政府統計處 census and statistics department common fallacies in the use and presentation of...

政府統計處Census and Statistics Department

Common Fallacies in the Use and Presentation of S

tatistics


(I) Reference Periods in Statistics not Clearly Stated

A stand-alone statement like “the number of students has grown by 30%” is not meaningful.

It is necessary to specify that the growth has taken place over a certain interval of time, say one month, one year, three years, etc.


(II) Imprecise Description of Statistics

Statements like the following which sometimes appear in newspapers and magazines are not meaningful:

“CPI (Consumer Price Index) in July was 1.5%.”“GDP (Gross Domestic Product) last quarter declin

ed by 0.5%.”


(II) Imprecise Description of Statistics (Cont’d)

These statements should be written in a more precise manner:

“The year-on-year rate of increase of the CPI in July was 1.5%.” or “CPI in July this year was 1.5% higher than that in July last year.”

“The year-on-year growth rate of GDP in the last quarter was 3.5%, which was lower by half a percentage point when compared with the 4.0% year-on-year growth rate in the quarter earlier.”



As a ratio to GDP (Gross Domestic Product)The following statement is incorrect : “Expen

diture on education services comprised 4% of the GDP in 2002/03.”

While we can express the education expenditure as a proportion (or a percentage) to total public expenditure; we should not relate it as a proportion to GDP, as education expenses are not “part” of GDP.



The correct statement should read as “Education expenses, expressed as a ratio to GDP, was 4% in 2002/03.”

Points to Note• It should be noted that proportion is a special ca

se of ratio which relates a “part” to the “whole”.• The correct description of the relationship betwe

en expenditure on any type of social services and GDP / GNP should be expressed by means of “ratio”.


(III) Illusion in Interpreting Absolute Figures

By simply comparing the numbers of hospital beds as shown in the table (1), one may think that the provision of hospital beds is most inadequate in Hong Kong among the three selected areas.

Country/Territory No. of hospital beds (2001)

Hong Kong 35 000Republic of Korea 211 000Philippines 79 000

Country/Territory No. of hospital beds (2001)

Hong Kong 35 000Republic of Korea 211 000Philippines 79 000

Table (1)


(III) Illusion in Interpreting Absolute Figures (Cont’d)

To compare the degree of availability of hospital beds in different areas, we should use the “rate” (i.e. the number of beds per 1000 population) rather than the number.

Country/Territory No. of hospital beds per 1 000 population

(2001)

Hong Kong 5.2Republic of Korea 4.5Philippines 1.0

Country/Territory No. of hospital beds per 1 000 population

(2001)

Hong Kong 5.2Republic of Korea 4.5Philippines 1.0

Table (2)


(III) Illusion in Interpreting Absolute Figures (Cont’d)

It can be seen that from Table (2) though the number of hospital beds is the lowest in Hong Kong, the number of hospital beds per 1 000 population is the highest.

Hence, it is inappropriate to say that hospital beds are less adequately provided in Hong Kong by simply looking at the number of beds.


(IV) Interpretation of Small-based Figures

Top Ten Government Departments that Cannot Fulfill the Requests of Information Enquirers

Rank Department Percentage of cases that no information or

only partial information was provided

(1) Constitutional Affairs Bureau 100% (2) Legal Aid Department 54.5% (3) Land Registry 52.4% (4) Courts and Tribunals of Judiciary 45.5% (5) Rating and Valuation Department 42.9% (6) Inland Revenue Department 33.3% (7) Security Bureau 28% (8) Chief Secretary for Administration’s Office and

Financial Secretary’s Office 20%

(9) Buildings Department 17.2% (10) Information Technology Broadcasting Bureau 16.7% (11) Department of Justice 16.7% (12) Financial Services Bureau 16.7%


(IV) Interpretation of Small-based Figures

Top Ten Government Departments that Cannot Fulfill the Requests of Information Enquirers

Rank Department No. of cases Percentage of cases that no information or

only partial information was provided

(1) Constitutional Affairs Bureau 1 100% (2) Legal Aid Department 11 54.5% (3) Land Registry 21 52.4% (4) Courts and Tribunals of Judiciary 22 45.5% (5) Rating and Valuation Department 14 42.9% (6) Inland Revenue Department 18 33.3% (7) Security Bureau 25 28% (8) Chief Secretary for Administration’s Office and

Financial Secretary’s Office 5 20%

(9) Buildings Department 29 17.2% (10) Information Technology Broadcasting Bureau 48 16.7% (11) Department of Justice 18 16.7% (12) Financial Services Bureau 6 16.7%


(V) Improper Averaging of Percentages and Ratios

Sex Ratio for Hong Kong should be 959, but not 949.

Area Male Female Sex ratio

(No. of males per 1000 females)

Hong Kong Island 631 854 703 615 898

Kowloon 998 754 1 025 225 974

New Territories 1 650 658 1 692 388 975

Total 3 281 266 3 421 228 959

Average = 949


(VI) Mis-interpretation of Changes

Increased by x timesJohn's monthly salary is $3,000. When we s

ay that his monthly salary is going to be increased by 2 times (or 200%), his new salary would be:

$(3,000 + 3,000 x 2) = $9,000Some people may think that the answer is $3,

000 x 2 = $6,000, which is incorrect.


(VI) Mis-interpretation of Changes (Cont’d)

Dropped by x timesSales volume dropped from $100,000 in 1995

to $50,000 in 1996Wrong description: “Sales volume dropped by tw

o times.”• Sales cannot drop two times (200%). By droppin

g one time (100%), it already becomes zero!

Correct description: “Sales volume dropped by half or 50%.”



Increased by x percentage pointsSuppose the passing rates for the mid-term a

nd final examinations for a class of students were 91% and 93% respectively.

Is it correct to say that “the passing rate has increased by 2%” ?

No! The correct change should be recorded as “the passing rate has increased by 2 percentage points” .



Increased by x%If the total market turn over has increased fr

om $200 to $220 billion. Should we say that “the total turnover has increased by 10 percentage points” ?

No ! The proper way is to say there has been an increase of 10%.



Increased by x index-pointsConsider the statement “The wage index in 1996 inc

reased by 5 index-points as compared with that in the previous year.” Does it imply that the wage level has increased by 5%?

If the wage index increases from 100 to 105, it would happen to be a 5 percent rise ( ).

However, a rise of 5 index-points from 200 to 205 is equivalent to 2.5 percent increase

( ) only.

%5%100100

100105

%5.2%100200

200205



Point to note :There are various ways of presenting change

s. When interpreting and analyzing them, one should apply the appropriate method, lest wrong conclusions would be drawn.


(VII) Mis-representation of Data in Chart

Illusions caused by Improper vertical scale

This is bound to exaggerate the true relationship and convey a distorted impression! For example, in the charts above, the figure in 2002 appears to be several times that in 1999 which is not true.

1,000

1,100

1,200

1999 2000 2001 2002

$

1,000

1,100

1,200

1999 2000 2001 2002

$


(VII) Mis-representation of Data in Chart (Cont’d)

The proper way (broken-scale)

This method of presentation enables the data variations among the years to be presented clearly yet still reminds user to watch out for the possible distorted impression which may be conveyed.

0

1,000

1,100

1,200

1999 2000 2001 2002

Year

$

0

900

1,000

1,100

1,200

1999 2000 2001 2002

Year

$



Illusions caused by expanding/ contracting the grid

Original Scale Arrangement

Contracting Vertical Scale

Expanding Vertical Scale



Illusions caused by expanding/ contracting the grid (Cont’d)

Original Scale Arrangement

Expanding Horizontal Scale

ContractingHorizontal Scale



Illusions causedby skipping grid

0

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40

60

80

100

120

140

1961 1980 1995 1996 1997 1998 1999 2000 2001

Year

HK$ (million)

0

20

40

60

80

100

120

140

1960 1965 1970 1975 1980 1985 1990 1995 2000

Year

HK$ (million)

140

120

20

40

60

80

100

0

1961

政府統計處 census and statistics department common fallacies in the use and presentation of...

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