate

6000

5000

4000

3000

2000

1000

0

Sector

Num

ber

of w

orke

rs

Stacked bar charts by sector

PrivatePublic


100

9080

70

60

50

4030

20

100

Profession

Per

cent

by

sect

or

Segmented bar charts by profession

PrivatePublic


4000

3000

2000

1000

0

Profession

Num

ber

of w

orke

rs

Clustered bar chart for number of health professionals

PrivatePublic


0

1000

2000

3000

4000

5000

6000

Profession

Num

ber

of w

orke

rs

Stacked bar chart for number of health professionals

PrivatePublic


010

20

3040

50

60

70

8090

100

Profession

Per

cent

by

sect

or

Segmented bar charts by profession


PublicPrivate

4000

3000

2000

1000

0

Sector

Num

ber

of w

orke

rs

Clustered bar chart of number of health professionals


PublicPrivate

6000

5000

4000

3000

2000

1000

0

Sector

Num

ber

of w

orke

rs

Stacked bar charts by sector


PublicPrivate

100

9080

70

60

50

4030

20

100

Sector

Per

cent

with

in s

ecto

r

Percentage bar charts by sector


PublicPrivate

100

9080

70

60

50

4030

20

100

Sector

Per

cent

with

in s

ecto

r

Segmented bar charts by sector

Time Trend

Exaggerate visually the increase in # prescriptions written per person by starting at 8 rather than 0

Stacked bar chart of yearly mortality rate per 1000 births

Pagano & Gauvreau (1999) Principles of Biostatistics, Duxbury.

Table*1:*Response*under*two*treatments*

Response to Treatment

None Partial

Complete

Total

A 3

15 9

27

B 2 22 30

54

Treatment

NonePartial

Complete

BA

100

9080

70

60

50

4030

20

100

Treatment

With

in tr

eatm

ent p

erce

ntag

e

treatmentResponse to

Can compare the response type percentages for the two treatments

NonePartialComplete

A B

010

20

3040

50

60

70

8090

100

Treatment

With

in tr

eatm

ent p

erce

ntag

etreatmentResponse to

Stacked bar charts for percentage figures Histogram Divide the range of the data into a suitably chosen number of intervals, all of the same

width The number of observations that fall

within each interval is plotted

Relative frequency histogram Plot the proportions of observations that

fall within the class intervals

40 60 80 100 120 140 160 180 200 220

0

10

20

SysVol

Fre

quen

cy

Heart Attack PatientsHistogram of End-Systolic Volume for 45 Male

40 60 80 100 120 140 160 180 200 220

0

10

20

30

40

SysVol

Per

cent

Relative frequency polygon for SysVol

Histogram*

Exercise 3-5, Histogram

05

10152025303540

19 20-24 25-29 30-34 35

Percentage age distribution of pregnant women

Thrombosis cases

Step[up*chart*Exercise 3.8 Cumulative percetage o finfants

6.6716.67

36.67

60

90100

0

20

40

60

80

100

120

0 5 10

Cumulativepercetage ofinfants

Cumula-ve*frequency*curve*Exercise 3.9 Ogive

0

20

40

60

80

100

120

15-24 25-34 35-44 45-54 55-64 65-74 75-84 > 85

Percentage cumulative frequency curves of age for male suicide attempters and later succeeders

Attempting suicideLater successful

4.*Describing*data*from*its*distribu-onal*shape*

1.*symmetric*mound[shaped*distribu-ons*Exercise 3-5, Histogram

05

10152025303540

19 20-24 25-29 30-34 35

Percentage age distribution of pregnant women

Thrombosis cases

Non-Symmetrical Histograms

These histograms are skewed.

Common Shapes of Histograms

Skewed Histograms

Skewed left (negative skew)

Skewed right (positive skew)

Common Shapes of Histograms

Skewed Histograms

Skewed left (negative skew)

Skewed right (positive skew)

Note: the SKEW follows the TAIL

Skewed*distribu-ons*Exercise 4.2 shape

020406080

100120140160

15-24

25-34

35-44

45-54

55-64

65-74

75-84

>85

Age distribution for female suicide attempters and later succeeders

Attempting suicide

Shape*of*data*distribu-ons*******

Symmetrical*or*skewed*

Right-Skewed Left-Skewed Symmetric Mean = Median = Mode Mean Median Mode Median Mean Mode

Bimodal*distribu-ons*

A*bimodal*distribu-on*is*one*with*two*dis-nct*humps*or*peaks*

Scaeer*Plots*

Scaeer*plots*are*similar*to*line*graphs*in*that*each*graph*uses*the*horizontal*(*x*)*axis*and*ver-cal*(*y*)**axis*to*plot*data*points.*

* Scaeer*plots*are*most*ogen*used*to*show*correla-ons*or*rela-onships*among*data.*

Scaeer*Plots**Posi-ve*Correla-on*

Study Time Class Grade

0 55

0.5 61

1 67

1.5 73

2 81

2.5 89

3 91

3.5 93

4 95

4.5 97

How Study Time Affects Grades

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time in hours

Ove

rall

grad

e

Scaeer*Plots**Nega-ve*Correla-on*Work out time Weight

0 200

0.5 205

1 190

1.5 195

2 180

2.5 190

3 170

3.5 177

4 160

4.5 170

5 150

5.5 168

6 140

6.5 150

7 130

7.5 170

8 120

8.5 130

9 110

9.5 115

10 100

10.5 120

11 90

11.5 90

12 80

Weight Loss Over Time

0

50

100

150

200

250

0 2 4 6 8 10 12

Days worked out per month

Wei

ght

Weight

Scaeer*Plot*of*the*Data*

Sandwich

Total Fat (g) (X)

Total Calories (y)

Hamburger 9 260

Cheeseburger 13 320

Quarter Pounder 21 420

Quarter Pounder with Cheese 30 530

Big Mac 31 560

Arch Sandwich Special 31 550

Arch Special with Bacon 34 590

Crispy Chicken 25 500

Fish Fillet 28 560

Grilled Chicken 20 440

Grilled Chicken Light 5 300

Fat Grams and Calories in Food

0

100

200

300

400

500

600

700

0 5 10 15 20 25 30 35 40

Total Fat Grams

Tota

l Cal

orie

s

Damaged*for*life*by*too*much*TV*

N Z Herald (04/10/2005)



TV watching

Hea

lth S

core

r = - 0.93

Causal relationship?

5.*Describing*data*with*numeric*summary*value*

1.*numbers,*percentages*and*propor-ons* 2.*summary*measures*of*central*loca-on/central*tendency*

3.*summary*measures*of*spread/dispersion*

5.1.*Numbers,*percentages*and*propor-ons**

Numbers[the*numerical*summaries*of*data* A*percentage*is*a*propor-on*mul-plied*by*100.**

1)*Prevalence:*number*of*exis-ng*cases*in*some*popula-on*at*a*given*-me.*

2)*Incidence*(incep-on):*the*number*of*new*cases*occurring*per*100,*or*per*1000,*of*the*popula-on,*during*some*period*of*-me.*

5.2.*Summary*measures*of*Central*loca-on*

1)*Mode:*category*or*value*occurs*the*most*ogen,*****[*Categorical,*numerical,*discrete*2)*Median:*middle*value*(data*in*ascending*order),*central[ness.*

****[*Use:*ordinal*and*numerical*data.*3)*Mean*(average):*divide*the*sum*of*the*values*by*the*number*of*values*

4)*Percen>le:*divide*the*total*number*of*the*values*into*100*equal[sized*groups.*

Choosing*the*most*appropriate*measure*

mode median mean

Nominal

Ordinal

Numerical discrete Numerical continuous

yes

yes

yes

yes

no

yes

Yes, if markedly skewed

Yes, if markedly skewed

no

no

yes

yes

5.3.*Summary*measure*of*spread/dispersion/variability*

* Range:*maximum*value**minimum*value*

IQR*(interquar>le*range):*=*(75th**25th)*percen-le************************************************=*Q3*Q1**

BoxHand*whiskerplot:*graphical*summary*of*the*three*quar-le*values,*the*minimum*and*maximum*values,*and*outliers.*

Box[and[Whisker*Plot*

*****Graphical*Display*of*Data*Using** *5HNumber*Summary*

Median

4 6 8 10 12

Q 3 Q 1 X Maximum value

X Minimum value

Standard*devia-on*

The*spread*in*a*set*of*data;**average*distance*of*all*the*data*values*from*the*mean*value.**

The*smaller*the*average*distance*is,*the*narrower*the*spread,*and*vice*versa.*

Use:*numerical*data*only.*

3. describing & presenting data

Documents

variables frequency

data age of mother

numerica chart

mp variables

counn example

class upper limit table

years old weight of

group width