Some Application of Statistical Methods in

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• Some Application of Statistical Methods in
• Data Analysis
• Assoc. Prof. Dr. Abdul Hamid b. Hj. Mar Iman,
• Former Director,
• Centre for Real Estate Studies,
• Universiti Teknologi Malaysia.

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Forms of statistical relationship

• Correlation
• Contingency
• Cause-and-effect
• Causal
• Feedback
• Multi-directional
• Recursive
• The last two categories are normally dealt with
  through regression

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Statistical Data Analysis Methods A Summary
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One-Sample Test

• McNemar Test tests for change in a sample upon a
  treatment.
• Example. Two condominium projects KL.
  Respondents decide their preferences for K or L
  before and after advertising.
• Hypothesis Advertising does not influence buyers
  to change their mind on product choice

40 people switch from K to L and 50 people switch
from L to K before and after
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One-Sample Test (contd.)

• Test statistics

Thus, Q (40-45)2/(4045) 25/85
0.29 ?(2-1)(2-1) 0.05 3.84 Ho
not rejected. No influence of advertising on
choice of project
r c Q ??(0ij Eij)2/Eij i1
j1
where E (AD)/2
Therefore,
r c Q ??(0ij Eij)2/Eij i1
j1
A-(AD)/22 D-(AD)/22
(A-D)2 -----------------
---------------- -------
(AD)/2 (AD)/2 AD
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One-Sample Test (contd.)

• Friedman Test tests for equal preferences for
  something of various characteristics.
• Example. Buyers rank of preference for three
  condominium types A, B, C.
• Hypothesis Buyers preferences for all condo
  type do not differ

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One-Sample Test (contd.)

• Test statistics
• (n-1)k k
• Fr ---------- ? Rj2 3n(k1)
• nk(k1) j1
• where n sample size, k number of
  categories R is columns total
• For large n and k, Fr follows X2(k-1)a

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One-Sample Test (contd.)

• (5-1)3
• F ------------ 82 112 112 3x5(31)
• 5x3(31)
• 1.2
• X2(3-1) 0.05 5.99
• Ho not rejected. Buyers do not show different
  preference for condo type

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One-Sample Test (contd.)

• Repeated measures ANOVA tests outcome of a
  phenomenon under different conditions.
• Example. Waiting time at junctions in the city
  area to determine level of congestion at
  different times of the day.
• Test statistics
• t/(m-1)
• F ----------------
• r/(n-1)(m-1)
• where t sum of squares due to treatment, r
  sum of squares of residual, m number of
  treatment, n number of observations.
• Critical region based on F v1. v2 a
• 
  where v1 (m-1), v2 (n-1)(m-1)

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One-Sample Test (contd.)
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One-sample test (contd.)
t n ? ( - M)2 10 W t r r W t
23.34 10 13.34

• m n
• T ? ?(cij M)2
• i1 j1
• 30
• Wi ?(cij )2
• 23.34
• B m?( - M)2
• 6.65

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One-Sample Test (contd.)

• 10/(3-1)
• Fc ---------------------- 2.99
• 13.34/(5-1)(3-2)
• Ft (3-1),(3-1)(5-1) 0.05 4.46
• Ho not rejected. Congestion is quite the same at
  all times during the day.

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Two-Sample Test

• Two-way Contingency Table test whether two
  independent groups differ on a given
  characteristic.
• Hypothesis choice for type of house does not
  relate to location.
• Test

r c Q ??(0ij Eij)2/Eij i1 j1
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Two-Sample Test (contd.)

• D.o.f. (r-1)(c-1),
• where rnumber of
• rows, cnumber of columns
• Eij RiCj/N

Q (50-55.6)2/55.6 (30-24.4)2/24.4
(75-69.4)2/69.4 (25-30.6)2/30.6
3.33 ?(2-1)(2-1) 0.05 3.84 Ho not rejected
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K Independent Test - 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)
• Co-dependent, independent
• But, nothing to do with C-A-E r/ship!

Formula

• 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?

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K Independent Test - Correlation and regression
matrix approach
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Correlation and regression matrix approach
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Correlation and regression matrix approach
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Correlation and regression matrix approach
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Correlation and regression matrix approach
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Test yourselves!

• Q1 Calculate the min and std. variance of the
  following data
• Q2 Calculate the mean price of the following
  low-cost houses, in various
• localities across the country

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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.

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Test yourselves!
Q5 Find ?(AGE gt 30-34) ?(AGE 20-24) ?(
35-39 AGE lt 50-54)
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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 peoples 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.

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Q 7. You have surveyed a group of local people
and asked them to express their feeling about a
new project that will attract a new population
and thus a new neighbourhood. You believe that
the local people are concerned about the negative
influence the new neighbourhood will have on them
as a result of the proposed project. Using the
collected data, test your hypohesis.
Perception about Influence of New Neighbourhood
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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.
• 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.