MODULE 3

SOURCE OF DATA

Data are the basic inputs to any decision making process.

Data collection is a term used to describe a process of preparing and collecting data.

Systematic gathering of data for a particular purpose from various sources that has

been systematically observed, recorded, organized is referred as data collection.

The purpose of data collection are

o to obtain information

o to keep on record

o to make decisions about important issues

o to pass information on to others

Sources of data can be primary, secondary and tertiary sources.

PRIMARY SOURCES

Data which are collected from the field under the control and supervision of an

investigator.

Primary data means original data that has been collected specially for the purpose in

mind.

These types of data are generally a fresh and collected for the first time.

It is useful for current studies as well as for future studies.

SECONDARY SOURCES

Data gathered and recorded by someone else prior to and for a purpose other than the

current project.

It involves less cost, time and effort.

Secondary data is data that is being reused. Usually in a different context.

EXAMPLES OF PRIMARY AND SECONDARY SOURCES

PRIMARY SOURCES SECONDARY SOURCES

Data and Original Research Newsletters

Diaries and Journals Chronologies

Speeches and Interviews Monographs (a specialized book or

article)

Letters and Memos Most journal articles (unless written at

the time of the event

Autobiographies and Memoirs Abstracts of articles

Government Documents Biographies

COMPARISON OF PRIMARY AND SECONDARY SOURCES

PRIMARY SOURCES SECONDARY SOURCES

Real time data Past data

Sure about sources of data Not sure about sources of data

Help to give results/finding Refining the problem

Costly and Time consuming process. Cheap and No time consuming

process

Avoid biasness of response data Cannot know if data biasness or not

More flexible Less Flexible

TERITARY SOURCES

A teritary source presents summaries or condensed versions of materials, usually with

references back to the primary and/or secondary sources.

They can be a good place to look up acts or get a general overview of a subject, but

they rarely contain original material.

Examples :- Dictionaries, Encyclopaedias, Handbooks

TYPES OF DATA

Categorical Data

Nominal Data

Ordinal Data

CATEGORICAL DATA

A set of data is said to be categorical if the values or observations belonging to it can

be stored according to category.

Each value is chosen from a set of non-overlapping categories.

Eg:-

NOMINAL DATA

A set of data is said to be nominal if the values or observations belonging to it can be

a code in the form of a number where the numbers are simply labels.

It is possible to count but not order or measure nominal data.

Eg :- in a data set males can be coded as 0 and female as 1; marital status of an

individual could be coded as Y if married and N if single.

ORDINAL DATA

A set of data is said to be ordinal if the values or observations belonging to it can be

ranked or have a rating scale attached.

Ordinal scales (data) ranks objects from one largest to smallest or first to last and so

on.

It is possible to count and order but not measure ordinal data.

METHODS OF COLLECTING DATA

Data are the raw numbers or facts which must be processed to give useful

information.

Data collection is expensive, so it is sensible to decide what the data will be used for

before they are collected.

In principle, there is an optimal amount of data which should be collected. These data

should be as accurate as possible.

1. OBSERVATION METHOD

Observation method is a technique in which the behavior of research subjects is

watched and recorded without any direct contact.

CHARACTERISTICS

It is the main method of Psychology and serves as the basis of any scientific enquiry.

Primary material of any study can be collected by this method.

Observational method of research concerns the planned watching, recording and

analysis of observed method.

This method requires careful preparation and proper training for the observer.

TYPES OF OBSERVATION

STRUCTURED OBSERVATION UNSTRUCTURED OBSERVATION

• In structured observation, the

researcher specifies in detail what

is to be observed and how the

measurements are to be recorded.

• It is appropriate when the problem

is clearly defined and the

• In unstructured observation, the

researcher monitors all aspects of

the phenomenon that seem relevant.

• It is appropriate when the problem

has yet to be formulated precisely

and flexibility is needed in

information needed is specified.

observation to identify key

components of the problem and to

develop hypotheses.

PARTICIPANT OBSERVATION NON PARTICIPANT OBSERVATION

• If the observer observes by making

himself, more or less, a member of

the group he is observing so that he

can experience what the members

of the group experience, then the

observation is called participant

observation.

• When the observer observes as a

detached emissary without any

attempt on his part to experience

through participation what others

feel, the observation of this type is

known as non-participant

observation.

CONTROLLED OBSERVATION UNCONTROLLED OBSERVATION

If the observation takes place

according to definite pre-arranged

plans, involving experimental

procedure, the same is termed as

controlled observation

• If the observation takes place in the

natural setting, it may be termed as

uncontrolled observation.

OBSERVATION

ADVANTAGES DISADVANTAGES

Most direct measure of behavior

Provides direct information

Easy to complete, saves time

Can be used in natural or

experimental settings

• May require training

• Observer’s presence may create

artificial situation

• Potential to overlook meaningful

aspects

• Potential for misinterpretation

• Difficult to analyze

FIELD INVESTIGATION

Any activity aimed at collecting primary (original or otherwise

unavailable) data, using methods such as face-to-face interviewing, surveys and case

study method is termed as field investigation.

SURVEY

The survey is a non-experimental, descriptive research method.

Surveys can be useful when a researcher wants to collect data on phenomena

that cannot be directly observed (such as opinions on library services).

In a survey, researchers sample a population.

The Survey method is the technique of gathering data by asking questions to

people who are thought to have desired information.

A formal list of questionnaire is prepared. Generally a non disguised approach

is used.

The respondents are asked questions on their demographic interest opinion.

CASE STUDY METHOD

Case study method is a common technique used in research to test theoretical

propositions or questions in relation to qualitative inquiry.

The strength of the case study approach is that it facilitates simultaneous

analysis and comparison of individual cases for the purpose of identifying

particular phenomena among those cases, and for the purpose of more general

theory testing, development or construction.

A case study is a form of research defined by an interest in individual cases. It

is not a methodology per se, but rather a useful technique or strategy for

conducting qualitative research.

The more the object of study is a specific, unique, bounded system, the more

likely that it can be characterized as a case study.

Once the case is chosen, it can be investigated by whatever method is deemed

appropriate to the aims of the study.

Case studies are particularly useful for examining a phenomena in context.

The case study methodology is designed to study a phenomenon or set of

interacting phenomena in context ―when the boundaries between phenomenon

and context are not clearly evident.‖

The lack of distinction between phenomenon and context make case studies

ideal for conducting exploratory research designed to stand alone or to guide

the formulation of further quantitative research.

Some case studies may be a ‘snap shot’ analysis of a particular event or

occurrence.

Other case studies may involve consideration of a sequence of events, often

over an extended period of time, in order to better determine the causes of

particular phenomena.

INTERVIEWS

Interview is the verbal conversation between two people with the objective of

collecting relevant information for the purpose of research.

It is possible to use the interview technique as one of the data collection

methods for the research.

It makes the researcher to feel that the data what he collected is true and

honest and original by nature because of the face to face interaction.

DIRECT STUDIES

On the basis of reports, records and experimental observations.

SAMPLING

THE SAMPLING DESIGN PROCESS

SAMPLING TECHNIQUES

Sampling techniques are the processes by which the subset of the population from

which you will collect data are chosen.

There are TWO general types of sampling techniques:

1) PROBABILITY SAMPLING

2) NON-PROBABILITY SAMPLING

CLASSIFICATION OF SAMPLING TECHNIQUES

PROBABILITY SAMPLING

A sample will be representative of the population from which it is selected if each

member of the population has an equal chance (probability) of being selected.

Probability samples are more accurate than non-probability samples

They allow us to estimate the accuracy of the sample.

It permit the estimation of population parameters.

TYPES

Simple Random Sampling

Stratified Random Sampling

Systematic Sampling

Cluster Sampling

1) SIMPLE RANDOM SAMPLING

Selected by using chance or random numbers

Each individual subject (human or otherwise) has an equal chance of being

selected

Examples:

Drawing names from a hat

Random Numbers

2) SYSTEMATIC SAMPLING

Select a random starting point and then select every kth

subject in the

population

Simple to use so it is used often

3) STRATIFIED SAMPLING

Divide the population into at least two different groups with common

characteristic(s), then draw SOME subjects from each group (group is called

strata or stratum)

Results in a more representative sample

4) CLUSTER SAMPLING

Divide the population into groups (called clusters), randomly select some of

the groups, and then collect data from ALL members of the selected groups

Used extensively by government and private research organizations

Examples:

Exit Polls

NON-PROBABILITY SAMPLING

DEFINITION

The process of selecting a sample from a population without using (statistical) probability

theory.

NOTE THAT IN NON-PROBABILITY SAMPLING

each element/member of the population DOES NOT have an equal chance of being

included in the sample, and

the researcher CANNOT estimate the error caused by not collecting data from all

elements/members of the population.

TYPES

Quota Sampling

Judgemental Sampling

Sequential Sampling

1) QUOTA SAMPLING

Selecting participant in numbers proportionate to their numbers in the larger

population, no randomization.

For example you include exactly 50 males and 50 females in a sample of 100.

2) JUDGMENTAL SAMPLING

It is a form of sampling in which population elements are selected based on the

judgment of the researcher.

3) SEQUENTIAL SAMPLING

Sequential sampling is a non-probability sampling technique wherein the researcher

picks a single or a group of subjects in a given time interval, conducts his study,

analyzes the results then picks another group of subjects if needed and so on.

DATA PROCESSING AND ANALYSIS STRATEGIES

EDITING

o The process of checking and adjusting responses in the completed

questionnaires for omissions, legibility, and consistency and readying them for

coding and storage.

o Types

Field Editing

Preliminary editing by a field supervisor on the same day as the

interview to catch technical omissions, check legibility of

handwriting, and clarify responses that are logically or

conceptually inconsistent.

In-house Editing

Editing performed by a central office staff; often dome more

rigorously than field editing

DATA CODING

o A systematic way in which to condense extensive data sets into smaller

analyzable units through the creation of categories and concepts derived from

the data.

o The process by which verbal data are converted into variables and categories

of variables using numbers, so that the data can be entered into computers for

analysis.

CLASSIFICATION

o Most research studies result in a large volume of raw data which must be

reduced into homogeneous groups if we are to get meaningful relationships.

o Classification can be one of the following two types, according to the nature of

the phenomenon involved.

Classification according to attributes : Data are classified on the basis

of common characteristics which can be either descriptive or

numerical.

Classification according to class interval : Data are classified on the

basis of statistics of variables.

TABULATION

When a mass of data has been assembled, it becomes necessary for the

researcher to arrange the same in some kind of concise and logical order. This

procedure is referred to as tabulation.

Tabulation is an orderly arrangement of data in rows and columns.

Tabulation is essential because :

It conserves space and reduces explanatory and descriptive statement

to a minimum.

It facilitates the process of comparison.

It provides a basis for various statistical computation.

It facilitates the summation of items and detection of errors and

omissions.

GRAPHICAL REPRESENTATION

Graphs are pictorial representations of the relationships between two (or more)

variables and are an important part of descriptive statistics. Different types of graphs can be

used for illustration purposes depending on the type of variable (nominal, ordinal, or interval)

and the issues of interest. The various types of graphs are :

Line Graph: Line graphs use a single line to connect plotted points of interval and, at times,

nominal data. Since they are most commonly used to visually represent trends over time, they

are sometimes referred to as time-series charts.

Advantages - Line graphs can:

clarify patterns and trends over time better than most other graphs be visually simpler

than bar graphs or histograms

summarize a large data set in visual form

become more smooth as data points and categories are added

be easily understood due to widespread use in business and the media

require minimal additional written or verbal explanation

Disadvantages - Line graphs can:

be inadequate to describe the attribute, behavior, or condition of interest

fail to reveal key assumptions, norms, or causes in the data

be easily manipulated to yield false impressions

reveal little about key descriptive statistics, skew, or kurtosis

fail to provide a check of the accuracy or reasonableness of calculations

Bar graphs are commonly used to show the number or proportion of nominal or ordinal data

which possess a particular attribute. They depict the frequency of each category of data points

as a bar rising vertically from the horizontal axis. Bar graphs most often represent the number

of observations in a given category, such as the number of people in a sample falling into a

given income or ethnic group. They can be used to show the proportion of such data points,

but the pie chart is more commonly used for this purpose. Bar graphs are especially good for

showing how nominal data change over time.

Advantages – Bar graphs can:

show each nominal or ordinal category in a frequency distribution

display relative numbers or proportions of multiple categories

summarize a large data set in visual form

clarify trends better than do tables or arrays

estimate key values at a glance

permit a visual check of the accuracy and reasonableness of calculations

be easily understood due to widespread use in business and the media

Disadvantages – Bar graphs can:

require additional written or verbal explanation

be easily manipulated to yield false impressions

be inadequate to describe the attribute, behavior, or condition of interest

fail to reveal key assumptions, norms, causes, effects, or patterns

Histograms are the preferred method for graphing grouped interval data. They depict the

number or proportion of data points falling into a given class. For example, a histogram

would be appropriate for depicting the number of people in a sample aged 18-35, 36-60, and

over 65. While both bar graphs and histograms use bars rising vertically from the horizontal

axis, histograms depict continuous classes of data rather than the discrete categories found in

bar charts. Thus, there should be no space between the bars of a histogram.

Advantages - Histograms can:

begin to show the central tendency and dispersion of a data set

closely resemble the bell curve if sufficient data and classes are used

show each interval in the frequency distribution

summarize a large data set in visual form

clarify trends better than do tables or arrays

estimate key values at a glance permit a visual check of the accuracy and

reasonableness of calculations

be easily understood due to widespread

use in business and the media use bars whose areas reflect the proportion of data

points in each class

Disadvantages - Histograms can:

require additional written or verbal explanation

be easily manipulated to yield false impressions

be inadequate to describe the attribute, behavior, or condition of interest

fail to reveal key assumptions, norms, causes, effects, or pattern

DESCRIPTIVE AND INFERENTIAL DATA ANALYSIS

Descriptive analysis is the study of distributions of one variable (described as

unidimensional analysis) or two variables (described as bivariate analysis) or more

than two variables (described as multivariate analysis).

Is devoted to summarization and description of data.

Inferential analysis is mainly on the basis of various test of significance for testing

hypothesis inorder to determine with what validity data can be said to indicate some

conclusions.

Uses sample data to make inferences about a population

CORRELATION ANALYSIS

Correlation a LINEAR association between two random variables.

Correlation analysis shows us how to determine both the nature and strength of

relationship between two variables.

When variables are dependent on time correlation is applied.

Correlation lies between +1 to -1.

A zero correlation indicates that there is no relationship between the variables.

A correlation of –1 indicates a perfect negative correlation.

A correlation of +1 indicates a perfect positive correlation.

SPEARMAN’S RANK COEFFICIENT

A method to determine correlation when the data is not available in numerical form

and as an alternative method, the method of rank correlation is used.

Thus when the values of the two variables are converted to their ranks, and there from

the correlation is obtained, the correlations known as rank correlation.

Spearman’s rank correlation coefficient ρ can be calculated when:

Actual ranks given

Ranks are not given but grades are given but not repeated

Ranks are not given and grades are given and repeated

Where, di = difference between ranks of ith pair of two variables

n = no. of pairs of observations

KARL PEARSON’S COEFFICIENT OF CORRELATION

Correlation is a useful technique for investigating the relationship between two

quantitative, continuous variables. Pearson's correlation coefficient ( ) is a measure

of the strength of the association between the two variables.

Karl Pearson’s coefficient of correlation, = ∑

---- Standard deviation of random variable x,y

, ------ average/arithmetic mean

LEAST SQUARE METHOD

The method of least squares is a standard approach to the approximate solution of

over determined systems, i.e., sets of equations in which there are more equations

than unknowns.

"Least squares" means that the overall solution minimizes the sum of the squares of

the errors made in the results of every single equation.

The goal is to find the parameter values for the model which ―best‖ fits the data.

PROBLEM STATEMENT

The objective consists of adjusting the parameters of a model function to best fit a

data set.

A simple data set consists of n points (data pairs) , i = 1, ..., n, where is an

independent variable and is a dependent variable whose value is found by

observation.

The model function has the form f(x,β), where the m adjustable parameters are held in

the vector β.

The least squares method finds its optimum when the sum, S, of squared residuals

∑

,

where

is a minimum.

A residual is defined as the difference between the actual value of the dependent

variable and the value predicted by the model.

DATA ANALYSIS USING STATISTICAL PACKAGES

I) CHI-SQUARE TEST

The chi-square test is an important test amongst the several tests of significance

developed by statisticians.

It was developed by Karl Pearson in1900.

CHI SQUARE TEST is a non parametric test not based on any assumption or

distribution of any variable.

This statistical test follows a specific distribution known as chi square distribution.

In general, the test we use to measure the differences between what is observed and

what is expected according to an assumed hypothesis is called the chi-square test.

STEPS FOR CHI SQUARE TEST

1) Set up the null hypothesis that there is goodness of fit between observed and expected

frequencies.

2) Find the value of using the formula ∑

where O : observed frequencies ,

E : expected frequencies

3) Degree of freedom is n-1 where n is the no. of frequencies given.

4) Obtain the table value.

5) If the calculated is less than table value, conclude that there is goodness of fit.

The goodness of fit indicates that the difference if any is only due to fluctuations in sampling.

EXAMPLE

HO: Horned lizards eat equal amounts of leaf cutter, carpenter and black ants.

HA: Horned lizards eat more amounts of one species of ants than the others.

Leaf Cutter

Ants

Carpenter

Ants

Black Ants Total

Observed 25 18 17 60

Expected 20 20 20 60

O-E 5 -2 -3 0

(O-E)2

E

1.25 0.2 0.45 χ2

= 1.90

∑

Calculate degrees of freedom: (n-1)= 3-1 = 2

Under a critical value of your choice (e.g. α = 0.05 or 95% confidence), look up Chi-square

statistic on a Chi-square distribution table.

Chi-square statistic: χ2

= 5.991 Our calculated value: χ2

= 1.90

*If chi-square statistic > your calculated value, conclude that there is goodness of fit.

5.991 > 1.90 ∴ we accept the hypothesis that there is goodness of fit between observed and

expected values..

II) ANALYSIS OF VARIANCE (ANOVA)

ANalysis Of VAriance (ANOVA) is the technique used to determine whether more

than two population means are equal.

Types of ANOVA

1) One way ANOVA 2) Two way ANOVA

ONE WAY ANOVA

The ANOVA used for the studying the differences among the influence of various

categories of independent variables on a dependent variable is called one way

ANOVA.

Q) Below are given the yield (in kg per acre for 5 trial plots of 4 varieties of treatment

PLOT

NO.

TREATMENT

1 2 3 4

1 42 48 68 80

2 50 66 52 94

3 62 68 76 78

4 34 78 64 82

5 52 70 70 66

Carry out an analysis of variance and state your conclusions.

Solution

I (x1) II (x2) III (x3) IV (x4)

42 48 68 80

50 66 52 94

62 68 76 78

34 78 64 82

52 70 70 66

240 330 330 400

• T = Sum of all the observations = 42+50+….+66 = 1300

•

=

= 84500

• SST = Sum of the squares of all observations -

= (

• SSC = ∑

+

∑

+ ….. -

=

+

+

- 84500 = 2580

• SSE = SST – SSC = 4236 – 2580 =1656

• MSC = SSC/(k-1) = 2580/3 = 860

• MSE = SSE/(N-k) = 1656/(20-4) =103.5

• The degree of freedom = (k-1,N-k) = (3,16)

• k: no. of columns; N : total no. of observations

ANOVA TABLE

Sources of Variation Sum of Squares Degree of freedom Mean Square

Between Samples SSC = 2580 K-1 = 3 MSC = 860

Within Samples SSE = 1656 N-k = 1 MSE = 103.5

Total SST = 4236 N-1 = 19

F = 860/103.5 = 8.3

NOTE: If MSC>MSE, F = MSC/MSE; If MSC<MSE, F = MSE/MSC

Table value of F at (3,16) = 3.24

Since calculated value is more than table value, null hypothesis is rejected.

So treatments do not have same effect

TWO WAY ANOVA

ANOVA used for studying the difference among the influence of various categories

of two independent variables on a dependent variable is called two way ANOVA.

HYPOTHESIS TESTING

Hypothesis: An assertion (assumption) about some characteristic of the population(s), which

should be supported or rejected on the basis of empirical evidence obtained from the

sample(s).

Research Hypothesis: An assumption about the outcome of research (solution to the

problem facing the society or answer to the question).

Statistical Hypothesis: An assumption about any characteristic of the population(s),

expressed in statistical terms (parameter such as population mean, population variance,

population proportion, form of the population distribution etc.).

PARAMETRIC AND NON PARAMETRIC TEST

PARAMETRIC TEST

• If the information about the population is completely known by means of its

parameters then statistical test is called parametric test

• ∗ Eg: t- test, f-test, z-test, ANOVA test

NON- PARAMETRIC TEST

• If there is no knowledge about the population or parameters, but still it is required to

test the hypothesis of the population. Then it is called non-parametric test

• ∗ Eg: Chi-square test, Mann-Whitney, rank sum test, Kruskal-Wallis test

NULL HYPOTHESIS vs. ALTERNATIVE HYPOTHESIS

Null Hypothesis

• Statement about the value of a population parameter

• Represented by H0

• Always stated as an Equality

Alternative Hypothesis

• Statement about the value of a population parameter that must be true if the null

hypothesis is false

• Represented by H1

• Stated in on of three forms

• >, <,

• Example: Consider a set of children having complan and another set having horlicks:

if both have same result for the children then this is consider as null hypothesis and

have difference is alternate hypothesis. After data analysis, if there is a difference in

result then null hypothesis is rejected so there is a scope for the further research.

There can be errors while testing a hypothesis. These errors can be classified into two:

TYPE I vs TYPE II ERROR

Type I error – Rejecting Ho when Ho is true

Type II error – Accepting Ho when Ho is false

LEVEL OF SIGNIFICANCE

• In hypothesis testing, the null hypothesis is either accepted or rejected, depending on

whether the p value is above or below a predetermined cut-off point, known as the

Significance level of the test, usually it is taken as 5% level.

P value

• P is the probability of being wrong when H0 rejected.

• When the level of Significance is set at 5% and the test statistics fall in the region of

rejection, then the p value must be less than 5% i.e (p<0.05).

• When we will accept H0 (p>0.05).

ALPHA vs. BETA

α is the probability of Type I error

β is the probability of Type II error

The experimenters (you and I) have the freedom to set the -level for a particular

hypothesis test. That level is called the level of significance for the test. Changing α

can (and often does) affect the results of the test—whether you reject or fail to reject

H0.

ONE TAILED TEST

In left tailed test, calculated value is less than table value, we reject Ho

In right tailed test, calculated value is greater than table value, we reject Ho

TWO TAILED TEST

If calculated value lies in the acceptance region, then we accept null hypothesis

If calculated value is outside acceptance region, we reject null hypothesis

STEPS FOR HYPOTHESIS TESTING

INTERPRETATION

• Interpretation refers to the task of drawing inferences from the collected facts after an

analytical and/or experimental study.

• Task of interpretation:

• The effort to establish continuity in research through linking the results of a

given study with those of another

• The establishment of some explanatory concepts