Whatever method of sample selection we use it is vital that the method is described. How do we know if the characteristics of a sample we take match the characteristics of the population we are sampling? The short answer is we don’t. We can, however, take steps that make it as likely as possible that the sample will be representative of the

population. Two simple and effective methods of doing this are making sure the sample size is large and making sure it is randomly selected. A large sample size is more likely to be representative of a population than a small one.

Think of extreme cases. If we want to know the average height of the population and we select just one person and measure their height it is unlikely to be close the population average. If we took 1,000,000 people, measured their heights and took the average, this figure would be likely to be close to the population average.

Types of Sampling

The type of enquiry you want to have and the nature of data that you want to collect fundamentally determines the technique or method of selecting a sample.

The procedure of selecting a sample may be broadly classified under the following three heads:

Non-Probability Sampling Methods: Subjective or

Judgement Sampling

Probability Sampling

Mixed Sampling

Now let us discuss these in detail. We will start with the non probability sampling then we will move on to probability sampling.

Non-Probability Sampling Methods

The common feature in non probability sampling methods is that subjective judgments are used to determine the population that are contained in the sample .We classify non-probability sampling into four groups:

1. Convenience Samples

2. Judgement Samples

3. Quota Samples

4. Snowball samples

A. Convenience Samples

These types of samples are used primarily for reasons of convenience.

It is used for exploratory research and speedy situations.

It is often used for new product formulations or to provide

gross-sensory evaluations by using employees, students, peers, etc. Convenience sampling is extensively used in marketing studies and otherwise.

This would be clear from the following examples

1. Suppose a marketing research study aims at estimating the proportion of Pan (Beetle leaf) shops in Delhi, which store a particular drink Maaza. It is decided to take a sample of size 150. What the investigator does is to visit 150 Pan shops

near his place of office as it is very convenient to him and observe whether a Pan shop stores Maaza or not.

This is definitely not a representative sample, as most Pan shops in Delhi had no chance of being selected. It is only

those Pan shops which were near the office of the investigator has a chance of being selected

2. The other example where convenience sampling is often used is in test marketing. There might be some cities whose

demographic make-ups are approximately the same as national average. While conducting marketing tests for new

products, the researcher may take samples of consumers from such cities and obtain consumer evaluations about

these products as these are supposed to represent “national” tastes.

3. A ball pen manufacturing company is interested in knowing the opinions about the ball pen (like smooth flow of ink,

resistance to’ breakage of the cover etc.) it is presently manufacturing with a view to modify it to suit customers

need. The job is given to a marketing researcher who visits a college near his place of residence and asks a few students (a convenient sample) their opinion about the ‘ball pen” in question.

4. As another example a researcher might visit a few shops to observe what brand of vegetable oil people are buying so as to make inference about the share of a particular brand he is interested in. 

B. Judgement Samples

It is that sample in which the selection criteria are based upon your (researcher’s) personal judgment that the members of the sample are representative of the population under study.

It is used for most test markets and many product tests conducted in shopping malls.If personal biases are avoided,

then the relevant experience and the acquaintance of the investigator with the population may help to choose a

relatively representative sample from the population. It is not possible to make an estimate of sampling error as we

cannot determine how precise our sample estimates are. Judgement sampling is used in a number of cases, some of which are:

1. Suppose we have a panel of experts to decide about the launching of a new product in the next year. If for some

reason or the other, a member drops out, from the panel, the chairman of the panel may suggest the name of another

person whom he thinks has the same expertise and experience to be a member of the said panel. This new member was chosen deliberately - a case of Judgment sampling.

2. The method could be used in a study involving the performance of salesmen. The salesmen could be grouped

into top-grade and low-grade performer according to certain specified qualities. Having done so, the sales manager may

indicate who in his opinion, would fall into which category. Needless to mention this is a biased method. However in

the absence of any objective data, one might have to resort to this type of sampling.

C. Quota Samples

This is a very commonly used sampling method in marketing research studies. Here the sample is selected on the basis of certain basic parameters such as age, sex, income and occupation that describe the nature a population so as to make of it representative of the population.

The Investigators or field workers are instructed to choose a sample that conforms to these parameters.The field workers are assigned quotas of the number of units satisfying the required characteristics on which data should be collected.

However, before collecting data on these units the investigators are supposed to verify that the units qualify these characteristics. Suppose we are conducting a survey to study the buying behavior of a product and it is believed that the buying behaviour is greatly influenced by the income level of the consumers. We assume that it is possible to divide our population into three income strata such as high-income group, middle-income group and low-income group. Further it is known that 20% of the population is in high income group, 35% in the middle-income group and 45% in the

low-income group. Suppose it is decided to select a sample of size 200 from the population. Therefore, samples of size 40, 70 and 90 should come from high income, middle income and low income groups respectively. Now the various field workers are assigned quotas to select the sample from each group in such a way that a total sample of 200 is selected in the same proportion as mentioned above. For example, the first field

Selection is done by non-probability means and are based upon the researcher’s judgement of appropriate demographics.

D. Snowball Sampling

It is that samples in which the selection of additional respondents (after the first small group of respondents is

selected) is based upon referrals from the initial set of respondents.

It is used to sample low incidence or rare populations

It is done for the efficiency of finding the additional, hardto- find members of the sample.

Advantages of Non-probability Samples

It is much cheaper to probability samples.

It is acceptable when the level of accuracy of the research results is not of utmost importance.

Less research time is required than probability samples.

It often produces samples quite similar to the population of interest when conducted properly.

Disadvantages of Nonprobability Samples

You cannot calulate Sampling error. Thus, the minimum required sample size cannot be calculated which suggests that

the you (researcher) may sample too few or too many members of the population of interest.

You do not know the degree to which the sample is representative of the population from which it was drawn.

The research results cannot be projected (generalized) to the total population of interest with any degree of confidence.

Probability Sampling

Probability sampling is the scientific method of selecting samples according to some laws of chance in which each unit in the population has some definite pre-assigned probability of being selected in the sample. The different types of probability sampling are :

1. where each unit has an equal chance of being selected.

2. Sampling units have different probabilities of being selected

3. Probability of selection of a unit is proportional to the sample size.

Simple Random Sampling

It is the technique of drawing a sample in such a way that each unit of the population has an equal and independent chance of being included in the sample. In this method an equal probability of selection is assigned to each unit of population at the first draw.It also implies an equal probability of selecting in the subsequent draws.

Thus in simple random sample from a population of size N, the probability of drawing any unit in the first draw is 1/N.The probability of drawing a second unit in the second draw is 1/N- 1 .

The probability of selecting a specified unit of population at any given draw is equal to the probability of its being selected at the first draw.  

Selection of a Simple Random Sample

As we all know Simple Random Sample refers to that method of selecting a sample in which each and every unit of population is given independent and equal chance to be included in the sample. But, Random Sample does not depend only upon selection of units but also on the size and nature of the population. One procedure may be good and simple for a small sample but it may not be good for the large population.

Generally, the method of selecting a sample must be independent of the properties of sampled population. Proper precautions should be taken to ensure that your selected sample is random. Although human bias is inherent in any

sampling scheme administered by human beings. Random selection is best for two reasons - it eliminates bias and

statistical theory is based on the idea of random sampling. We can select a simple random sample through use of tables of random numbers , computerized random number generator or lottery method . Thus, the three methods of drawing simple random sample are:

Mechanical method and using tables of random numbers,

sealed envelopes (lottery system) etc.

Lottery Method

This is the simplest method of selecting a random sample. We will illustrate it by means of example for better

understanding: Suppose, we want to select “r” candidates out of “n”. We assign the numbers from 1 to n i.e to each and every candidate we assign only one exclusive number.

These numbers are then written on n slips which are made as homogeneous as possible in shape, size, colour, etc.

These slips are then put in a bag and thoroughly shuffled and then “r” slips are drawn one by one. The “r” candidates

corresponding to numbers on the slips drawn will constitute a random sample.

This method of selecting a simple random sample is independent of the properties of population. Generally in place of slips you can use cards also. We make one card corresponding to one unit of population by writing on it the number assigned to that particular unit of population. The pack of cards is a miniature of population for sampling purposes. The cards are shuffled a number of times and then a card is drawn at random from them. This is one of the most reliable methods of selecting a random sample.

Mechanical Randomisation or Random Numbers Method

The explained method of lottery is very time consuming and cumbersome to use if population is very large.

Therefore the most practical and inexpensive method of selecting a random sample consists in the use of Random

Numbers Tables, which has been constructed that each of the digits 0,1,2,3,4,5,6,7,8,9 appear with approximately the same frequency and independently of each other. If we have to select a simple random sample from a population

of size N(d”99) then the numbers can be combined two by two to give pairs from 00 to 99.

Similarly if Nd”999 or Nd”9999 and so on, then combining the digits three by three ( or four by four and so on ), we get numbers from 000 to 999 or (0000 to 9999) and so on. Since each of the digits 0,1,2,3,4,5,6,7,8,9 appear with approximately the same frequency and independently of each other, so does each of the pairs 00 to 99 or triplets from 000 to 999 or quadruplets 0000 to 9999 and so on .

Thus, the method of drawing the random sample consists in the following steps:

i. Identify the N units in the population with the numbers from 1 to N

ii. Select at random, any page of the random number tables and pick up the numbers in any row or column or diagonal at random.

iii. The population units corresponding to the number of unit selected in step (ii) comprise the random sample.

I will tell you about the different sets of random numbers commonly used in practice. The numbers in these tables have

been subjected to various statistical tests for randomness of a series and their randomness has been well established for all practical purposes.

1. Tippets (1927) Random Number Table: (Tracts for computers No. 15 Cambridge University Press) Tippet number tables consist of 10,400 four digited numbers, giving in all 10,400 x 4 , i.e.,41600 digits selected at random from the British Census Report.

2. Fisher and Yates (1938) Tables (in statistical tables for biological, Agricultural and Medical Research) comprise 15,000 digits arranged in twos. Fisher and Yates obtained these tables by drawing numbers at random from 10th to 19th digits of A.S.Thomson’s 20- figure logarithmic tables.

3. Kendall and Babington Smith’s (1939) random tables consist of 1,00,000 digits grouped into 25,000 sets of 4 digited

random numbers (Tracts for computers No. 24 Cambridge University Press)

4. Rand Corporation (1955) (free oress, Illinois) random number tables consist of one million random digits

consisting of 5 digits each.

5. TI-82: Generating Random Numbers You can generate random numbers on the TI-82 calculator using the following sequence. N is the number of different values, which could be, and S is the minimum number. int (N*rand+S)

If you have two values (A and B) that you need random numbers between, then you can generate them using the following formule N=B-A+1 int (N*rand+A) Notice it is B-A+1 not B-A. Everyone agrees there are 10 numbers

between 1 and 10 (inclusive). But, if you take 10-1, you get 9, not 10. Also, in the formula above, replace the N by the actual number of different values.

Since the calculator remembers the last formula put in, and evaluates it when you hit enter, to generate more random numbers, just hit enter again. Each time you hit enter, you will get another random

number.

Merits and Limitations of Simple Random Sampling Merits

1. Since samples units are selected at random providing equal chance to each and every unit of population to be selected , the element of subjectivity or personal bias is completely eliminated. Therefore, we can say that simple random sample is more representative of population than purposive or judgement sampling.

2. You can ascertain the efficiency of the estimates of the parameters by considering the sampling distribution of the

statistic (estimates) For example:One measure of calculating precision is sample size. Sample mean becomes an unbiased mean of population mean or a more efficient estimate of population mean as sample size increases.

Limitations

1. The selection of simple random sample requires an up- to - date frame of population from which samples are to be

drawn. Although it is impossible to have knowledge about each and every unit of population if population happens to

be very large. This restricts the use of simple random sample.

2. A simple random sample may result in the selection of the sampling units, which are widely spread geographically and in such a case the administrative cost of collecting the data may be high in terms of time and money.

3. Sometime, a simple random sample might give most nonrandom looking results, which I will explain with the help

of an illustration next.

4. For a given precision, simple random sample usually requires larger sample size as compared to stratified random

sampling which we will be studying next. The limitations of simple random sample will be clear from the example.

If I were conducting a study looking at two treatments, A and B then one way I could allocate patients to treatment groups would be by using a table of random numbers. The following set of random numbers came from a popular

statistics tables (most statistics textbooks have them): 65246356854282020026

I could allocate patients to treatment A if the number were odd and B if it were even. This would result in successive patients being allocated in the sequence: BABBBAABBABBBBBBBBBB

Randomly selected numbers often seem to have patterns in them, like long runs of the same number. This is not a problem if we are conducting a large study, everything evens out over time. But if the above study had stopped after recruiting 20 patients then we would have had four patients on treatment A and sixteen on B. This would not be a very good basis for comparing the two treatments.

Therefore, some of the randomly allocated sample prove very non-random. This type of problem can be eliminated by use of Stratified Random Sampling, in which the population is divided into different strata.

Now, we will move into details of stratified random sampling.

Stratified Random Sampling

We have understood that in simple random sampling, the variance of the sample estimate of the population is

a. Inversely proportional to the sample size, and

b. Directly proportional to the variability of the sampling units in the population. We also know that the precision is defined as reciprocal of its sampling variance. Therefore as sample size increases precision increases.

Apart from increasing the sample size or sampling fraction n/N, the only way of increasing the precision of sample mean is to devise a sampling technique which will effectively reduce variance, the population heterogeneity. One such technique is Stratified Sampling.

There are two points which you have to keep in mind while drawing a stratified random sample.

Proper classification of the population into various strata, and

A suitable sample size from each stratum. Both these points are important to be considered because if your

stratification is faulty, it cannot be compensated by taking large samples.

Principle advantages of Stratified Random Sampling

1. More Representative

In an non-stratified random sample some strata may be over represented, others may be under-represented while some may be excluded altogether. Stratified sampling ensures any desired representation in the sample of the various strata in the population. It over-rules the possibility of any essential group of the population being completely excluded in the sample. Stratified sampling thus provides a more representative cross section of the population and is frequently regarded as the most efficient system of sampling. 

2. Greater Accuracy

Stratified sampling provides estimates with increased precision . Moreover, stratified sampling enables us to obtain the results of known precision for each stratum.

3. Administrative Convenience

As compared with simple random sample, the stratified random samples are more concentrated geographically. Accordingly, the time and money involved in collecting the data and interviewing the individuals may be considerably reduced and the supervision of the field work could be allocated with greater ease and convenience.

4. Sometimes you will notice that sampling problems may differ markedly in different parts of population. For example

Literates and Illiterate .People living in ordinary homes and people living in institutions, hostels, hospitals etc.

In such cases we will deal with the problem through stratified sampling by regarding the different parts of the population as stratum and tackling the problems of the survey within each stratum independently.

Note: You can allocate the sample sizes for different strata can be done in two ways:

1. Proportional allocation

2. Optimum allocation

In proportional allocation, allocation of ni , the sample size of each strata is called proportional if the sample fraction is constant for each stratum i.e.,

n1 = n2 = - - - - - - - - - - - = nk

N1 N2 Nk

Optimum Allocation is another guiding principle in the determination of the ni is to choose them so as to :

1. Minimise the variance (i.e., maximize the variance) of the estimate for (i) fixed sample size, (ii) fixed cost

2. Minimise the total cost for fixed desired precision

Systematic Random Sampling

If you have the complete and up-to-date list of sampling units is available you can also employ a common technique of selection of sample , which is known as systematic sampling. In systematic sampling you select the first unit at random, the rest being automatically selected according to some predetermined pattern involving regular spacing of units.

Now let us assume that the population size is N. We number all the sampling units from 1 to N in some order and a sample of size n is drawn in such a way that N = nk i.e. k = N/n

Where k, usually called the sampling interval, is an integer.

Merits and Demerits of Systematic Random Sampling

Now students we will discuss the merits and demerits of systematic random sampling

Merits

I. .Systematic sampling is operationally more convenient than simple random sampling or stratified random sampling.

It saves your time and work involved.

II. This sampling is more efficient to simple random sample, provided the frame (the list from which you have drawn the sample units ) is arranged wholly at random

Demerits

I. The main disadvantage of systematic sampling is that systematic sampling is that systematic samples are not in

general random samples since the requirement in merit two is rarely fulfilled.

II. If N is not a multiple of n, then

The actual sample size is different from that required, and

Sample mean is not an unbiased estimate of the population mean.

III.It does not provide the sampling error

IV.Systematic sampling may yield highly biased estimates if

there are periodic features associated with the sampling interval, I.e., if the frame (list) has a periodic feature and k is

equal to or a multiple of the period.

Cluster Sampling

In this type of sampling you divide the total population , depending upon the problem under study, into some recognizable sub-divisions which are termed as clusters and a simple random sample of n blocks is drawn.

The individuals which you have selected from the blocks constitute the sample.

Multistage Sampling

One better way of selecting a sample is to resort to sub-sampling within the clusters , instead of enumerating all the sampling units in the selected cluster. This technique is called two-stage sampling, clusters being termed as primary units and the units within the clusters being termed as primary units and the units within the clusters as secondary units.

This technique can be generalized to multistage sampling. We regard population as a number of primary units each of which is further composed of secondary stage units and so on , till we ultimately reach a stage where desired sampling units are obtained. In multi-stage sampling each stage reduces the sample size.

Merits and Limitations

i. Multistage sampling is more flexible as compared to other methods .It is simple to carry out and results in administrative convenience by permitting the field work to be concentrated and yet covering large area.

ii. It saves a lot of operational cost as we need the second stage frame only for those units which are selected in the first stage sample .

iii. It is generally less efficient than a suitable single- stage sampling of the same size.This brings an end on today’s

discussion on sampling techniques. Thus in the nutshell we can say that Non probabilistic sampling such as Convenience sampling, Judgement Sampling and Quota sampling are sometimes used although representativeness of such a sample cannot be ensured. Whereas a probabilistic sampling to each unit of the population to be included in the sample and in

this sense it is a representative sample of the population.

Points to Ponder

Sampling is based on two premises. One is that there is enough similarity among the elements in a population that a

few of these elements will adequately represent the characteristic of the total population.

The second premises is that while some elements in a sample underestimate th population value, others

overestimate the value.

The results of these tendencies are that a sample mean is generally a good estimate of population mean.

A good sample has both accuracy & precision. An accurate sample is one which there is little or no bias or systematic

variance. A sample with adequate precision is one that has a sampling error that is within acceptable limits.

A variety of sampling technique is available, of which probability sampling is based on random selection – a

controlled procedure that ensures that each population element is given a known nonzero chance of selecion.

In contrast -nonprobability selection is not random. When each sample element is drawn individually from the

population at large, it is unrestricted sampling.                 

                     

Factor Analysis

What is Factor Analysis?

The main objective of Factor analysis is to summarize a large number of underlying factors into a smaller number of variables or factors which represent the basic factors underlying the data. Factor analysis is used to uncover the latent structure (dimensions) of a set of variables. It reduces attribute space from a larger number of variables to a smaller number of factors and as such is a “nondependent” procedure (that is, it does not assume a dependent variable is specified).

WE can best explain factor analysis with a non technical analogy: A mother sees various bumps and shapes under a blanket at the bottom of a bed. When one shape moves toward the top of the bed, all the other bumps and shapes move toward the top also, so the mother concludes that what is under the blanket is a single thing, most likely her child. Similarly, factor analysis takes as input a number of measures and tests which are analogous to the bumps and shapes. Those that move together are considered a single thing and are labeled a factor. That is, in factor analysis the researcher is assuming that there is a “child” out there in the form of an underlying factor, and he or she takes simultaneous movement (correlation) as evidence of its existence. If correlation is spurious for some reason, this inference will be mistaken, of course, so it is important when conducting factor analysis that possible variables which might introduce

spuriousness, such as anteceding causes, be included in the analysis.

Typical Problem Studied Using Factor Analysis

Factor analysis is used to study a complex product or service to identify the major characteristics considered important by consumers.

The two major uses of factor analysis

1. To simplify a set of data by reducing a large number of measures (which in some way may be interrelated and causing

multicollinearity) for a set of respondents to a smaller more manageable set which are not interrelated and still retain most of the original information .

2. To identify the underlying structure of the data in which a very large number of variables may really be measuring a small number of basic characteristics or constructs of our sample. For e.g a survey may throw up bet 15-20 attributes which a consumer considers when buying a product. However there is a need to find out what are the key drivers.

Factor analysis identifies latent or underlying factors from an array of seemingly imp variables.

Uses of Factor Analysis

To reduce a large number of variables to a smaller number of factors for modeling purposes, where the large number of variables precludes modeling all the measures individually. As such, factor analysis is integrated in structural equation modeling (Sem), helping create the latent variables modeled by Sem. However, factor analysis can be and is often used on a stand-alone basis for similar purposes.

To select a subset of variables from a larger set, based on which original variables have the highest correlations with the principal component factors.

To create a set of factors to be treated as uncorrelated variables as one approach to handling multicollinearity in such procedures as multiple regression

To validate a scale or index by demonstrating that its constituent items load on the same factor, and to drop proposed scale items which cross-load on more than one factor.

To establish that multiple tests measure the same factor, thereby giving justification for administering fewer tests.

To identify clusters of cases and/or outliers.

To determine network groups by determining which sets of people cluster together (using Q-mode factor analysis, discussed below)

Applications

The main applications of factor analysis are in marketing research. Some of the application are as follows:

1. Developing perceptual maps; Factor analysis is often used to determine the dimensions or critieria by which consumers evaluate brands and how each brand is seen on each dimension.

2. Determining the underlying dimensions of the data.: A factor analysis of data on TV viewing indicates that there are

seven different types of programmes that are independent of the network offering as perceived by the viewers: movies, adult entertainment, westerns, family entertainment, adventure plots, unrealistic events, sin

3. Identifying market segments; and positioning of products; An example of this is a factor analysis of data on desires sought on the last vacation taken by 1750 respondents revealed six benefit segements for vacationers:

Those who vacation for the purpose of visiting friends  and relatives, and not sight seeing,

2, Visiting friends and relatives and plus sight seeing,

3, Sightseeing,

4, Outdoor vacations 5

Resort vacationing

6. Foreign Vacationing.

3. It can be used for condensing or simplifying data: An example of this : In a study of consumer involvement

across a number of product categories, 19 items were reduced to four factors of :

1. Perceived product importance/ perceived importance s of negative consequences of a mispurchase

2. Subjective probability of a mispurchase

3. Pleasure of owing/using product. The value of the product as a cue to the type of person who owns it Each of these

factors was independent and there was no multicollinearity.

4. Testing of hypotheses about the structure of a data set. Confirmatory factor analysis can be used to test whether the

variables in a data set come from a specifies number of factors.

Basic Principles of Factor Analysis

Factor analysis is part of the multiple general linear hypothesis (MLGH) family of procedures and makes many of the same assumptions as multiple regression:

Linear relationships,

Interval or near-interval data, ,

Proper specification (relevant variables included,

extraneous ones excluded),

Lack of high multicollinearity, and

Assumption of multivariate normality for purposes of significance testing. There are several different types of factor analysis, with the most common being principal components analysis (PCA). However, principal axis factoring (PAF), also called common factor analysis, is preferred for purposes of confirmatory factory analysis.

Factor Analysis-The Theory

Factor analysis is a complex statistical technique which works on the basis of consumer responses to identify similarities or associations across factors. It analyzes correlations between variables, reduces their numbers by grouping them in to fewer factors.

How it Works

Factor analysis applies an advanced form of correlation analysis to a no. of factors / statements or attributes. If several of the statements are highly correlated, it is thought that these statements measure some factor common to all of them.

A typical study will throw up many such factors. For each such the researchers have to use their judgment to determine what a particular factor represents. Factor analysis can only be applied to continuous or intervally scaled variables.

Factor Analysis - The Process

We now take the case of a marketing research study where factor analysis is most popularly used. We begin by administering a questionnaire to all consumers. What factor analysis does is it identifies two or more questions that result in responses that are highly correlated. Thus it looks at interdependencies or interrelationships among data.The analysis begins by observing the correlation and determining whether there are significant correlations between them. Factor analysis is best illustrated with the help of an example:

Example

A two wheeler manufacturer is interested in determining which variables his customers think of as being imp when they consider his product. The respondents were asked indicate on a 7 pt scale(1: completely agree, 7 : completely disgree) with a set of 10 statements relating to their perceptions and some attributes about two wheelers. Factor analysis would then aim to reduce 10 factors to a few core factors.

The statements are as:

1. I use a two-wheeler because it’s affordable.

2. It gives me a sense of freedom to own a two wheeler

3. Low maintenance costs make it very economical in long run

4. A two-wheeler is essentially a man’s vehicle.

5. I feel very powerful when I am on my two-wheeler.

6. Some of my friend’s who don’t have one are jealous of me.

7. I feel good whenever I see ads for my two wheeler on TV ormagazines

8. My vehicle gives me a comfortable ride.

9. I think two wheelers are a safe way to travel.

10.Three people should be allowed to travel on a 2 wheeler. The answers given by 20 resp is inputed into the computer.

What the factor analysis does statistically is to group together those variables whose responses are highly correlated. Then from the groups of factors or statements we choose an overall factorwhich appears to represent what all the factors in the group appear to mean.

 

Questionnaire

 

Measurement & Scaling    

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