Use and Misuse of Statistics

Dr. Rishi BhartiMD ,DFM (RCGP)

What is statistics?“A branch of mathematics dealing with the analysis and interpretation of masses of numerical data” Merrian-Webster Dictionary

“The study of how information should be employed to reflect on, and give guidance for action, in a practical situation involving uncertainty” Vic Barnett

Statistical Methods

StatisticalMethods

DescriptiveStatistics

InferentialStatistics

Types of Statistics

Methods of… collecting organizing presenting

and analyzing data

Science of… making inferences

about a population, based on

sample information.

Descriptive Inferential

Descriptive Statistics

•1. Involves– Collecting Data– Presenting Data– Characterizing Data

•2. Purpose– Describe Data

X = 30.5 S2 = 113

0

25

50

Q1 Q2 Q3 Q4

$

Inferential Statistics

•1. Involves– Estimation– Hypothesis

Testing

•2. Purpose– Make Decisions About

Population Characteristics

Graphs for quantitative data Histogram Frequency polygon Pie Charts Scatters DiagramBar Chart etc.

Uses of statistics

Central TendencyMeanModeMedian

DispersionStandard Deviation Variance

Who uses Statistics?Those using Statistical techniques include :

Marketers

Accountants

Hospitals

Investors

EconomistsSports people

StatisticiansConsumers

EducatorsQuality Controllers

Politicians Physicians

Broken-line Graphs1. Understanding Broken-line Graphs

i. A broken-line graph is used to show the change in the data over a period of time and their overall tendency.E.g.

Year

Annual profits of a company

Pie Charts1. Understanding Pie Charts

i. A pie chart is appropriate to present the various statistical items as percentages of the whole.

Favourite ball games played by F.1 students in a school

E.g.

Misuse of statistics

As you begin to study statistical methods, you are cautioned to take what you see

published as “statistical facts”

… an average may not be representative of all the data

… graphs can also be misleading

… be sure to study the sampling methods

Misuse of Statistical Diagrams

‧ Statistical diagrams are sometimes used deliberately

to exaggerate or conceal the truth, and to mislead the

readers.

What should we be careful when we are reading statistical diagrams?

‧ Check whether the scales on the two axes have been drawn correctly.

‧ The items of two statistical graphs cannot be compared by the sizes of the angles in the graphs alone.

‧ Check whether the sizes of the groups have been distorted or exaggerated in such a way to mislead people.

Review the following three slides and notice the effect

that the different scales

have on your interpretation of the pattern between Crime and Unemployment

Rates.

1986 - 1999

0 1 2 3 4 5 6 7 8 9 10 11 12

3200300028002600240022002000Cr

ime

Rate

(in th

ousa

nds)

Unemployment Rate (%)

1986 -1999

7 8 9 10 11 12

30002500200015001000 500 0Cr

ime

Rate

(in th

ousa

nds)

Unemployment Rate (%)

500

0

1000

1500

2000

2500

3000

1986 -19993200300028002600240022002000Cr

ime

Rate

(in th

ousa

nds)

Unemployment Rate (%)7 8 9 10 11 12

The following graph is a bar chart shown in the advertisement of the Hurryson Telecommunications Company.

Charges on long-distance callsC

harg

e pe

r m

inut

e ($

)

Telecommunications Company

(a) Measure the lengths of the bars of HK United and

Hurryson, express the length of the bar of Hurryson

Telecommunications Company as a fraction of that

of HK United.

(b) Now express the actual charges of Hurryson as a

fraction of HK United and compare this result with

that obtained in (a). Do you agree that this bar chart

is misleading? Explain your answer.

(a) The length of the bar for Hurryson is that of HK United.51

(b) Actual charge per minute of HK United = $3.2

Actual charge per minute of Hurryson = $3

1615

2.3$3$ The required fraction =

Since , the bar chart has a misleading effect.51

1615

The Money Commercial College used the following diagram to show the highest monthly salary of their fresh graduates in the years 2004 and 2005.

Mon

thly

sala

ry ($

)

Year

(a) Find the areas of the two triangles A and B in the statistical diagram shown above. Express the area of B as a multiple of the area of A.

(b) Find out, from the diagram, the actualhighest monthly salaries in the twoyears. Express the one in 2005 as amultiple of that in 2004.

(a) Suppose each small square in the figure has a side of 1 unit:

Area of triangle B = units sq. 301621

= 240 sq. units

Area of triangle A = units sq. 15821

= 60 sq. units

∴ The required multiple = 460240

Thus, the area of B is 4 times that of A.

Fulfill Exercise Objective

Questions on statistical diagrams in which the sizes of figures are distorted or exaggerated.

(b) From the diagram,

the highest monthly salary in 2005 = $12 000

the highest monthly salary in 2004 = $6 000

∴ The required multiple = 2000 6$000 12$

∴ The highest monthly salary in

2005 was 2 times that in 2004.

Fig. A below shows the profits of ABC company from 2000 to 2004. In order to show the shareholders that the company’s profit has increased a lot since 1990. The managing director of the company added the profit of the company in 1990 to the graph (Fig. B).

Profit of ABC company from 2000 to 2004

Year

Prof

it ($

mill

ion)

Fig. AYear

Profit of ABC company from 1990 to 2004

Prof

it ($

mill

ion)

Fig. B

(a) As compared with Fig. A, does

Fig. B give the readers an

impression that the company’s

profit increases rapidly?

(b) Do you think that the managing director is

misleading the readers in Fig. B? Why?

Fulfill Exercise Objective

Questions on statistical diagrams showing only a part of data.

(a) Yes, Fig. B gives the readers an impression that the

company’s profit increases rapidly.

(b) Yes, the managing director is misleading the readers in

Fig. B. Because the profits in the years 1991 to 1999 are

not shown, people may be misled to think that the profit

increases rapidly from 1990 to 2000.

Response under two treatments

Response to Treatment

NonePartial

Complete

Total

A

3159

27

B

22230

54

Treatment

AB

CompletePartialNone

30

20

10

0

Response to treatment

Fre

quen

cy

A misleading bar chart

By design, there are twice as many patients receiving treatment B

NonePartial

Complete

BA

100

90

80

70

60

50

40

30

20

10

0

Treatment

With

in tr

eatm

ent p

erce

ntag

e

treatmentResponse to

Can compare the response type percentages for the two treatments

Thank You