政府統計處 Census and Statistics Department Common Fallacies in the Use and Presentation of Statistics

政府統計處 Census and Statistics Department (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.

政府統計處 Census and Statistics Department (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 declined by 0.5%.”

政府統計處 Census and Statistics Department (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.”

政府統計處 Census and Statistics Department (II) Imprecise Description of Statistics (Cont’d)  As a ratio to GDP (Gross Domestic Product)  The following statement is incorrect : “Expenditure 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.

政府統計處 Census and Statistics Department (II) Imprecise Description of Statistics (Cont’d)  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 case of ratio which relates a “part” to the “whole”. The correct description of the relationship between expenditure on any type of social services and GDP / GNP should be expressed by means of “ratio”.

政府統計處 Census and Statistics Department (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 Republic of Korea Philippines Country/Territory No. of hospital beds (2001) Hong Kong Republic of Korea Philippines Table (1)

政府統計處 Census and Statistics Department (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 population (2001) Hong Kong 5.2 Republic of Korea 4.5 Philippines 1.0 Country/Territory No. of hospital beds per population (2001) Hong Kong 5.2 Republic of Korea 4.5 Philippines 1.0 Table (2)

政府統計處 Census and Statistics Department (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 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.

政府統計處 Census and Statistics Department (IV) Interpretation of Small-based Figures

政府統計處 Census and Statistics Department (IV) Interpretation of Small-based Figures

政府統計處 Census and Statistics Department (V) Improper Averaging of Percentages and Ratios  Sex Ratio for Hong Kong should be 959, but not 949. AreaMaleFemaleSex ratio (No. of males per 1000 females) Hong Kong Island Kowloon New Territories Total Average = 949

政府統計處 Census and Statistics Department (VI) Mis-interpretation of Changes  Increased by x times  John's monthly salary is $3,000. When we say that his monthly salary is going to be increased by 2 times (or 200%), his new salary would be: $(3, ,000 x 2) = $9,000  Some people may think that the answer is $3,000 x 2 = $6,000, which is incorrect.

政府統計處 Census and Statistics Department (VI) Mis-interpretation of Changes (Cont’d)  Dropped by x times  Sales volume dropped from $100,000 in 1995 to $50,000 in 1996  Wrong description: “Sales volume dropped by two times.” Sales cannot drop two times (200%). By dropping one time (100%), it already becomes zero!  Correct description: “Sales volume dropped by half or 50%.”

政府統計處 Census and Statistics Department (VI) Mis-interpretation of Changes (Cont’d)  Increased by x percentage points  Suppose the passing rates for the mid-term and 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”.

政府統計處 Census and Statistics Department (VI) Mis-interpretation of Changes (Cont’d)  Increased by x %  If the total market turn over has increased from $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%.

政府統計處 Census and Statistics Department (VI) Mis-interpretation of Changes (Cont’d)  Increased by x index-points  Consider the statement “The wage index in 1996 increased 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.

政府統計處 Census and Statistics Department (VI) Mis-interpretation of Changes (Cont’d)  Point to note :  There are various ways of presenting changes. When interpreting and analyzing them, one should apply the appropriate method, lest wrong conclusions would be drawn.

政府統計處 Census and Statistics Department (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, $ 1,000 1,100 1, $

政府統計處 Census and Statistics Department (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, Year $ ,000 1,100 1, Year $

政府統計處 Census and Statistics Department (VII) Mis-representation of Data in Chart (Cont’d)  Illusions caused by expanding/ contracting the grid

政府統計處 Census and Statistics Department (VII) Mis-representation of Data in Chart (Cont’d)  Illusions caused by expanding/ contracting the grid (Cont’d) Contracting Horizontal Scale

政府統計處 Census and Statistics Department (VII) Mis-representation of Data in Chart (Cont’d)  Illusions caused by skipping grid