use and misuse of statistics-dr rishi
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Use and Misuse of Statistics
Dr. Rishi BhartiMD ,DFM (RCGP)
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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
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Statistical Methods
StatisticalMethods
DescriptiveStatistics
InferentialStatistics
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Types of Statistics
Methods of… collecting organizing presenting
and analyzing data
Science of… making inferences
about a population, based on
sample information.
Descriptive Inferential
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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
$
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Inferential Statistics
•1. Involves– Estimation– Hypothesis
Testing
•2. Purpose– Make Decisions About
Population Characteristics
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Graphs for quantitative data Histogram Frequency polygon Pie Charts Scatters DiagramBar Chart etc.
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Uses of statistics
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Central TendencyMeanModeMedian
DispersionStandard Deviation Variance
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Who uses Statistics?Those using Statistical techniques include :
Marketers
Accountants
Hospitals
Investors
EconomistsSports people
StatisticiansConsumers
EducatorsQuality Controllers
Politicians Physicians
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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
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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.
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Misuse of statistics
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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
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Misuse of Statistical Diagrams
‧ Statistical diagrams are sometimes used deliberately
to exaggerate or conceal the truth, and to mislead the
readers.
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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.
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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.
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1986 - 1999
0 1 2 3 4 5 6 7 8 9 10 11 12
3200300028002600240022002000Cr
ime
Rate
(in th
ousa
nds)
Unemployment Rate (%)
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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
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1986 -19993200300028002600240022002000Cr
ime
Rate
(in th
ousa
nds)
Unemployment Rate (%)7 8 9 10 11 12
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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
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(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.
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(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
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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
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(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.
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(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.
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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.
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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
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(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?
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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.
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Response under two treatments
Response to Treatment
NonePartial
Complete
Total
A
3159
27
B
22230
54
Treatment
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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
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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
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Thank You