Data analysis

Techniques of Data Analysis

Assoc. Prof. Dr. Abdul Hamid b. Hj. Mar Iman

Director
Centre for Real Estate Studies
Faculty of Engineering and Geoinformation Science
Universiti Tekbnologi Malaysia
Skudai, Johor

Objectives

 Overall: Reinforce your understanding from the main
lecture

 Specific:
* Concepts of data analysis
* Some data analysis techniques
* Some tips for data analysis

 What I will not do:
* To teach every bit and pieces of statistical analysis
techniques

Data analysis – “The Concept”
 Approach to de-synthesizing data, informational,
and/or factual elements to answer research
questions

 Method of putting together facts and figures
to solve research problem

 Systematicprocess of utilizing data to address
research questions

 Breaking down research issues through utilizing
controlled data and factual information

Categories of data analysis
 Narrative (e.g. laws, arts)
 Descriptive (e.g. social sciences)
 Statistical/mathematical (pure/applied sciences)
 Audio-Optical (e.g. telecommunication)
 Others

Most research analyses, arguably, adopt the first
three.

The second and third are, arguably, most popular
in pure, applied, and social sciences

Statistical Methods
 Something to do with “statistics”
 Statistics: “meaningful” quantities about a sample of
objects, things, persons, events, phenomena, etc.
 Widely used in social sciences.
 Simple to complex issues. E.g.
* correlation
* anova
* manova
* regression
* econometric modelling
 Two main categories:
* Descriptive statistics
* Inferential statistics

Descriptive statistics
 Use sample information to explain/make
abstraction of population “phenomena”.
 Common “phenomena”:
 * Association (e.g. σ1,2.3 = 0.75)
* Tendency (left-skew, right-skew)
 * Causal relationship (e.g. if X, then, Y)
 * Trend, pattern, dispersion, range
 Used in non-parametric analysis (e.g. chi-
square, t-test, 2-way anova)

Examples of “abstraction” of phenomena
350,000
200000 300,000

No. of houses
250,000
150000
200,000 1991
100000 150,000 2000
100,000
50000
50,000
0
1 2 3 4 5 6 7 8
0
Loan t o pr opert y sect or (RM 32635.8 38100.6 42468.1 47684.7 48408.2 61433.6 77255.7 97810.1

Kl u

M ggi
ta ng

Se tian

at
rB t

Po ar
ng
ho h a

r
million)

ah

u

m
Ko ua

si
n

M
J o Pa

n
ga
Ti

er
Demand f or shop shouses (unit s) 71719 73892 85843 95916 101107 117857 134864 86323

tu
Supply of shop houses (unit s) 85534 85821 90366 101508 111952 125334 143530 154179

Ba
Year (1990 - 1997)

Trends in property loan, shop house dem and & supply District

14
12
Proportion (%)

10
8
6
4
2
0
4

4

4

4
4

4

4

4
-1

-2

-3

-4

-5

-6

-7
0-

10

20

30

40

50

60

70

Age Category (Years Old)

Examples of “abstraction” of phenomena
200

50.00
180 %
prediction

Distance from Rakaia (km)
160 40.00 error
Price (RM/sq.ft. built area)

140 30.00 100.00
80.00
60.00
40.00
120 20.00 20.00
0.00
-20.00
100 10.00 -40.00
-60.00
-80.00
80 -100.00
20 40 60 80 100 120 10.00 20.00 30.00 40.00 50.00 60.00
Distance from Ashurton (km)
Demand (% sales success)

Inferential statistics
 Using sample statistics to infer some
“phenomena” of population parameters
 Common “phenomena”: cause-and-effect
* One-way r/ship Y = f(X)

* Multi-directional r/ship Y1 = f(Y2, X, e1)
Y2 = f(Y1, Z, e2)
* Recursive Y1 = f(X, e1)
Y2 = f(Y1, Z, e2)

 Use parametric analysis

Examples of relationship
Dep=9t – 215.8

Dep=7t – 192.6

Coefficientsa

Unstandardized Standardized
Coefficients Coefficients
Model B Std. Error Beta t Sig.
1 (Constant) 1993.108 239.632 8.317 .000
Tanah -4.472 1.199 -.190 -3.728 .000
Bangunan 6.938 .619 .705 11.209 .000
Ansilari 4.393 1.807 .139 2.431 .017
Umur -27.893 6.108 -.241 -4.567 .000
Flo_go 34.895 89.440 .020 .390 .697
a. Dependent Variable: Nilaism

Which one to use?
 Nature of research
* Descriptive in nature?
* Attempts to “infer”, “predict”, find “cause-and-effect”,
“influence”, “relationship”?
* Is it both?
 Research design (incl. variables involved). E.g.
 Outputs/results expected
* research issue
* research questions
* research hypotheses

At post-graduate level research, failure to choose the correct data
analysis technique is an almost sure ingredient for thesis failure.

Common mistakes in data analysis
 Wrong techniques. E.g.
Issue Data analysis techniques
Wrong technique Correct technique
To study factors that “influence” visitors to Likert scaling based on Data tabulation based on
come to a recreation site interviews open-ended questionnaire
survey

“Effects” of KLIA on the development of Likert scaling based on Descriptive analysis based
Sepang interviews on ex-ante post-ante
experimental investigation

Note: No way can Likert scaling show “cause-and-effect” phenomena!

 Infeasible techniques. E.g.
How to design ex-ante effects of KLIA? Development
occurs “before” and “after”! What is the control treatment?
Further explanation!
 Abuse of statistics. E.g.
 Simply exclude a technique

Common mistakes (contd.) – “Abuse of statistics”
Issue Data analysis techniques
Example of abuse Correct technique
Measure the “influence” of a variable Using partial correlation Using a regression
on another (e.g. Spearman coeff.) parameter
Finding the “relationship” between one Multi-dimensional Simple regression
variable with another scaling, Likert scaling coefficient
To evaluate whether a model fits data Using R2 Many – a.o.t. Box-Cox
better than the other χ2 test for model
equivalence
To evaluate accuracy of “prediction” Using R2 and/or F-value Hold-out sample’s
of a model MAPE
“Compare” whether a group is different Multi-dimensional Many – a.o.t. two-way
from another scaling, Likert scaling anova, χ2, Z test

To determine whether a group of Multi-dimensional Many – a.o.t. manova,
factors “significantly influence” the scaling, Likert scaling regression
observed phenomenon

How to avoid mistakes - Useful tips
 Crystalize the research problem → operability of
it!
 Read literature on data analysis techniques.
 Evaluate various techniques that can do similar
things w.r.t. to research problem
 Know what a technique does and what it doesn’t
 Consult people, esp. supervisor
 Pilot-run the data and evaluate results
 Don’t do research??

Principles of analysis
 Goal of an analysis:
* To explain cause-and-effect phenomena
* To relate research with real-world event
* To predict/forecast the real-world
phenomena based on research
* Finding answers to a particular problem
* Making conclusions about real-world
event
based on the problem
* Learning a lesson from the problem

Principles of analysis (contd.)

 Data can’t “talk”
 An analysis contains some aspects of scientific
reasoning/argument:
* Define
* Interpret
* Evaluate
* Illustrate
* Discuss
* Explain
* Clarify
* Compare
* Contrast

Principles of analysis (contd.)
 An analysis must have four elements:
* Data/information (what)
* Scientific reasoning/argument (what?
who? where? how? what happens?)
* Finding (what results?)
* Lesson/conclusion (so what? so how?
therefore,…)
 Example

Principles of data analysis
 Basic guide to data analysis:
* “Analyse” NOT “narrate”
* Go back to research flowchart
* Break down into research objectives and
research questions
* Identify phenomena to be investigated
* Visualise the “expected” answers
* Validate the answers with data
* Don’t tell something not supported by
data

Principles of data analysis (contd.)
Shoppers Number
Male
Old 6
Young 4
Female
Old 10
Young 15
More female shoppers than male shoppers
More young female shoppers than young male shoppers
Young male shoppers are not interested to shop at the shopping complex

Data analysis (contd.)
 When analysing:
* Be objective
* Accurate
* True
 Separate facts and opinion
 Avoid “wrong” reasoning/argument. E.g.
mistakes in interpretation.

Introductory Statistics for Social Sciences

Basic concepts
Central tendency
Variability
Probability
Statistical Modelling

Basic Concepts
 Population: the whole set of a “universe”
 Sample: a sub-set of a population
 Parameter: an unknown “fixed” value of population characteristic
 Statistic: a known/calculable value of sample characteristic
representing that of the population. E.g.
μ = mean of population, = mean of sample

Q: What is the mean price of houses in J.B.?
A: RM 210,000
= 300,000 = 120,000
1
2
SD SST
= 210,000
3
J.B. houses
DST
μ=?

Basic Concepts (contd.)
 Randomness: Many things occur by pure
chances…rainfall, disease, birth, death,..
 Variability: Stochastic processes bring in
them various different dimensions,
characteristics, properties, features, etc.,
in the population
 Statistical analysis methods have been
developed to deal with these very nature
of real world.

“Central Tendency”
Measure Advantages Disadvantages
Mean ∗ Best known average ∗ Affected by extreme values
(Sum of ∗ Can be absurd for discrete data
∗ Exactly calculable
all values
÷ ∗ Make use of all data (e.g. Family size = 4.5 person)
no. of ∗ Useful for statistical analysis ∗ Cannot be obtained graphically
values)

Median ∗ Not influenced by extreme ∗ Needs interpolation for group/
(middle values aggregate data (cumulative
value)
∗ Obtainable even if data frequency curve)
distribution unknown (e.g. ∗ May not be characteristic of group
group/aggregate data) when: (1) items are only few; (2)
∗ Unaffected by irregular class distribution irregular
width ∗ Very limited statistical use
∗ Unaffected by open-ended class

Mode ∗ Unaffected by extreme values ∗ Cannot be determined exactly in
(most group data
∗ Easy to obtain from histogram
frequent
value) ∗ Determinable from only values ∗ Very limited statistical use
near the modal class

Central Tendency – “Mean”,
 For individual observations, . E.g.
X = {3,5,7,7,8,8,8,9,9,10,10,12}
= 96 ; n = 12
 Thus, = 96/12 = 8
 The above observations can be organised into a frequency
table and mean calculated on the basis of frequencies
x 3 5 7 8 9 10 12
f 1 1 2 3 2 2 1
= 96; = 12
Σf 3 5 14 24 18 20 12

Thus, = 96/12 = 8

Central Tendency–“Mean of Grouped Data”
 House rental or prices in the PMR are frequently
tabulated as a range of values. E.g.

Rental (RM/month) 135-140 140-145 145-150 150-155 155-160

Mid-point value (x) 137.5 142.5 147.5 152.5 157.5

Number of Taman (f) 5 9 6 2 1

fx 687.5 1282.5 885.0 305.0 157.5

 What is the mean rental across the areas?
= 23; = 3317.5
Thus, = 3317.5/23 = 144.24

Central Tendency – “Median”
 Let say house rentals in a particular town are tabulated as
follows:
Rental (RM/month) 130-135 135-140 140-145 155-50 150-155
Number of Taman (f) 3 5 9 6 2
Rental (RM/month) >135 > 140 > 145 > 150 > 155
Cumulative frequency 3 8 1 23 25

 Calculation of “median” rental needs a graphical aids→
1. Median = (n+1)/2 = (25+1)/2 =13th. 5. Taman 13th. is 5th. out of the 9
Taman
Taman
2. (i.e. between 10 – 15 points on the
vertical axis of ogive). 6. The interval width is 5

3. Corresponds to RM 140- 7. Therefore, the median rental can
145/month on the horizontal axis be calculated as:
4. There are (17-8) = 9 Taman in the 140 + (5/9 x 5) = RM 142.8
range of RM 140-145/month

Central Tendency – “Median” (contd.)

Central Tendency – “Quartiles” (contd.)

Upper quartile = ¾(n+1) = 19.5th.
Taman
UQ = 145 + (3/7 x 5) = RM
147.1/month
Lower quartile = (n+1)/4 = 26/4 =
6.5 th. Taman
LQ = 135 + (3.5/5 x 5) =
RM138.5/month
Inter-quartile = UQ – LQ = 147.1
– 138.5 = 8.6th. Taman
IQ = 138.5 + (4/5 x 5) = RM
142.5/month

“Variability”
 Indicates dispersion, spread, variation, deviation
 For single population or sample data:

where σ2 and s2 = population and sample variance respectively, xi =
individual observations, μ = population mean, = sample mean, and n
= total number of individual observations.
 The square roots are:

standard deviation standard deviation

“Variability” (contd.)
 Why “measure of dispersion” important?
 Consider returns from two categories of shares:

* Shares A (%) = {1.8, 1.9, 2.0, 2.1, 3.6}
* Shares B (%) = {1.0, 1.5, 2.0, 3.0, 3.9}

Mean A = mean B = 2.28%
But, different variability!
Var(A) = 0.557, Var(B) = 1.367

* Would you invest in category A shares or
category B shares?

 Coefficient
of variation – COV – std. deviation as
% of the mean:

 Could
be a better measure compared to std. dev.
COV(A) = 32.73%, COV(B) = 51.28%

 Std. dev. of a frequency distribution
The following table shows the age distribution of second-time home buyers:

x^

“Probability Distribution”
 Defined as of probability density function (pdf).
 Many types: Z, t, F, gamma, etc.
 “God-given” nature of the real world event.
 General form: (continuous)

(discrete)

 E.g.

“Probability Distribution” (contd.)

Dice2
Dice1
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12


Discrete values Discrete values

Values of x are discrete (discontinuous)

Sum of lengths of vertical bars Σp(X=x) = 1
all x

8 ▪ Many real world phenomena
take a form of continuous
random variable

6 ▪ Can take any values between
two limits (e.g. income, age,
weight, price, rental, etc.)

4
F
n
u
q
y
c
e
r

2

Mean = 4.0628
Std. Dev. = 1.70319
N = 32
0
2.00 3.00 4.00 5.00 6.00 7.00
Rental (RM/sq.ft.)


P(Rental = RM 8) = 0 P(Rental < RM 3.00) = 0.206

P(Rental < RM7) = 0.972 P(Rental ≥ RM 4.00) = 0.544

 Ideal distribution of such phenomena:

* Bell-shaped, symmetrical
μ = mean of variable x
σ = std. dev. Of x
* Has a function of
π = ratio of circumference of a
circle to its diameter = 3.14
e = base of natural log = 2.71828

“Probability distribution”

μ ± 1σ = ? = ____% from total observation

* Has the following distribution of observation

 There are various other types and/or shapes of
distribution. E.g.

Note: Σp(AGE=age) ≠ 1
How to turn this graph into
a probability distribution
function (p.d.f.)?

 Not “ideally” shaped like the previous one

“Z-Distribution”
 φ(X=x) is given by area under curve
 Has no standard algebraic method of integration → Z ~ N(0,1)
 It is called “normal distribution” (ND)
 Standard reference/approximation of other distributions. Since there
are various f(x) forming NDs, SND is needed
 To transform f(x) into f(z):
x-µ
Z = --------- ~ N(0, 1)
σ
160 –155
E.g. Z = ------------- = 0.926
5.4

 Probability is such a way that:
* Approx. 68% -1< z <1
* Approx. 95% -1.96 < z < 1.96
* Approx. 99% -2.58 < z < 2.58

“Z-distribution” (contd.)

 When X= μ, Z = 0, i.e.

 When X = μ + σ, Z = 1
 When X = μ + 2σ, Z = 2
 When X = μ + 3σ, Z = 3 and so on.
 It can be proven that P(X1 <X< Xk) = P(Z1 <Z< Zk)
 SND shows the probability to the right of any
particular value of Z.
 Example

Normal distribution…Questions
Your sample found that the mean price of “affordable” homes in Johor
Bahru, Y, is RM 155,000 with a variance of RM 3.8x107. On the basis of a
normality assumption, how sure are you that:

(a) The mean price is really ≤ RM 160,000
(b) The mean price is between RM 145,000 and 160,000

Answer (a):
160,000 -155,000
P(Y ≤ 160,000) = P(Z ≤ ---------------------------)
= P(Z ≤ 0.811) √3.8x10
7

= 0.1867
Using Z-table , the required probability is:
1-0.1867 = 0.8133

Always remember: to convert to SND, subtract the mean and divide by the std. dev.

Answer (b):

X1 - μ 145,000 – 155,000
Z1 = ------ = ---------------- = -1.622
σ √3.8x107

X2 - μ 160,000 – 155,000
Z2 = ------ = ---------------- = 0.811
σ √3.8x10 7

P(Z1<-1.622)=0.0455; P(Z2>0.811)=0.1867
∴P(145,000<Z<160,000)
= P(1-(0.0455+0.1867)
= 0.7678

You are told by a property consultant that the
average rental for a shop house in Johor Bahru is
RM 3.20 per sq. After searching, you discovered
the following rental data:

2.20, 3.00, 2.00, 2.50, 3.50,3.20, 2.60, 2.00,
3.10, 2.70

What is the probability that the rental is greater
than RM 3.00?

“Student’s t-Distribution”

 Similar to Z-distribution:
* t(0,σ) but σn→∞→1
* -∞ < t < +∞
* Flatter with thicker tails
* As n→∞ t(0,σ) → N(0,1)
* Has a function of
where Γ=gamma distribution; v=n-1=d.o.f; π=3.147
* Probability calculation requires information on
d.o.f.


 Given n independent measurements, xi, let

where μ is the population mean, is the sample
mean, and s is the estimator for population
standard deviation.

 Distributionof the random variable t which is
(very loosely) the "best" that we can do not
knowing σ.


 Student's t-distribution can be derived by:

* transforming Student's z-distribution using

* defining

 The resulting probability and cumulative
distribution functions are:


fr(t) =

=

Fr(t) =

=

=

where r ≡ n-1 is the number of degrees of freedom, -∞<t<∞,Γ(t) is the gamma function,
B(a,b) is the beta function, and I(z;a,b) is the regularized beta function defined by


Forms of “statistical” relationship
 Correlation
 Contingency
 Cause-and-effect
* Causal
* Feedback
* Multi-directional
* Recursive
 The last two categories are normally dealt with
through regression

Correlation
 “Co-exist”.E.g.
* left shoe & right shoe, sleep & lying down, food & drink
 Indicate “some” co-existence relationship. E.g.
* Linearly associated (-ve or +ve)
Formula:
* Co-dependent, independent
 But, nothing to do with C-A-E r/ship!
Example: After a field survey, you have the following
data on the distance to work and distance to the city
of residents in J.B. area. Interpret the results?

Contingency
 A form of “conditional” co-existence:
* If X, then, NOT Y; if Y, then, NOT X
* If X, then, ALSO Y
* E.g.
+ if they choose to live close to workplace,
then, they will stay away from city
+ if they choose to live close to city, then, they
will stay away from workplace
+ they will stay close to both workplace and city

Correlation and regression – matrix approach

Test yourselves!

Q1: Calculate the min and std. variance of the following data:

PRICE - RM ‘000 130 137 128 390 140 241 342 143
SQ. M OF FLOOR 135 140 100 360 175 270 200 170

Q2: Calculate the mean price of the following low-cost houses, in various
localities across the country:

PRICE - RM ‘000 (x) 36 37 38 39 40 41 42 43

NO. OF LOCALITIES (f) 3 14 10 36 73 27 20 17

Test yourselves!
Q3: From a sample information, a population of housing
estate is believed have a “normal” distribution of X ~ (155,
45). What is the general adjustment to obtain a Standard
Normal Distribution of this population?

Q4: Consider the following ROI for two types of investment:

A: 3.6, 4.6, 4.6, 5.2, 4.2, 6.5
B: 3.3, 3.4, 4.2, 5.5, 5.8, 6.8

Decide which investment you would choose.

Test yourselves!

Q5: Find:
φ(AGE > “30-34”)
φ(AGE ≤ 20-24)
φ( “35-39”≤ AGE < “50-54”)

Test yourselves!
Q6: You are asked by a property marketing manager to ascertain
whether
or not distance to work and distance to the city are “equally” important
factors influencing people’s choice of house location.

You are given the following data for the purpose of testing:

Explore the data as follows:
• Create histograms for both distances. Comment on the shape of the
histograms. What is you conclusion?
• Construct scatter diagram of both distances. Comment on the output.
• Explore the data and give some analysis.
• Set a hypothesis that means of both distances are the same. Make
your conclusion.

Test yourselves! (contd.)

Q7: From your initial investigation, you belief that tenants of
“low-quality” housing choose to rent particular flat units just
to find shelters. In this context ,these groups of people do
not pay much attention to pertinent aspects of “quality
life” such as accessibility, good surrounding, security, and
physical facilities in the living areas.

(a) Set your research design and data analysis procedure to address
the research issue
(b) Test your hypothesis that low-income tenants do not perceive
“quality life” to be important in paying their house rentals.

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