Methods of Presenting Data

Training Course on Basic Statistics for Research

August 24-28, 2009

STATISTICAL RESEARCH AND TRAINING CENTERJ and S Building, 104 Kalayaan Avenue, Diliman, Quezon City

Methods of Presenting Data

Most of the notes are from the “Elementary Statistics” book by Almeda, Capistrano, and Sarte, 2009

Prepared by:Josefina V. AlmedaProfessor and College SecretarySchool of StatisticsUniversity of the Philippines, DilimanAugust 2009

2

Statistical Research and Training Center Training Course on Basic Statistics for ResearchAugust 24 - 28, 2009

3 Ways of Presenting Data

* Textual

* Tabular

* Graphical

3


Textual Presentation

* is putting important figures in the text of the report

* figures may be summary statistics like the minimum, maximum, mean, median, standard deviation, percentage,

or total

* allows us to highlight the significant figures of the study

* it confirms deductions and answers to the research problem

4


Example of Textual Presentation

In terms of relative data availability for progress monitoring of the Millenium Develoment Goals, the Philippines ranked first in 2003 among the 11 countries in the ASEAN region. Based on the 2003 report of the United Nations Economic and Social Commission for Asia and the Pacific (UN-ESCAP), the Philippines obtained a rating of 27.9% followed by Thailand with 25.2% and Indonesia with 24.6%. The Philippines ranked fourth among all countries in the Asia and the Pacific Region, with Australia topping the list with 29.1%, followed by Japan, 29.0%, and Republic of Korea, 28.7%. According to the UNESCAP, the theoretical maximum is for a country to have 767 data values (59 series x 13 years) and a country is counted to have data available when data exist for one or more years.

Source: Statistical Yearbook 2005, NSCB

5


Tabular Presentation

* Arrangement of figures in rows and columns for easy reading and analysis

* It allows us to compare and look for relationships among the variables of interest

* The table can have frequency counts, proportions, percentages, and other summary measures such as totals and averages.

6


Formal Statistical Table

* contains all the important parts of a table like table number, table title, head note, stub head, box

head, column headings, footnotes, source notes, etc.

* can stand alone even without an introductory statement.

7


Definitions of the Different Parts of a Table

Heading consists of the table number, title, and head note. It is located on top of the table of figures.

Table Number identifies the position of the table in a sequence.

Table Title gives the subject, classification, time, and area segments.

Head note specifies the unit of measurement of the data and may provide additional explanation about the figures in the table. It is located below the table title and above the top cross rule of the table.

8


Box Head contains spanner heads and column headings.

Spanner Head is an identifying label for the column headings.

Column Heading is a descriptive label for the column cells.

Panel consists of several column heads under the same

spanner head.

9


Stub contains the stub head, center head, and row captions. Its position is at the first column of the table.

Stub head is a descriptive label for the center heads and row captions.

Center head is an identifying label for the row captions.

Row caption is a descriptive label for the row cells.

Block contains row captions under the same center head.

10


Field is set of numerical figures in the table.

Line is a row of cell figures. Column is a column of cell figures. Cell is the numerical figure in the intersection of a row

caption and column heading.

Footnote is an explanatory text about a specific part or the whole table. Its position is at the bottom of the table.

Source note gives the name of the agency that collected the data. Its position is at the bottom of the table.

11


The Parts of a Formal Statistical Table

blockk

Line

field

TABLE NO. - Title of the Table (head note)

Spanner head Spanner Head The Column

Stubhead Column Head

Column Head

Column Head

Column Head

Column Head Column Head TOTAL

CENTER HEADTotal line captionRow captionRow captionRow captionRow caption

CENTER HEADTotal line captionRow captionRow captionRow captionRow caption

Cell Cell Cell CellCellCellCellCellCellCellCellCellCell

Cell Cell

*Footnote Source note:

panel

12


The Title is descriptive of the table It answer four (4) questions about the subject

matter of its table:

• WHAT?

• HOW CLASSIFIED?

• WHERE?

• WHEN?

Table Titles

13


Table 1. Amount of Pag-ibig Provident Benefits Refunded and Number of Claimants By Regional Group; January to May 2002

Regional GroupAmount

(in million pesos)Number of Claimants

NCR 1,018.965 35,065

Luzon 851.725 23,846

Bicol-Visayas 598.461 17,248

Mindanao 690.665 20,429

Total 3,159.816 96,588

Universe

Segment

Classification and Area Segment

Time Reference Segment

14


Example of a formal statistical table TABLE 2. Total Number of Families, Total and Average Annual Family Income and Expenditure by Income Class, Urban and Rural in the Philippines: 2000 (in thousand pesos) head note

row captions

Total no. Income Expenditure

Income Class of Families Total Average TotalAverag

e

URBAN center head

Total 7,489,8531,535,250,06

4 2051,234,285,34

3 165

Under P10,000 6,840 56,801 8 59,693 9

10,000 - 19,999 50,326 812,883 16 908,440 18

20,000 - 29,999 126,398 3,209,473 25 3,389,398 27

30,000 - 39,999 206,629 7,286,107 35 7,620,222 37

40,000 - 49,999 309,445 13,998,124 45 14,125,894 46

50,000 - 59,999 356,091 19,611,853 55 19,066,504 54

60,000 - 79,999 742,181 51,834,409 70 49,559,978 67

80,000 - 99,999 761,548 68,497,516 90 63,900,511 84

100,000 -149,999 1,522,669 187,488,838 123 168,737,118 111

150,000 -249,999 1,718,997 331,582,321 193 278,565,606 162

250,000 -499,999 1,236,285 419,348,347 339 326,570,009 264

500,000 and over 452,445 431,577,392 954 301,781,968 667

heading

Note: Totals may not add up due to rounding footnote

Source: NSO source note

Spanner head

15


Graphical Presentation

* It is a good means of communicating the numerical figures found in tables

* Charts facilitate analysis when it reveals probable relationships among variables

* It allows comparison of different series or groups

* Placing figures in charts permits us to validate conclusions made in the study.

16


Notes: * Charts show only approximations and the general picture of the data set.* A good chart must be accurate, clear, simple, professional looking, and has a well-designed layout.* The arithmetic scale should have equal increments to represent equal numerical units.* The chart should have no visual illusions with the incorrect use of shadings or patterns.* We should put chart titles, scale figures and labels, and legends, if necessary.

17


Types of statistical charts

* line chart

* vertical bar chart

* horizontal bar chart

* pictograph

* pie chart

* statistical map

18


Definitions of Parts of a Chart

Chart Title * gives the subject, data classification, time reference, and area segment of the data set * located above or below the chart

Coordinate Axes * are the horizontal and vertical axes * spacing of the units may be different for the horizontal and vertical axes but must remain constant within the same axes.

Point of Origin * is the intersection of the horizontal and vertical axes.

19


Scale Divisions * are the ticks to denote the scale points of the horizontal and vertical axes Grid Lines or Coordinate Lines * may be horizontal or vertical

* guides the reader in reading the numerical figures * must be lighter than the curves on the chart to maintain the focus on the chart * choice of horizontal or vertical grid line depends upon the type of chart.

20


Scale Figures * run from left to right for the horizontal axis and from bottom to top for the vertical axis * use multiples of five or other easy to work with multiples for scale values * for big scale values, limit the number of digits of the scale figures to one or two, then; place the unit of measurement in the scale legend * position the scale figures near the coordinate axes * scale figure of the vertical axis starts with zero (for line chart and vertical bar charts) * if we only need the upper part of the coordinate fields to portray the data, we still retain the zero but exclude the lower part of the figures by putting a break on the vertical scale

21


Figure 1a Figure 1b

80 80 60 60 40 40

0 0

Time Period Time Period

Example of Putting a Break on the Vertical Axis

22


Scale Labels or Scale Legends * describes both horizontal and vertical axes

Curves * represent the plot of the data series * differentiate several curves by using different patterns or colors. Curve Legends * give the type of data series * legend symbol follows the color or patterns selected for a particular curve * we prefer the use of curve labels than curve legends.

23


Footnote

* brief explanation to any part of the chart

* located at the bottom of the chart

Source Note

* indicates the source of the data

* located at the bottom of the chart

24


Line Chart

* appropriate for time series data

* emphasis is on the movement

* shows trends, patterns, forecasts

* applicable for one or more time series data for comparison purposes

25


Notes for Line Chart:

* put the variable of interest on the vertical axis and the time on the horizontal axis

* put appropriate scale legends for both axes

* position the scale figures on the tick marks

* ratio of height of width should be 2 to 3 or 3 to 4

26


Figure 2. Different Parts of a Line Chart

Figure title

Scale figures

Grid linesReported cases

Death cases

Curve label

Source: Department of HealthSource Note

Border

Figure 2. Number of Reported Cases and Deaths Due to Dengue Fever in the Philippines: 1992 to 2000

0

5

10

15

20

25

30

35

40

45

50

92 93 94 95 96 97 98 99 2000

in th

ousa

nds

27


FIGURE 3. Stretched Out Vertical and Horizontal Axes and Its Consequences

FIGURE 3a. Stretched Out Vertical Axis of the Grid

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10

TIME

Sal

es

in M

illio

ns

FIGURE 3b. Stretched Out Horizontal Axis of the Grid

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10

TIME

Sal

es

in M

illio

ns

28


Good Grid Proportions

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10

TIME

Sal

es in

Mill

ions

FIGURE 3c. Line Chart with Good Grid Proportions

29


0

5

10

15

20

1 2 3 4 5 6 7 8 9 10

TIME

Sal

es in

mill

ions

FIGURE 4. Line Chart with Two Curves and Large Observed Values

30


Figure 5a. Simple Line Chart • has only one curve• appropriate for one series of time data.

Figure5b. Multiple Line Chart• shows two or more curves• to compare the trends in two or more data series

FIGURE 5. Types of Line Chart

Figure No.: Case Outflow in the Supreme Court: 1999 to 2004

0

1

2

3

4

5

6

99 00 01 02 03 04

Case

Out

flow

in th

ousa

nds

Figure No.: Case Outflow in the Supreme Court and Court of Appeals: 1999 to 2004

0

2

4

6

8

10

12

14

99 00 01 02 03 04

Cas

e O

utflo

w in

thou

sand

s

Supreme Court

Court of Appeals

31


Column Charts

* for showing comparisons of amount of a variable of interest collected over time

* emphasis is on the magnitude of the data set

32


FIGURE NO. Unemployment Rate of 15-24 Years Old in the Philippines: 1990 to 2003

0

5

10

15

20

25

90 91 92 93 94 95 96 97 98 99 00 01 02 03

Une

mpl

oym

ent R

ate

FIGURE 6. Different Parts of a Column Chart

* The height of the column represents the amount of a specific time.* Columns must not be too long or too short, not too wide or too narrow.* The space between the bars must not be too wide or narrow. * The usual space between bars is around one-fourth of the width of the

column.

Figure title

Horizontal grid lines

Scale label

Source: NSOSource note

border

33


FIGURE 8a. Too Narrow Columns

0

5

10

15

20

25

90 91 92 93 94 95 96 97 98 99 00 01 02 03

Une

mpl

oym

ent R

ate

FIGURE 8b. Too Wide Columns

0

5

10

15

20

25

90 91 92 93 94 95 96 97 98 99 00 01 02 03

Une

mpl

oym

ent R

ate

FIGURE 7. Illustrations of Incorrect Width and Spacing of Columns

34


Notes on Column Charts:

* vertical scale of the column chart should start with zero* do not put a break on the vertical scale* use scale figures that are multiples of 5, 10,…,50

* if the observed values are small, use multiples of 2* put a scale label to identify the variable of interest* put horizontal grid lines* for one series of data, use only one color or pattern* for two or more series of data, use different colors,

shadings or patterns* avoid wavy or unconventional patterns

35


FIGURE 9a. Uneven Shading

0

2

4

6

8

10

12

90 91 92 93 94 95 96 97 98 99 2000

FIGURE 9b. Wavy Patterns

0

2

4

6

8

10

12

90 91 92 93 94 95 96 97 98 99 2000

FIGURE 9b. Wavy Patterns

0

2

4

6

8

10

12

90 91 92 93 94 95 96 97 98 99 2000

FIGURE 9d. Correct Shading

0

2

4

6

8

10

12

90 91 92 93 94 95 96 97 98 99 2000

FIGURE 8. Examples of Poor and Good Choices of Patterns

36


Types of Column Charts

* Simple Column Chart

* Grouped Column Chart

* Subdivided Column Chart

* 100% Subdivided Column Chart

* Net Deviation Column Chart

37


• for one time series data• emphasizes on the amount of increase or decrease• columns must have only one pattern, color, or shading

• for comparing two or more time

series data by using different colors, shading, or patterns

FIGURE 9a. Simple Column Chart FIGURE 9b. Grouped Column Chart

Figure No.: Case Outflow in the Supreme Court: 1999 to 2004

0

1

2

3

4

5

6

99 00 01 02 03 04

Cas

e O

utflo

w in

thou

sand

sFigure No.: Case Outflow in the Supreme Court and Court

of Appeals: 1999 to 2004

0

2

4

6

8

10

12

14

99 00 01 02 03 04

Cas

e O

utflo

w in

thou

sand

s

Supreme Court

Court of Appeals

38


FIGURE 9c. Subdivided Column Chart FIGURE 9d. 100% Subdivided Column Chart

• to show the component parts of a series of values• Use different shades, patterns or colors show the different components of the column.

• components are in percentages• facilitates comparison of two or more series• Use different shades, patterns, or colors to show the component parts in percentages


0

5

10

15

20

99 00 01 02 03 04

Cas

e O

utflo

w in

thou

sand

s

Court of Appeals

Supreme Court


0%

20%

40%

60%

80%

100%

99 00 01 02 03 04

Cas

e O

utflo

w in

thou

sand

s

Court of Appeals

Supreme Court

39


FIGURE No. Percent Change of Peso-Dollar Exchange Rate in the Philippines:

February to December 2001

-6

-5

-4

-3

-2

-1

0

1

2

3

4

Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

FIGURE 9e. Net Deviation Column Chart

• for showing increases and decreases, gains and losses, and positive and negative numbers over time.• vertical axis will have positive and negative scales

40


Horizontal Bar Charts

* for qualitative types of data given a specific time

* to compare the magnitudes of the different categories of a qualitative variable

* place the categories of the qualitative variable on the y-axis and the amount or number is on the horizontal axis

* use vertical grid lines

41


FIGURE NO. Top 6 Diseases in the Philippines: 2002

0 20 40 60 80

Tuberculosis

Hypertension

Influenza

Bronchitis

Diarrhea

Pneumonia

number in ten thousands

FIGURE 10. Different Parts of a Simple Horizontal Bar Chart

Source: DOH

Figure title

Scale label

Source note

Scale figure

Border Vertical grid lines

42


Notes on Horizontal Bar Chart:

* the length of the bar represents the value for the category* the bars should not be too wide or narrow or too long or too short* the spaces in between the bars may be one-fifth to one-half the width of the bar* arranging the bars according to length facilitates comparisons* use appropriate colors or patterns for the bars* place the title of the chart at the center of either the top or bottom of the chart

43


Types of Horizontal Bar Charts

* Simple Bar Chart

* Grouped Bar Chart

* Subdivided Bar Chart

* Subdivided 100% Bar Chart

44


FIGURE 11a. Simple Bar Chart FIGURE 11b. Grouped Bar Chart

• for showing the magnitude of the different categories of a qualitative type of variable• length of the bar represents the value of each category

• compares the amounts of two or more data sets with the same set of categories• number of bars per category depends upon the number of groups in the data set

Figure No.: Court Caseload by Type of Higher Court in the Philippines: 2004

0 10 20 30 40

Court of Tax Appeals

Sandiganbayan

Supreme Court

Court of Appeals

court caseload in thousands

Figure No.: Court Caseload by Type of Higher Court in the Philippines: 2003 and 2004

0 5 10 15 20 25 30 35 40

Court of TaxAppeals

Sandiganbayan

Supreme Court

Court of Appeals


2003

2004

45


• for various categories, we divide one bar into several components• uses absolute numbers in the scale values

• It indicates the parts of a whole such that the parts total to 100%.

FIGURE 11c. Subdivided Bar Chart FIGURE 11d. Subdivided 100% Bar Chart


0 10 20 30 40 50 60 70 80

Court of TaxAppeals

Sandiganbayan

Supreme Court

Court of Appeals


2004

2003


0% 20% 40% 60% 80% 100%

Court of TaxAppeals

Sandiganbayan

Supreme Court

Court of Appeals

court caseload

2004

2003

46


Pie Chart

* circle divided into several sections* each section indicates the proportion of each component or category* useful for data sorted into categories for a

specific period* purpose is to show the components parts with

respect to the total in terms of the percentage distribution

* use the pie chart if there are less than 6 categories in the data set

47


FIGURE 12. Illustration of Pie Chart

Figure No.: Percentage Distribution of Reported Cases of Drug Abuse by Type of Substance in the Philippines: 2004

68%

25%

3%

1%

3%

Shabu

Marijuana

Cough Preparation

Injectable

Inhalants

48


Notes on Pie Chart:

* arrange components of the pie chart according to magnitude

* If there is an “Others” category, we put it in the last section

* Use different colors, shadings, or patterns to distinguish one section of the pie to the other sections

* Plot the biggest slice at 12 o clock

49


Pictograph

* gives an approximation only of the actual figures

* compares the different categories

* symbols selected should be self-explanatory and easy to understand

* each symbol represents a number

50


1980

1990

2000

1995

=10,000,0001980

1990

2000

1995

1980

1990

2000

1995

=10,000,000=10,000,000=10,000,000

Population in the Philippines for Census Years 1980 to 2000

Source: NSO

Figure 13. Illustration of a Pictograph

51


Statistical Maps

* to show data in geographical areas

* also called cross-hatched maps or shaded maps

* geographic areas may represent barangays, cities, district, provinces, and countries

* figures in the map can be numbers, ratios, rates,

percentages, and indices.

52


Types of Statistical Maps

Shaded Map* use shading with this type of map to indicate

the degree of magnitude of the figures* shading commonly runs gradually from dark to light* darker shading of the map means larger magnitude and lighter shading of the map implies smaller magnitude

Dot Map* gives either the location or the number of

establishments in a certain geographic area

53


Figure 14. Illustration of a Shaded Map

Legend 850 to 1,120 1,121 to 6,116 6,117 to 9,339 9,340 to 20,954 20,955 and above

Total Population in Quezon City: 1995

54


Using ‘Chart Junk’

No Relative Basis in Comparing Data Batches

Compressing the Vertical Axis

No Zero Point on the Vertical Axis

Errors in Presenting Data

55


Good Presentation

1960: P100.00

1970: P160

1980: P310

1990: P380

Minimum Wage Minimum Wage

0

2

4

1960 1970 1980 1990

P

Bad Presentation

“Chart Junk”

56


Good PresentationMonthly Income Monthly Income

Bad Presentation

0

39

42

45

J F M A M J

$

36

39

42

45

J F M A M J

$

Graphing the first six months of income.

36

No Zero Point

57


Good Presentation

Monthly Income Monthly Income

Bad Presentation

0

20

40

60

J F M A M J

$

36

39

42

45

J F M A M J

$

Graphing the first six months of income.

No Zero Point

58


Workshop

Critique the following Graphs

59


Male26%

Female24%

Both Sexes50%

Figure 1. Percentage Distribution of Population in Municipality A by Sex

60


0

5000

10000

15000

20000

25000

30000

1992 1993 1994 1995 1996 1997 1998 1999

Palay Corn Coconut Sugarcane

( In 1,000 metric tons)

Figure 5.2 Production of Selected Agricultural Crops; Philippines:1992-1999

61


Figure 5.2 Production of Selected Agricultural Crops; Philippines:1992-1999

0

10000

20000

30000

40000

50000

60000

1992 1993 1994 1995 1996 1997 1998 1999

Corn

Palay

Sugarcane

Coconut

( In 1,000 metric tons)

62


Figure 2. Annual Per Capita Poverty Thresholds of Families by Region

10%8%

8%

7%8%7%6%7%6%

6%

6%7%

8% 6%

NCRCARIlocos RegionCagayan ValleySouthern LuzonBicol RegionWestern VisayasCentral VisayasEastern VisayasWestern MindanaoNorthern MindanaoSouthern MindanaoCentral MindanaoARMM

63


Figure 2. Annual Per Capita Poverty Thresholds of Families by Region

0 2000 4000 6000 8000

NCRCAR

Ilocos RegionCagayan ValleySouthern Luzon

Bicol RegionWestern VisayasCentral VisayasEastern Visayas

Western MindanaoNorthern Mindanao

SouthernCentral Mindanao

ARMM

64


Figure 6. Agricultural Area: Philippines, 1989-1998

10500

11000

11500

12000

12500

13000

13500

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998

65


Figure 7. Severity of Traffic Accidents by Region

0

100

200

300

400

500

Fatal Non-Fatal

Training Course on Basic Statistics for Research

August 24-28, 2009

STATISTICAL RESEARCH AND TRAINING CENTERJ and S Building, 104 Kalayaan Avenue, Diliman, Quezon City

Thank you.

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Methods of Presenting Data

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