Advance Research Advance Research MethodsMethods

Vishnu ParmarVishnu Parmar

Assistant Professor, IBAAssistant Professor, IBA

University of Sindh, JamshoroUniversity of Sindh, Jamshoro

WHAT IS STATISTICS?WHAT IS STATISTICS?

DefinitionDefinition StatisticsStatistics is a group of methods used is a group of methods used

to collect, analyze, present, and to collect, analyze, present, and interpret data and to make decisions.interpret data and to make decisions.

What is statistics?What is statistics? a branch of mathematics that provides a branch of mathematics that provides

techniques to analyze whether or not techniques to analyze whether or not your data is significant (meaningful)your data is significant (meaningful)

Statistical applications are based on Statistical applications are based on probability statementsprobability statements

Nothing is “proved” with statisticsNothing is “proved” with statistics Statistics are reportedStatistics are reported Statistics report the probability that Statistics report the probability that

similar results would occur if you similar results would occur if you repeated the experimentrepeated the experiment

Why Statistics ?Why Statistics ?

   "The objective of a national statistical system "The objective of a national statistical system

is to provide relevant, comprehensive, is to provide relevant, comprehensive, accurate and objective statistical information. accurate and objective statistical information. Generally, statistics are valuable for Generally, statistics are valuable for monitoring the country’s economic and social monitoring the country’s economic and social conditions, the planning and evaluation of conditions, the planning and evaluation of government and private sector programmes government and private sector programmes and investment, policy debates and advocacy, and investment, policy debates and advocacy, and the creation and maintenance of an and the creation and maintenance of an informed public." informed public."

Why Statistics ? Cont’dWhy Statistics ? Cont’d

Essential in:Essential in: Official decision-making, policy Official decision-making, policy

formulationformulation Policy Analysis & ResearchPolicy Analysis & Research Academic, business, industrial & other Academic, business, industrial & other

researchresearch Business planning & CRMBusiness planning & CRM Citizens/residents being informed about Citizens/residents being informed about

performance of governmentsperformance of governments

Why Statistics ?Why Statistics ?

Facilitate comparison across countries/regionsFacilitate comparison across countries/regions BenchmarkingBenchmarking ‘‘Best Practices’Best Practices’ Evaluation of performanceEvaluation of performance

However, good statistics must be However, good statistics must be collected in accordance with agreed collected in accordance with agreed international standards using international standards using appropriate methods for data collection, appropriate methods for data collection, processing and disseminationprocessing and dissemination..

TYPES OF STATISTICSTYPES OF STATISTICS

DefinitionDefinition Descriptive StatisticsDescriptive Statistics consists of consists of

methods for organizing, displaying, methods for organizing, displaying, and describing data by using tables, and describing data by using tables, graphs, and summary measures.graphs, and summary measures.

TYPES OF STATISTICSTYPES OF STATISTICS

DefinitionDefinition Inferential StatisticsInferential Statistics consists of consists of

methods that use sample results to methods that use sample results to help make decisions or predictions help make decisions or predictions about a population.about a population.

POPULATION VERSUS POPULATION VERSUS SAMPLESAMPLE

DefinitionDefinition A A populationpopulation consists of all consists of all

elements – individuals, items, or elements – individuals, items, or objects – whose characteristics are objects – whose characteristics are being studied. The population that is being studied. The population that is being studied is also called the being studied is also called the target populationtarget population..

POPULATION VERSUS POPULATION VERSUS SAMPLE cont.SAMPLE cont.

DefinitionDefinition A portion of the population selected A portion of the population selected

for study is referred to as a for study is referred to as a samplesample..

Figure 1.1Figure 1.1 Population and sample. Population and sample.

Population

Sample

POPULATION VERSUS POPULATION VERSUS SAMPLE cont.SAMPLE cont.

DefinitionDefinition A survey that includes every number A survey that includes every number

of the population is called a of the population is called a censuscensus. . The technique of collecting The technique of collecting information from a portion of the information from a portion of the population is called a population is called a sample sample surveysurvey..

POPULATION VERSUS POPULATION VERSUS SAMPLE cont.SAMPLE cont.

DefinitionDefinition A sample that represents the A sample that represents the

characteristics of the population as characteristics of the population as closely as possible is called a closely as possible is called a representative samplerepresentative sample..

POPULATION VERSUS POPULATION VERSUS SAMPLE cont.SAMPLE cont.

DefinitionDefinition A sample drawn in such a way that A sample drawn in such a way that

each element of the population has a each element of the population has a chance of being selected is called a chance of being selected is called a random samplerandom sample. If the chance of . If the chance of being selected is the same for each being selected is the same for each element of the population, it is called element of the population, it is called a a simple random samplesimple random sample..

TYPES OF VARIABLESTYPES OF VARIABLES

Quantitative VariablesQuantitative Variables– Discrete VariablesDiscrete Variables– Continuous VariablesContinuous Variables

Qualitative or Categorical VariablesQualitative or Categorical Variables

Quantitative VariablesQuantitative Variables

DefinitionDefinition A variable that can be measured A variable that can be measured

numerically is called a numerically is called a quantitative quantitative variablevariable. The data collected on a . The data collected on a quantitative variable are called quantitative variable are called quantitative dataquantitative data..

Quantitative Variables cont.Quantitative Variables cont.

DefinitionDefinition A variable whose values are countable A variable whose values are countable

is called a is called a discrete variablediscrete variable. In other . In other words, a discrete variable can assume words, a discrete variable can assume only certain values with no intermediate only certain values with no intermediate values. (e.g, 100 students in section A, values. (e.g, 100 students in section A, or 2 or 3 bedrooms in an apartment, or 2 or 3 bedrooms in an apartment, there won’t be 2.5. in an home)there won’t be 2.5. in an home)

Quantitative Variables cont.Quantitative Variables cont.

DefinitionDefinition A variable that can assume any A variable that can assume any

numerical value over a certain interval numerical value over a certain interval or intervals is called a or intervals is called a continuous continuous variablevariable. (e.g, 1.5kg bag of rice, or . (e.g, 1.5kg bag of rice, or flight is late for 2 hrs and 30 min.)flight is late for 2 hrs and 30 min.)

Qualitative or Categorical Qualitative or Categorical VariablesVariables

DefinitionDefinition A variable that cannot assume a A variable that cannot assume a

numerical value but can be classified numerical value but can be classified into two or more nonnumeric into two or more nonnumeric categories is called a categories is called a qualitativequalitative or or categorical variablecategorical variable. The data . The data collected on such a variable are called collected on such a variable are called qualitative dataqualitative data..

Qualitative, attitude, or Qualitative, attitude, or Categorical Variables, cont…Categorical Variables, cont…

Qualitative data is often summarized Qualitative data is often summarized in bar graphs and chartsin bar graphs and charts

E.g, % of minority population in an E.g, % of minority population in an areaarea– What % of population has blue eyes?What % of population has blue eyes?– What % of women is highly educated?What % of women is highly educated?

Figure 1.2 Figure 1.2 Types of variables.Types of variables.

Variable

Quantitative Qualitative orcategorical (e.g.,

make of a computer,hair color, gender)

Continuous(e.g., length,age, height,weight, time)

Discrete (e.g.,number of

houses, cars,accidents)

Levels of MeasurementLevels of Measurement

Measurement Measurement is the process of is the process of assigning numbers to quantities. The assigning numbers to quantities. The process is so familiar that perhaps process is so familiar that perhaps we often overlook its fundamental we often overlook its fundamental characteristics.characteristics.

Levels (or Scales) of Levels (or Scales) of MeasurementMeasurement

Measurement is a process whereby values (scores) areMeasurement is a process whereby values (scores) areassigned to properties of people, places, things, or events.assigned to properties of people, places, things, or events.You might rate preferences of perfumes or TV show. YouYou might rate preferences of perfumes or TV show. Youmay collect data about marital status or gender, or countmay collect data about marital status or gender, or countthe number of times people report feeling depressed.the number of times people report feeling depressed.These different measures all have different properties,These different measures all have different properties,which in turn, lead to different sorts of appropriatewhich in turn, lead to different sorts of appropriateStatistical tests. The level of measurement refers to theStatistical tests. The level of measurement refers to theamount of information the measurement procedure canamount of information the measurement procedure canconvey about the actual quantity of the variable presentconvey about the actual quantity of the variable presentand about the differences individuals with different scores.and about the differences individuals with different scores.

Properties of Numbers and Properties of Numbers and AttributesAttributes

NominalNominal (Same-Different). My income is the (Same-Different). My income is the same as yours or different.same as yours or different.

Ordinal Ordinal (Ordering). If our incomes are (Ordering). If our incomes are different, mine is greater or less than yours.different, mine is greater or less than yours.

IntervalInterval (Relative Differences). The (Relative Differences). The difference between my income and yours difference between my income and yours might be, say, twice as great as the different might be, say, twice as great as the different between my income and the governor’s.between my income and the governor’s.

RatioRatio (Ratios and Zero Point). My brother’s (Ratios and Zero Point). My brother’s income is about 10 times what mine is.income is about 10 times what mine is.

Levels (or Scales) of Levels (or Scales) of MeasurementMeasurement

11. Nominal scale:. Nominal scale: based on categories or names, based on categories or names, and tells us nothing about magnitude.and tells us nothing about magnitude.2. Ordinal scale:2. Ordinal scale: a rank-order scale that reflects a rank-order scale that reflects differences in magnitude, but the intervals differences in magnitude, but the intervals between values may not be equal and there is between values may not be equal and there is no absolute zero.no absolute zero.3.3.Interval scale:Interval scale: also measures magnitude and also measures magnitude and

has has equal intervals between values, but the scale equal intervals between values, but the scale has no absolute zero.has no absolute zero.4.4.Ratio scale:Ratio scale: Has equal intervals between all its Has equal intervals between all its values and an absolute zero point.values and an absolute zero point.

Nominal ScaleNominal Scale

The nominal scale is the most basic. It seeks toThe nominal scale is the most basic. It seeks toname things, to categorize or classify them.name things, to categorize or classify them.Nominal scales satisfy only the property ofNominal scales satisfy only the property ofidentity. Examples are gender, job title, religion,identity. Examples are gender, job title, religion,marital status, etc. Numbers can also be used tomarital status, etc. Numbers can also be used toidentify or categorize, such asidentify or categorize, such asthe numbers of players on the football team. Thethe numbers of players on the football team. Thenumbers themselves do not indicate magnitude,numbers themselves do not indicate magnitude,and it would make no sense to try to add orand it would make no sense to try to add ormultiply the numbers on football jerseysmultiply the numbers on football jerseys..

Properties of Nominal DataProperties of Nominal Data

Data categories are mutually Data categories are mutually exclusive, so an object belongs to exclusive, so an object belongs to only categoryonly category

Data Category have logical orderData Category have logical order

Mutually Exclusive and Mutually Exclusive and ExhaustiveExhaustive

Mutually ExclusiveMutually Exclusive means an means an individual, object, or measurement is individual, object, or measurement is included in only categoryincluded in only category

Exhaustive:Exhaustive: Each individual object or Each individual object or measurement must appear in a measurement must appear in a categorycategory

Ordinal ScaleOrdinal Scale

The ordinal scale of measurement deals with The ordinal scale of measurement deals with order or ranking. Common examples are the order or ranking. Common examples are the grades of A, B, C, D, and F; the “top 20” grades of A, B, C, D, and F; the “top 20” ratings for sports teams; the “top 40” ratings ratings for sports teams; the “top 40” ratings for music. for music.

While an ordinal scale allows us to know which While an ordinal scale allows us to know which category is larger, higher, or better, it does notcategory is larger, higher, or better, it does notallow us to say anything about the interval allow us to say anything about the interval between the rankings, or how much better one between the rankings, or how much better one team or song is than another. The only team or song is than another. The only mathematical operation allowed on ordinal data mathematical operation allowed on ordinal data is ranking.is ranking.

Properties of Ordinal Level Properties of Ordinal Level DataData

The data categories are mutually The data categories are mutually exclusive and exhaustiveexclusive and exhaustive

Data categories are ranked or Data categories are ranked or ordered according to the particular ordered according to the particular trait they possesstrait they possess

Interval ScaleInterval ScaleThe interval scale of measurement tells us about the rankThe interval scale of measurement tells us about the rankorder and about the intervals between the numbers. On anorder and about the intervals between the numbers. On aninterval scale, a difference of 1 point always means theinterval scale, a difference of 1 point always means thesame thing. Temperatures measured with either thesame thing. Temperatures measured with either theCelsius or Fahrenheit scales provide scores on an intervalCelsius or Fahrenheit scales provide scores on an intervalscale. However, these thermometers do not have true zeroscale. However, these thermometers do not have true zeropoints: a temperature of 0° does not mean the absence ofpoints: a temperature of 0° does not mean the absence ofheat. The mathematical operations allowed are additionheat. The mathematical operations allowed are additionand subtraction, but never multiplication or division. 80° isand subtraction, but never multiplication or division. 80° isnot twice as hot as 40°not twice as hot as 40°

Properties of Interval Level Properties of Interval Level DataData

Data categories are mutually Data categories are mutually exclusive and exhaustiveexclusive and exhaustive

Data categories are scaled according Data categories are scaled according to the amount of the characteristics to the amount of the characteristics they possessthey possess

Equal difference in the characteristic Equal difference in the characteristic are represented by the equal are represented by the equal differences in the numbers assigned differences in the numbers assigned to the categoriesto the categories

Ratio LevelRatio Level

It is highest level of measurementIt is highest level of measurement It has all characteristics of interval It has all characteristics of interval

level but in addition the zero (o) level but in addition the zero (o) point is meaningful, and the ratio point is meaningful, and the ratio between two numbers is meaningfulbetween two numbers is meaningful

E.g, wages, Units of Production, E.g, wages, Units of Production, Weight, and HeightWeight, and Height

Properties of Ratio Level Properties of Ratio Level DataData

1.1. Data Categories are mutually exclusive Data Categories are mutually exclusive and exhaustiveand exhaustive

2.2. Data Categories are scaled according to Data Categories are scaled according to the amount of the characteristics they the amount of the characteristics they possesspossess

3.3. Equal difference in the characteristic are Equal difference in the characteristic are represented by equal differences in the represented by equal differences in the numbers assigned to the categoriesnumbers assigned to the categories

4.4. The point 0 reflects the absence of the The point 0 reflects the absence of the characteristiccharacteristic