DATA ANALYSIS IN RESEARCH Dr. N. NAGESHA Professor Dept. of Industrial & Production Engineering University BDT College of Engineering (A Constituent College

DATA ANALYSIS IN RESEARCH

Dr. N. NAGESHAProfessor

Dept. of Industrial & Production EngineeringUniversity BDT College of Engineering

(A Constituent College of VTU, Belagavi)

DAVANAGERE – 577 004

18 March 2015

Presentation Plan

Introduction (Definition of Research)

Classification of Research

Research Methodology Vs Methods

Process of Research

Research Design

Data analysis

(Univariate, Bivariate, and Multivariate)

2Dr.NN, VTU_3DWSRML_ROB

What is Research?

18 March 2015 Dr.NN, VTU_3DWSRML_ROB 3

“Research is the systematic approach to obtaining and confirming new and reliable knowledge”– Systematic and orderly (following a series of steps)– Purpose is new knowledge, which must be reliable

This is a general definition which applies to all disciplines

Research is not ……


Accidental Discovery1. Accidental discovery may occur in structured research process2. Usually takes the form of a phenomenon not previously noticed

Mere Data Collection 1. An intermediate step to gain reliable knowledge2. Collecting reliable data is part of the research process

Searching out Published Research results in Libraries/Internet1.This is an important early step of research2.The research process always includes synthesis and analysis3.But, just reviewing of literature is not research

But, Research is…


Searching for Explanation of Events, Phenomena, Relationships and Causes:

1. What, how, and why things occur2. Are there interactions

A Process: 1. Planned and managed – to make the information generated credible 2. The process is creative

3. All well designed and conducted research has potential application. 4. Researchers are also responsible to help users understand research implications

Types of Research


Basic Vs Applied Research• Basic – to determine or establish fundamental facts and relationships

within a discipline or field of study. It develop theories.

• Applied – undertaken specifically for the purpose of obtaining information to help resolve a particular problem.

• The distinction between them is the Application Basic has little application to real world policy and management but could be done to guide applied research.

Classification of Research


• Descriptive Research – the attempt to determine, describe, or identify something– The intent is often synthesis, which pulls knowledge or

information together• Analytic – the attempt to establish why something occurs or

how it came to be.

All disciplines generally engage in both

Methodology Vs Methods of Research


Methodology and Method are often (incorrectly) interchangeablyused

•Methodology – the study of the general approach to inquiry in a given field.

•Method – the specific techniques, tools or procedures applied to achieve a given objective

Research methods include regression analysis, mathematical

analysis, OR, DOE, surveys, data gathering, etc.

The Process of Research


1. Selection of topic

2. Reviewing the literature

3. Development of theoretical and conceptual frameworks

4. Clarification of research question/hypothesis

5. Research design

6. Data collection

7. Data analysis

8. Drawing conclusions



Asking the Research Question

Formulating theHypotheses

Evaluating the Hypotheses

Analyzing Data

Develop a research design

Contribute new

evidence to literature and begin

again

THEORY

Examine a social relationship, study the

relevant literature

Collecting Data

The Process of Research


• Research is a creative process• “…research includes far more than mere logic … It

includes insight, genius, groping, pondering – ‘sense’ … The logic we can teach; the art we cannot”

• Research requires (or at least works best) with imagination, initiative, intuition, and curiosity.

• There are different types of creativity, characteristic of different situations – “applied” and “theoretical” most closely associate with research

Fostering Creativity (Ladd 1987)


A. Gather and use previously developed knowledgeB. Exchange ideasC. Apply deductive logicD. Look at things alternate waysE. Question or challenge assumptionsF. Search for patterns or relationshipsG. Take risksH. Cultivate tolerance for uncertainty

Creativity may provide the difference between satisfactory and outstanding research





Analyzing Data


Contribute new

evidence to literature and begin

again

THEORY

Examine a social relationship, study the

relevant literature

Collecting Data

Research Design


• Decisions regarding what, where, when, how much • A research design – the arrangement of conditions for collection and analysis of data in a

manner that aims to combine relevance to the research purpose with economy in procedure.

Research Design


• The designing decisions happen to be in respect of:– (i) What is the study about?– (ii) Why is the study being made?– (iii) Where will the study be carried out?– (iv) What type of data is required?– (v) Where can the required data be found?– (vi) What periods of time will the study include?– (vii) What will be the sample design?– (viii) What techniques of data collection will be used?– (ix) How will the data be analyzed?– (x) In what style will the report be prepared?

Research Design


• Research design must, at least, contain– (a) a clear statement of the research problem;

– (b) procedures and techniques to be used for gathering information;

– (c) the population to be studied;

– (d) methods to be used in processing and analyzing data

Data Collection


Researchers must decide three things:– How to measure the variables of interest– How to select the cases for the research– What kind of data collection techniques to use

Levels of Measurements


Not every statistical operation can be used with every variable. The type of statistical operations one can employ depends on how the variables are measured.

Measurement Scales:

Nominal, Ordinal, Interval, Ratio

Measurement Scales


Nominal - Numbers or other symbols are assigned to a set of categories for the purpose of naming, labeling, or classifying the observations. (Place, Name, Religion, etc.)

Ordinal - Nominal variables that can be ranked from low to high. (Median, Percentile)

Interval -Variables where measurements for all cases are expressed in the same units and with equal interval. (Likert Scale) (Median, SD)

Ratio - Variables with a natural zero point, such as height and weight, are on ratio scale. (AM,GM,HM,SD,VA,CV, etc.)

Variable Types


• Discrete variables: Variables that have a minimum-sized unit of measurement, which cannot be sub-divided. Example: the number Refrigerators sold per month.

• Continuous variables: Variables that, in theory, can take on all possible numerical values in a given interval. Example: length, volume, pressure, etc.

• Dependent and independent variables – If one variable depends upon or is a consequence of the other variable ---

it is called a dependent variable

– the variable that is antecedent to the dependent variable ---

is called an independent variable

A concept which can take on different quantitative values is a variable

Variable Types


• Extraneous variable:

– Independent variables that are not related to the purpose of the study, but may affect the dependent variable.

– Whatever effect is noticed on dependent variable as a result of extraneous variable (s) is technically described as an ‘experimental error’.

– One important characteristic of a good research design is to minimize the influence or effect of extraneous variable (s).

• Confounded relationship– When the dependent variable is not free from the influence of extraneous

variable (s) the relationship between the dependent and independent variables is said to be confounded/confused by an extraneous variable (s).

Sampling


• Population: The total set of individuals, objects, groups,

or events in which the researcher is interested.

• Sample: A relatively small subset selected from a population.

Population Sample

Sampling


• Two basic types: probability and non-probability• Probability sampling can include random sampling, stratified random

sampling, and cluster sampling• Non-probability sampling can include quota sampling, haphazard

sampling, and convenience sampling

Random Sampling/Stratified Random Sampling


Random Sampling

•Every unit has an equal chance of selection

•Although it is relatively simple, members of specific subgroups may not be included in appropriate proportions

Stratified Random Sampling•The population is grouped according to meaningful characteristics or strata•This method is more likely to reflect the general population, and subgroup analysis is possible•However, it can be time consuming and costly

Systematic Sampling


• Every nth unit is selected (e.g., every 10th piece in a stock of flats may be selected)

• The method is convenient and close to random sampling if the starting point is randomly chosen

Cluster/ Multi Stage Sampling•Natural groups are sampled and then their members are sampled

•This method is convenient and can use existing units

Convenience Sampling


• This method uses readily available groups or units of individuals• It is practical and easy to use• However, it may produce a biased sample• Convenience sampling is acceptable if the purpose of the research is to test a

hypothesis that certain variables are related to one another

Snow ball Sampling •Previously identified members identify others

•This method is useful when a list of potential names is difficult to obtain

•However, it may produce a biased sample

Quota Sampling•The population is divided into subgroups and the sample is selected based on the proportions of the subgroups necessary to represent the population

•This method depends on reliable data about the proportions in the population

How Large Should a Sample Be?


Sample size can be determined following a formula that statisticians have created. It finds a sample size depending on:

@ How confident the researcher wants to be (usually 95%),

@ How much error can be tolerated (usually between 2-5%),

@ An estimate of how much variability (or heterogeneity) exists in the population, @ The size of the actual population to be studied.

A. Required sample size may be estimated using the following formula (for finite population (Kothari, 2001)).

n {Z2

.N.p2

} {(N-1).e2

Z2

.p2

}

where: n = Size of the sample required for a given precision and confidence level

N = Finite population size;

Z = Std. variate at a given confidence level (1.96 for 95% & 2.57 for 99% confidence level)

e = Acceptable error or the precision required (About 5% of mean value)

p = Std. deviation of the population (estimated through pilot study or past experience)

How Large Should a Sample Be?


B. Most conservative sample size for a confidence level of 90% and an error of 5% is z σp = 0.05, where σp = Standard error of proportions = √pq/n n = Sample size, p = binomial probability of success and q = 1-p

For 90% confidence level z = 1.64, substituting we get 1.64 √pq ∕ n = 0.05. p= 0.5, q = 1-p = 0.5; Thus n = 267

Another strategy considers the number of variables being examined and the number of hypotheses being tested. In general, a good rule of thumb is that the more details that are involved under the study, the larger the sample needs to be.

Analysis of Data


• The data may be collected by surveys, interviews, literature review, participant observation, Experiments, Simulation studies, etc.

• The measurements obtained in a research study are called the data.

• The goal of statistics is to help researchers organize and interpret the data.

Analysis of Data





Analyzing Data


Contribute new evidence to

literature and begin again

THEORY

Examine a social relationship, study the relevant literature

Collecting Data

Analysis of Data


• Descriptive statistics: Procedures that help us organize and describe data collected from either a sample or a population.

• Inferential statistics: The logic and procedures concerned with making predictions or inferences about a population from observations and analyses of a sample.

Overview: Quantitative Analysis


Univariate Data Analysis comprises

1.Frequency Tables2.Diagrams3.Measures of Central Tendency4.Measures of Dispersion5.Measures of Skewness6.Measures of Kurtosis

Data Analysis in Research may be Univariate, Bivariate, and

Multivariate

Frequency Tables


A frequency table provides the number of frequency of people (respondents) and the percentage belonging to each of the categories for the variable in question. It can be used in relation to all of the different types of variable. An example of a frequency table is shown:

School Students Staff

N % N %

A 50 16.4 34 19.7

B 52 17.1 40 23.1

C 27 8.9 31 17.9

D 54 17.8 38 22.0

E 47 15.5 30 17.3

TOTAL 304 100 173 100

Diagrams


Measures of Central Tendency


• Arithmetic Mean : AM = (ΣfXi ) / (Σfi ) This is the average as we understand it in everyday use• Geometric Mean : GM = (X1 .X2. X3………..Xn)1/n ;log G = (1/N)(Σfi

logX i.) It is suitable when the data is in terms of ratios or it represents rates of change Example: Rates of growth of population, Rates of growth of industrial production • Harmonic Mean: HM = (Σfi )/ (Σfi 1/X i.) This is most suitable when calculating the average speed of a vehicle. • Median This is the midpoint in a distribution of values • Mode This is the value that occurs most frequently in a distribution • Partition Values: Quartiles, Deciles, Percentiles: Q = l + (((N/n) –

F)/f) h

Measures of Dispersion


• Range: Xh- Xl

This is simply the difference between the maximum and minimum value in a distribution of value associated with interval or ratio scale variable. • Quartile Deviation: (Q3- Q1)/2

This is essentially the average difference between third and first quartiles.• Mean Deviation: (ΣIXi - X barI/ (Σfi )) This is essentially the arithmetic average of the deviation around the mean.• Standard Deviation: SQRT((Σfi (Xi - X bar)2/ (Σfi ))) This is essentially the average amount of variation around the mean.• Variance :(Σfi (Xi - X bar)2/ (Σfi )) This is the average of the square of deviations around the mean.• Co-efficient of Variation :(S.D/A.M)To avoid the error introduced by unit of measurement

Measures of Skewness


Skewness is a measure of asymmetricity in a distributionCo-efficient of skewness = (A.M – Mode)/SD

Measures of Kurtosis


Kurtosis is a measure of “peakedness” of a distribution

4 =(Σ(Xi - X bar)4/ n)

4 /4 = 3 (Normal Curve: Mesokurtic)

3 (Lepto kurtic) 3 (Platy kurtic)

Interquartile Range


A quartile is the value that marks one of the divisions that breaks a series of values into four equal parts.

The median is a quartile and divides the cases in half.

25th percentile is a quartile that divides the first ¼ of cases from the latter ¾.

75th percentile is a quartile that divides the first ¾ of cases from the latter ¼.

The interquartile range is the distance or range between the 25th percentile and the 75th percentile. Shown below, is the interquartile.

0 250 500 750 1000

25% of

cases

25% 25% of

cases

25%

Boxplot Construction


Bi-variate Data Analysis


Bivariate analysis is concerned with the analysis of two variables at a time in order to uncover whether or not the two variables are related.

• Contingency Tables or Cross Tabulations (Tables) • Correlations Analysis 1. Karl Pearson’s correlation coefficient, 2. Spearman’s Rank correlation coefficient, and 3. Kendal’s Rank correlation coefficient)

1. r = 1/n (Σ(X - X bar) (Y - Y bar))/ (xy))

2. rs = 1 - 6(Σdi 2)/ (n(n2-1)) ; {n: no of pairs, d: difference between ranks}

3. = (2s)/(n(n-1)) ; {s: sum of scores, n: no. of pairs}

Correlation Analysis


• The goal of a correlational study is to determine whether there is a relationship between two variables and to describe the relationship.

• A correlational study simply observes the two variables as they exist naturally.



Assesses the linear relationship between two variables Example: height and weight

Strength of the association is described by a correlation coefficient - r r = 0.0 - 0.2 low, probably meaningless r = 0.2 - 0.4 low, possible importance r = 0.4 - 0.6 moderate correlation r = 0.6 - 0.8 high correlation r = 0.8 –1.0 very high correlation

Can be positive or negative Pearson’s, Spearman’s, and Kendal’s correlation coefficient Correlation tells nothing about causation

Beware of Spurious correlation





Multi-Variate Analysis


Multivariate analysis entails the simultaneous analysis of 3 or more variables

– Multiple Linear Regression

– Factor Analysis

– Cluster Analysis

– Discriminant Analysis

– Multi-criteria Analysis

Documents

DATA ANALYSIS IN RESEARCH Dr. N. NAGESHA Professor Dept. of Industrial & Production Engineering University BDT College of Engineering (A Constituent College