episode 18 : research methodology ( part 8 )

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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 18 : Research Methodology ( Part 8 )

Techniques of Data Analysis

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

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.

In this lesson we look only into Quantitative Data Analysis

Mathematical & Statistical analysis

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!!!!!

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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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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• 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)

• 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

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

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)

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

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.

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

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


two-way anova, 2, Z test

To determine whether a group of factors “significantly influence” the observed phenomenon


manova, regression

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

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.)

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,…)

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 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

Data analysis (contd.)

• When analysing: * Be objective * Accurate * True• Separate facts and opinion• Avoid “wrong” reasoning/argument. E.g. mistakes in

interpretation.

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

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(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

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

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

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

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:

• E.g.

(continuous)

(discrete)

“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


Values of x are discrete (discontinuous)

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

Discrete values Discrete values


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.)


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


• 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

“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.

• 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.)?

“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

“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.

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


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


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 =gamma distribution; v=n-1=d.o.f; =3.147

* Probability calculation requires information on d.o.f.

http://en.wikipedia.org/wiki/Image:T_distribution_30df.png


• 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.


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

* transforming Student's z-distribution using

* defining

• The resulting probability and cumulative distribution functions are:


•

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) =

=

=

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) * 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:

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:

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

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.

Test yourselves!

Q5: Find:

(AGE > “30-34”)

(AGE ≤ 20-24)

( “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.

Summary

• 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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