Download - Episode 12 : Research Methodology ( Part 2 )
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SAJJAD KHUDHUR ABBASChemical Engineering , Al-Muthanna University, IraqOil & Gas Safety and Health Professional – OSHACADEMYTrainer of Trainers (TOT) - Canadian Center of Human Development
Episode 12 : Research Methodology ( Part 2 )
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Techniques of Data Analysis
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Data analysis ?? • 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
• Systematic process of utilizing data to address research questions
• Breaking down research issues through utilizing controlled data and factual information
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Qualitative & Quantitative ResearchQualitative Quantitative
"All research ultimately has a qualitative grounding"
- Donald Campbell
"There's no such thing as qualitative data.
Everything is either 1 or 0"- Fred Kerlinger
The aim is a complete, detailed description.
The aim is to classify features, count them, and construct statistical models in an attempt to explain what is observed.
Researcher may only know roughly in advance what he/she is looking for.
Researcher knows clearly in advance what he/she is looking for.
Recommended during earlier phases of research projects.
Recommended during latter phases of research projects.
The design emerges as the study unfolds.
All aspects of the study are carefully designed before data is collected. 4
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Qualitative Quantitative
Researcher is the data gathering instrument.
Researcher uses tools, such as questionnaires or equipment to collect numerical data.
Data is in the form of words, pictures or objects.
Data is in the form of numbers and statistics.
Subjective - individuals� interpretation of events is important ,e.g., uses participant observation, in-depth interviews etc.
Objective � seeks precise measurement & analysis of target concepts, e.g., uses surveys, questionnaires etc.
Qualitative data is more 'rich', time consuming, and less able to be generalized.
Quantitative data is more efficient, able to test hypotheses, but may miss contextual detail.
Researcher tends to become subjectively immersed in the subject matter.
Researcher tends to remain objectively separated from the subject matter.
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In this lesson we look only into Quantitative Data Analysis
Mathematical & Statistical analysis
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Statistical Methods
Statistics: Analysis of “meaningful” quantities about a sample of objects, things, persons, events, phenomena, etc. To infer scientific outcome
MEANINGFUL???
I checked 3 Proton Saga 2008 model cars. In two of them the gear box is not working properly.
Inference: Proton Saga 2008 model has a gear box defect!!!!!
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Important Statistical processesImportant Statistical processes
Correlation and Dependence
Correlation and dependence are any of a broad class of statistical relationships between two or more random variables or observed data values.
Correlations are useful because they can indicate a predictive relationship that can be exploited in practice.
For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather.
Correlations can also suggest possible causal, or mechanistic relationships; however, statistical dependence is not sufficient to demonstrate the presence of such a relationship.
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Student T-Test
A t-test is usually done to compare two sets of data. It is most commonly applied when the test statistic would follow a normal distribution.
For example, suppose we measure the size of a cancer patient's tumour before and after a treatment. If the treatment is effective, we expect the tumour size for many of the patients to be smaller following the treatment.
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Important Statistical processesImportant Statistical processes
Analysis of variance (ANOVA)
Analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance is partitioned into components due to different sources of variation.
In its simplest form ANOVA provides a statistical test of whether or not the means of several groups are all equal, and therefore generalizes Student's two-sample t-test to more than two groups.
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ANOVAs are helpful because they possess a certain advantage over a two-sample t-test.
Doing multiple two-sample t-tests would result in a largely increased chance of committing a type I error.
For this reason, ANOVAs are useful in comparing three or more means
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• Multivariate analysis of variance MANOVA
MANOVA is a generalized form of univariate analysis of variance (ANOVA). I
It is used in cases where there are two or more dependent variables.
As well as identifying whether changes in the independent variable(s) have significant effects on the dependent variables, MANOVA is also used to identify interactions among the dependent variables and among the independent variables
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Regression analysis
Regression analysis includes any techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables.
More specifically, regression analysis helps us understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.
Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables — that is, the average value of the dependent variable when the independent variables are held fixed
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Econometric modelling
Econometric models are statistical models used in econometrics.
An econometric model specifies the statistical relationship that is believed to hold between the various economic quantities pertaining a particular economic phenomena under study.
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Important Statistical processesImportant Statistical processes
• Two main categories:
* Descriptive statistics * Inferential statistics
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Descriptive statistics
• Use sample information to explain/make abstraction of population “phenomena”. Common “phenomena”:* Association* Central Tendency* Causality* Trend, pattern, dispersion, range
• Used in non-parametric analysis (e.g. chi-square, t-test, 2-way anova)
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• Association is any relationship between two measured quantities that renders them statistically dependent
• central tendency relates to the way in which quantitative data tend to cluster around some value
• Causality is the relationship between an event (the cause) and a second event (the effect), where the second event is a consequence of the first
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Examples of “abstraction” of phenomena
Trends in property loan, shop house demand & supply
0
50000
100000
150000
200000
Year (1990 - 1997)
Loan to property sector (RMmillion)
32635.8 38100.6 42468.1 47684.7 48408.2 61433.6 77255.7 97810.1
Demand for shop shouses (units) 71719 73892 85843 95916 101107 117857 134864 86323
Supply of shop houses (units) 85534 85821 90366 101508 111952 125334 143530 154179
1 2 3 4 5 6 7 8
0
50,000100,000
150,000200,000
250,000300,000
350,000
Batu P
ahat
Joho
r Bah
ru
Kluang
Kota Tingg
i
Mersing
Muar
Pontia
n
Segam
at
District
No. o
f hou
ses
1991
2000
0
2
4
6
8
10
12
14
0-410
-1420
-2430
-3440
-4450
-5460
-6470
-74
Age Category (Years Old)
Prop
ortio
n (%
)
Demand (% sales success)
120100806040200
Pric
e (R
M/s
q. f
t of b
uilt
are
a)
200
180
160
140
120
100
80
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Examples of “abstraction” of phenomena
Demand (% sales success)
12010080604020
Pric
e (R
M/s
q.ft
. bui
lt a
rea)
200
180
160
140
120
100
80
10.00 20.00 30.00 40.00 50.00 60.00
10.00
20.00
30.00
40.00
50.00
-100.00-80.00-60.00-40.00-20.000.0020.0040.0060.0080.00100.00
Dis ta nce fr om Ra kai a ( km )
Distance from Ashurton (km)
% prediction
error
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Inferential statistics
• Using sample statistics to infer some “phenomena” of population parameters
• Common “phenomena”:* One-way r/ship
* Multi-directional r/ship * Recursive
• Use parametric analysis
Y1 = f(Y2, X, e1)Y2 = f(Y1, Z, e2)
Y1 = f(X, e1)Y2 = f(Y1, Z, e2)
Y = f(X)
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Examples of relationship
Coefficientsa
1993.108 239.632 8.317 .000-4.472 1.199 -.190 -3.728 .0006.938 .619 .705 11.209 .0004.393 1.807 .139 2.431 .017
-27.893 6.108 -.241 -4.567 .00034.895 89.440 .020 .390 .697
(Constant)TanahBangunanAnsilariUmurFlo_go
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
Dependent Variable: Nilaisma.
Dep=9t – 215.8
Dep=7t – 192.6
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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)• 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.
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Common mistakes in data analysis• Wrong techniques. E.g.
• 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. • Simply exclude a technique
Note: No way can Likert scaling show “cause-and-effect” phenomena!
Issue Data analysis techniques
Wrong technique Correct technique
To study factors that “influence” visitors to come to a recreation site
“Effects” of KLIA on the development of Sepang
Likert scaling based on interviews
Likert scaling based on interviews
Data tabulation based on open-ended questionnaire survey
Descriptive analysis based on ex-ante post-ante experimental investigation
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Common mistakes (contd.) – “Abuse of statistics”
Issue Data analysis techniques
Example of abuse Correct technique
Measure the “influence” of a variable on another
Using partial correlation(e.g. Spearman coeff.)
Using a regression parameter
Finding the “relationship” between one variable with another
Multi-dimensional scaling, Likert scaling
Simple regression coefficient
To evaluate whether a model fits data better than the other
Using coefficient of determination, R2
Box-Cox 2 test for model equivalence
To evaluate accuracy of “prediction” Using R2 and/or F-value of a model
Hold-out sample’s MAPE
“Compare” whether a group is different from another
Multi-dimensional scaling, Likert scaling
two-way anova, 2, Z test
To determine whether a group of factors “significantly influence” the observed phenomenon
Multi-dimensional scaling, Likert scaling
manova, regression
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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?????????
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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
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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.)
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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,…)
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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
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Principles of data analysis (contd.)
Shoppers NumberMale Old Young
64
Female Old Young
1015
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
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Data analysis (contd.)
• When analysing: * Be objective * Accurate * True• Separate facts and opinion• Avoid “wrong” reasoning/argument. E.g. mistakes in
interpretation.
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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
J.B. houses
μ = ?
SST
DST
SD1= 300,000 = 120,000
2
= 210,0003
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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.
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“Central Tendency”
Measure Advantages Disadvantages
Mean(Sum of all values ÷no. of values)
Best known average Exactly calculable Make use of all data Useful for statistical analysis
Affected by extreme values Can be absurd for discrete data (e.g. Family size = 4.5 person) Cannot be obtained graphically
Median(middle value)
Not influenced by extreme values Obtainable even if data distribution unknown (e.g. group/aggregate data) Unaffected by irregular class width Unaffected by open-ended class
Needs interpolation for group/ aggregate data (cumulative frequency curve) May not be characteristic of group when: (1) items are only few; (2) distribution irregular Very limited statistical use
Mode(most frequent value)
Unaffected by extreme values Easy to obtain from histogram Determinable from only values near the modal class
Cannot be determined exactly in group data Very limited statistical use
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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
Thus, = 96/12 = 8
x 3 5 7 8 9 10 12
f 1 1 2 3 2 2 1
f 3 5 14 24 18 20 12
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Central Tendency–“Mean of Grouped Data”
• House rental or prices in the PMR are frequently tabulated as a range of values. E.g.
• What is the mean rental across the areas? = 23; = 3317.5 Thus, = 3317.5/23 = 144.24
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
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Central Tendency – “Median”• Let say house rentals in a particular town are tabulated as follows:
• Calculation of “median” rental needs a graphical aids→
Rental (RM/month) 130-135 135-140 140-145 155-50 150-155Number of Taman (f) 3 5 9 6 2
Rental (RM/month) >135 > 140 > 145 > 150 > 155Cumulative frequency 3 8 17 23 25
1. Median = (n+1)/2 = (25+1)/2 =13th. Taman
2. (i.e. between 10 – 15 points on the vertical axis of ogive).
3. Corresponds to RM 140-145/month on the horizontal axis
4. There are (17-8) = 9 Taman in the range of RM 140-145/month
5. Taman 13th. is 5th. out of the 9
Taman
6. The interval width is 5
7. Therefore, the median rental can
be calculated as:
140 + (5/9 x 5) = RM 142.8
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Central Tendency – “Median” (contd.)
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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
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“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
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“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?
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“Variability” (contd.)
• 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%
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“Variability” (contd.)
• Std. dev. of a frequency distribution The following table shows the age distribution of second-time home buyers:
x^
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“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:
• E.g.
(continuous)
(discrete)
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“Probability Distribution” (contd.)
Dice1Dice2 1 2 3 4 5 6
1 2 3 4 5 6 72 3 4 5 6 7 83 4 5 6 7 8 94 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
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“Probability Distribution” (contd.)
Values of x are discrete (discontinuous)
Sum of lengths of vertical bars p(X=x) = 1 all x
Discrete values Discrete values
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“Probability Distribution” (contd.)
2.00 3.00 4.00 5.00 6.00 7.00
Rental (RM/ sq.ft.)
0
2
4
6
8
Freq
uenc
y
Mean = 4.0628Std. Dev. = 1.70319N = 32
▪ Many real world phenomena take a form of continuous random variable
▪ Can take any values between two limits (e.g. income, age, weight, price, rental, etc.)
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“Probability Distribution” (contd.)
P(Rental = RM 8) = 0 P(Rental < RM 3.00) = 0.206
P(Rental < RM7) = 0.972 P(Rental RM 4.00) = 0.544
P(Rental 7) = 0.028 P(Rental < RM 2.00) = 0.053
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“Probability Distribution” (contd.)
• Ideal distribution of such phenomena:
* Bell-shaped, symmetrical
* Has a function of
μ = mean of variable x
σ = std. dev. Of x
π = ratio of circumference of a
circle to its diameter = 3.14
e = base of natural log = 2.71828
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“Probability distribution”
μ ± 1σ = ? = ____% from total observation
μ ± 2σ = ? = ____% from total observation
μ ± 3σ = ? = ____% from total observation
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“Probability distribution”
* Has the following distribution of observation
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“Probability distribution”
• There are various other types and/or shapes of distribution. E.g.
• Not “ideally” shaped like the previous one
Note: p(AGE=age) ≠ 1
How to turn this graph into a probability distribution function (p.d.f.)?
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“Z-Distribution”• (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
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“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.
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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): P(Y ≤ 160,000) = P(Z ≤ ---------------------------) = P(Z ≤ 0.811) = 0.1867Using , the required probability is: 1-0.1867 = 0.8133
Always remember: to convert to SND, subtract the mean and divide by the std. dev.
160,000 -155,000
3.8x107
Z-table
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Normal distribution…Questions
Answer (b):
Z1 = ------ = ---------------- = -1.622
Z2 = ------ = ---------------- = 0.811
P(Z1<-1.622)=0.0455; P(Z2>0.811)=0.1867P(145,000<Z<160,000) = P(1-(0.0455+0.1867) = 0.7678
X1 - μ
σ
145,000 – 155,000
3.8x107
X2 - μ
σ
160,000 – 155,000
3.8x107
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Normal distribution…Questions
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?
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“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 =gamma distribution; v=n-1=d.o.f; =3.147
* Probability calculation requires information on d.o.f.
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“Student’s t-Distribution”
• 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.
• Distribution of the random variable t which is (very loosely) the "best" that we can do not knowing σ.
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“Student’s t-Distribution”
• Student's t-distribution can be derived by:
* transforming Student's z-distribution using
* defining
• The resulting probability and cumulative distribution functions are:
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“Student’s t-Distribution”
•
where r ≡ n-1 is the number of degrees of freedom, -∞<t<∞,(t) is the gamma function, B(a,b) is the beta function, and I(z;a,b) is the regularized beta function defined by
•
fr(t) =
=
Fr(t) =
=
=
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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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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!
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?
Formula:
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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
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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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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:
PRICE - RM ‘000 130 137 128 390 140 241 342 143
SQ. M OF FLOOR 135 140 100 360 175 270 200 170
PRICE - RM ‘000 (x) 36 37 38 39 40 41 42 43
NO. OF LOCALITIES (f) 3 14 10 36 73 27 20 17
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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, 6.5B: 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 > “30-34”)
(AGE ≤ 20-24)
( “35-39”≤ AGE < “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 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.
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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.
(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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Summary
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• Main Points
• Qualitative research involves analysis of data such as words (e.g., from interviews), pictures (e.g., video), or objects (e.g., an artifact).
• Quantitative research involves analysis of numerical data.• The strengths and weaknesses of qualitative and
quantitative research are a perennial, hot debate, especially in the social sciences. The issues invoke classic 'paradigm war'.
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• The personality / thinking style of the researcher and/or the culture of the organization is under-recognized as a key factor in preferred choice of methods.
• Overly focusing on the debate of "qualitative versus quantitative" frames the methods in opposition. It is important to focus also on how the techniques can be integrated, such as in mixed methods research. More good can come of social science researchers developing skills in both realms than debating which method is superior.
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