qrm 00 introduction

7/21/2019 QRM 00 Introduction

1/15

Dr Bhargav Adhvaryu QRM: Introduction MTech IED CEPT Uni Slide 1 of 15

Lecture outline

1. Introduction and overview

a. What is research?

b. What is statistics?

2. Mathematics review

Introduction

This

document

is

for

use

ONLY

by

students

attending

the

lectu

res

and

should

NOT

be

circulated

and

used

outside

this

group

of

students.

Dr Bhargav AdhvaryuSemester-1: Monsoon 2013

Quantitative Research Methods


2/15


Research is a systematic and organised way offinding answers toquestions.

Systematic because there is a definite set of procedures and steps

(methodology) to be followed. The structure or organisation of

the research methodology will depend on the nature and scope of

the research. However, this is always a planned procedure and is

focused. The accuracy of research outputs are also a function of

the type of research methodology.

Finding answers is the end of all research. Whether it is the

answer to a hypothesis or even a simple question, research is

successful when we find answers. Sometimes the answer is no (or

different from expectations); nonetheless it is still an answer!

Questions are central to research. If there is no question, then the

answer is of no use. Research is focused on relevant, useful, and

important questions. Without a question, research has no focus,

drive, or purpose. (Adapted from: ht tp:/ / l inguist ics.byu.edu/faculty/henrichsenl/ResearchMethods/)

What is research?

Introduction and overview Mathematics review


3/15


A generic research process

3. Review of existing knowledge(literature review)

4. Data collection (or systematic observations)

1. Observation of existingphenomena/ situation

Sets the background or

context of the study

2. Research questions or problem

Sets the aims and objectives

5. Data analyses (quantitativeor qualitative)

6. Research outcomes, itsevaluation, and conclusions



4/15


Research design forms the core of a research study and entails

laying out the aims and objectives and selecting appropriate

method of data collection and analysis.

Data collection and analysis could take both quantitative and

qualitative forms.

Quantitative data would be numerical observations. Numerical

and statistical analyses form the core of research methodology.

There are a wide range of quantitative (statistical) techniques and

qualitative techniques available to analyse data, depending on the

nature of data collected.

Some such basic quantative techniques are covered in this course.

Research design(1)



5/15


Qualitative data uses non-numerical data such as interview and

focus group transcripts, open-ended survey responses, emails,

notes, feedback forms, photos, videos, etc.

This data in most cases is unstructured, ie the format of recording

data may be different for different respondents.

Sample size may be very small but is focused.

The aim is to gain insight into people's attitudes, behaviour, value

systems, concerns, motivations, aspirations, culture, or lifestyles.

Of course, some minimal quantitative analyses of filtered data

may be necessary.

Research design(2)



6/15


Qualitative v. quantitative research

Features of Qualitative & Quantitative Research

Quantitative Qualitative

"There's no such thing as qualitative data.Everything is either 1 or 0"

- Fred Kerlinger

"All research ultimately hasa qualitative grounding"

- Donald Campbell

The aim is to classify features, count them, andconstruct statistical models in an attempt toexplain what is observed.

The aim is a complete, detailed description.

Researcher knows clearly in advance what theyare looking for.

Researcher may only know roughly in advancewhat they are looking for.

Recommended during latter phases of researchprojects.

Recommended during earlier phases of researchprojects.

All aspects of the study are carefully designedbefore data is collected.

The design emerges as the study unfolds.

Researcher uses tools, such as questionnaires orequipment to collect numerical data.

Researcher is the data gathering instrument.

Data is in the form of numbers and statistics. Data is in the form of words, pictures, or objects.

Objective - seeks precise measurement andanalysis of target concepts, eg uses surveys,questionnaires, etc.

Subjective - individuals interpretation of events isimportant, eg uses participant observation, in-depth interviews, etc.

Quantitative data is more efficient, able to testhypotheses, but may miss contextual detail.

Qualitative data is more 'rich', time consuming,and less able to be generalised.

Researcher tends to remain objectively separatedfrom the subject matter.

Researcher tends to become subjectivelyimmersed in the subject matter.

So u r c e : h t t p : / / w i l d er d o m . c o m / r e s e ar c h / Q u a l it a t i v e V er s u s Qu a n t i t a t i v eR e se a r ch . h t m l ( l a st u p d at e d 2 8 Fe b 2 0 0 7 )

( T h e t w o q u o t e s a b o v e a r e f r o m M i l e s, M . B ., & H u b e r m a n , A . M . ( 1 9 9 4 ) . Q u a li t a t i v e d a t a a n a l y si s . S a g e ( p . 4 0 ) ) .



7/15


Statistics is a branch of mathematics that deals with:

Collection, organisation, and visualisation of data

Numerical analysis of data

Describing phenomena

Forecasting/ predictions (mathematical modelling)

Analysis of data has two basic braches:

Simple descriptive statistics

Inferential statistics

Forecasting involves building mathematical models based on past

data that can be used to predict values for the future, eg a

regression model.

What is statistics?



8/15


This branch of statistics deals with summarising data in terms of

time and space, and provides a single comprehensive measure

that meaningfully explains the characteristics of the data set.

Examples:

Tables, charts, and graphs

Frequency distributions (eg, histograms)

Measures of central tendency (eg, mean, median, mode, etc)

Measures of dispersion (eg, standard deviation)

Index numbers

SDS measures are intended to describe the data set based on

which they are calculated. The understanding CANNOT be

extended to other data sets.

Simple descriptive statistics



9/15


This branch of statistics deals with:

Drawing a small set of data (sample) from all possible

observations (population)

Analysing this sample data set

Drawing inferences (conclusion) from such analysis that could

be extended to the population.

Association between variables and its strength

Predictions

Inferential statistics



10/15


Types of numbers


Natural numbers ()Eg, , , , , ,

Whole numbers (0)

Eg, , , , , , ,

Integers ()

Eg,, , , , , , , , , , ,

Rational numbers ()

Those that can be expressed as

fractions (ie, , 0)Note that .

Irrational numbersThose that can NOT be

expressed as fractions

(ie, Eg: , 0)

Eg, , ,

Real numbers ()

Rational + Irrational numbers

The convention is to show:

Variables in roman typefaceConstants (parameters) inGreek letters

, , ,

, , , ( )


11/15


Scientific notation, operations


Scientific notation (also sometimes referred to as engineering

notations) is expressed in the form 10 to the power.

2042 = 2.042 103

0.000569 = 5.69 104

In spreadsheets (eg, Excel), the notation is expressed as:

2.042 E+3 = 2.042 103

5.69 E4 = 5.69 104

Remember the BODMAS (or BEDMAS or BIDMAS or PEDMAS) rule,

which states that order of operations is:

Brackets (Parentheses), Orders (ie, powers ofIndices or Exponents) Division Multiplication Addition Subtraction

Find the answer to:4/2*(2+3)+(2*(2)^2)^2-12/6


12/15


n

n

i

i

n

n

i

i

xxxxx

PROUDCT

xxxxx

SUM

...

...

321

1

321

1

Basic algebraic operations


Laws of indices

aaa

b ab

a

aa

yxxy

xx

xx

xx

xxx

)(

1

1

,1

1

10

End-point(upper limit)

Start-point(lower limit)

Symbol

nnnnnn

n

i

ij

n

j

nn

n

i

ii

xxxxxxxxxx

yxyxyxyxyx

.........

...

212221212111

11

332211

1

a

aa

ba

b

a

abba

baba

y

x

y

x

xx

x

xx

xxx

)(

Sum and product symbols


13/15



Logarithm of a number is the power (exponent) to which it must be raised to obtain a given number:

31000log

100010

10

3

In general, terms:

xy

yb

b

x

)(log

Often, the number e(which equals 2.718281828) is used as the base logarithms, in which case it iscalled natural logarithm and is denoted by ln, say eg:

The LHS of this equation is said as logarithm ofyto base b. In the above case, itwould be logarithm of 1000 to base 10.

2.3ln(10)

1.6)5ln(

Logarithms and exponentials(1)

Laws of logarithm

)ln(ln

)ln()ln(ln

)ln()ln()ln(

xnx

bab

a

baab

n

813 x

10

5

2.3

1.6

e

e

10)3.2exp(

5)6.1exp(

Alternativenotation:

)81ln()3ln( x

4)3ln(

)81ln(x

Example of solving andindicial equation usinglaws of logarithm


14/15



An exponential function is one which contains ex . eis a constant having an approximate value of2.7183 (sf4). As discussed in the previous slide, the exponent arises from the natural laws of growthand decay and is used as a base for natural logarithms.

The definition ofeis a follows:

en

OR

en

n

n

n

0 !

1

11lim

Logarithms and exponentials(2)

As the value ofntendto infinity, ewill tend

to 2.71828

Graph of y=exp(x) and y=exp(-x)


15/15



Exponential and sub-exponential growth

Graph of = ( )

Exponential growth

,...2,2,2,,22eg,variable.th eis

a ndconstantisb a s eth ew here,

43210x

x

Sub-exponential growth

,...,43,2,1,0eg,constant.is

a ndvar iableisb a s eth ew here,

22222

x

x

Graph of = ( )

qrm 00 introduction

Documents