Scaling and Measurement techniques

Measurement, Scaling, Instrument Designing and Sampling

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3UNITMeasurement, Scaling, Instrument Designing and Sampling


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In our daily life we are said to measure when we use some yardstick to determine weight, height, or some other feature of a physical object. We also measure when we judge how well we like a song, a painting or the personalities of our friends. We, thus, measure physical objects as well as abstract concepts. Measurement is a relatively complex and demanding task, specially so when it concerns qualitative or abstract phenomena. By measurement we mean the process of assigning numbers to objects or observations, the level of measurement being a function of the rules under which thenumbers are assigned.

Defining Measurement


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Defining MeasurementProperties like weight, height, etc., can be measured directly with some standard unit of measurement, but it is not that easy to measure properties like motivation to succeed, ability to stand stress and the like. We can expect high accuracy in measuring the length of pipe with a yard stick, but if the concept is abstract and the measurement tools are not standardized, we are less confident about the accuracy of the results of measurement.When we measure, we attempt to identify the dimensions, quantity, capacity, or degree of something. Measurement is formally defined as the act of measuring by symbols or numbers to something according to a specific set of rules.


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Technically speaking, measurement is a process of mapping aspects of a domain onto other aspects of a range according to some rule of correspondence.

In measuring, we devise some form of scale in the range (in terms of set theory, range may refer to some set) and then transform or map the properties of objects from the domain (in terms of set theory, domain may refer to some other set)onto this scale.


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For example, in case we are to find the male to female attendance ratio while conducting a study of persons who attend some show, then we may tabulate those who come to the show according to sex. In terms of set theory, this process is one of mapping the observed physical properties of those coming to the show (the domain) on to a sex classification (the range). The rule of correspondence is: If the object in the domain appears to be male, assign to “0” and if female assign to “1”. Similarly, we can record a person’s marital status as 1, 2, 3 or 4, depending on whether the person is single, married, widowed or divorced. We can as well record “Yes or No” answers to a question as “0” and “1” (or as 1 and 2 or perhaps as 59 and 60).


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Measurement ScaleThe most widely used classification of measurement scales are:

(a) nominal scale; (b) ordinal scale; (c) interval scale; and (d) ratio scale.


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(A) Nominal scaleNominal scale is simply a system of assigning number symbols to events in order to label them. The usual example of this is the assignment of numbers of basketball players in order to identify them. Such numbers cannot be considered to be associated with an ordered scale for their order is of no consequence; the numbers are just convenient labels for the particular class of events and as such have no quantitative value. Nominal scales provide convenient ways of keeping track of people, objects and events.


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One cannot do much with the numbers involved. For example, one cannot usefully average the numbers on the back of a group of football players and come up with a meaningful value. Neither can one usefully compare the numbers assigned to one group with the numbers assigned to another.The counting of members in each group is the only possible arithmetic operation when a nominal scale is employed. Accordingly, we are restricted to use mode as the measure of central tendency. There is no generally used measure of dispersion for nominal scales. Chi-square test is the most common test of statistical significance that can be utilized, and for themeasures of correlation, the contingency coefficient can be worked out.


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Nominal scale is the least powerful level of measurement. It indicates no order or distance relationship and has no arithmetic origin. A nominal scale simply describes differences between things by assigning them to categories. Nominal data are, thus, counted data. The scale wastes any information that we may have about varying degrees of attitude, skills, understandings, etc. In spite of all this, nominal scales are still very useful and are widely used in surveys and other ex-post-facto research when data are being classified by major sub-groups of the population.


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The lowest level of the ordered scale that is commonly used is the ordinal scale.The ordinal scale places events in order, but there is no attempt to make the intervals of the scale equal in terms of some rule. Rank orders represent ordinal scales and are frequently used in research relating to qualitative phenomena. A student’s rank in his graduation class involves the use of an ordinal scale. One has to be very careful in making statement about scores based on ordinal scales.

(B) Ordinal scale


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For instance, if Ram’s position in his class is 10 and Mohan’s position is 40, it cannot be said that Ram’s position is four times as good as that of Mohan. The statement would make no sense at all.Ordinal scales only permit the ranking of items from highest to lowest. Ordinal measures have no absolute values, and the real differences between adjacent ranks may not be equal. All that can be said is that one person is higher or lower on the scale than another, but more precise comparisons cannot be made.


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Thus, the use of an ordinal scale implies a statement of ‘greater than’ or ‘less than’ (an equality statement is also acceptable) without our being able to state how much greater or less. The real difference between ranks 1 and 2 may be more or less than the difference between ranks 5 and 6. Since the numbers of this scale have only a rank meaning, the appropriate measure of central tendency is the median. A percentile or quartile measure is used for measuring dispersion. Correlations are restricted to various rank order methods. Measures of statistical significance are restricted to the non-parametric methods.


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Any questions that ask respondent to rate something are using ordinal scales. E.g.

1. How would you rate the service of our wait-staff?•Excellent •Very good•Good•Fair•Poor

2. If there are 4 different brands of talcum powder and if a respondent ranks them based on say, “Freshness” in to Rank 1 having maximum Freshness Rank 2 the second maximum Freshness, and so on, and ordinal sacles results.


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(C) Interval scaleIn the case of interval scale, the intervals are adjusted in terms of some rule that has been established as a basis for making the units equal. The units are equal only in so far as one accepts the assumptions on which the rule is based.Interval scales can have an arbitrary zero, but itis not possible to determine for them what may be called an absolute zero or the unique origin. The primary limitation of the interval scale is the lack of a true zero; it does not have the capacity to measure the complete absence of a trait or characteristic.


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An interval scale tell us whether P is as much higher than Q as Y is than Z on a particular attribute.

In other words, in an interval scale, the difference between may two adjacent positions is the same as the one between any other two adjacent positions.


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The Fahrenheit scale is an example of an interval scale and shows similarities in what one can and cannot do with it. One can say that an increase in temperature from 30° to 40° involves the same increase in temperature as an increase from 60° to 70°, but one cannot say that the temperature of 60° is twice as warm as the temperature of 30° because both numbers are dependent on the fact that the zero on the scale is set arbitrarily at the temperature of the freezing point of water. The ratio of the two temperatures, 30° and 60°, means nothing because zero is an arbitrary point.


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Interval scales provide more powerful measurement than ordinal scales for interval scale also incorporates the concept of equality of interval. As such more powerful statistical measures can be used with interval scales. Mean is the appropriate measure of central tendency, while standard deviation is the most widely used measure of dispersion. Product moment correlation techniques areappropriate and the generally used tests for statistical significance are the ‘t’ test and ‘F’ test.


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(C) Ratio scaleRatio scales are the most sophisticated of scales, since it incorporates all the characteristics of nominal, ordinal and interval scales. As a result, a large number of descriptive calculations are applicable. This is a scale with a true zero point.It also has all of the lower level characteristics of equal intervals, rank order, and ability to mark a value with a name.Some examples are height, weight, response time, annual income etc..Here is an example of the presence of a true zero point; If your annual income exactly zero dollars then you earned no annual income at all. You can buy absolutely nothing with zero dollars. Zero means Zero.


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When a scale consists not only of equidistant points but also has a meaningful zero point, then we refer to it as a ratio scale.If we ask respondents their ages, the difference between any two years would always be the same, and “zero” signifies the absence of age or birth.Hence a 100-year old person is indeed twice as old as a 50-year old one .Sales figures, quantities purchased and market share are all expressed on a ratio scale.Ratio scales should be used to gather quantitative information, and we see them perhaps most commonly when respondents are asked for their age, income, years of participation, etc..


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Ratio scales are not widely used in marketing research unless a base item is made available for comparison.A ratio scale has a natural zero point and further numbers are placed at equally appearing intervals. For example scales for measuring physical quantities like – length, weight etc..The ratio scale, is commonly used in the physical sciences. To have a ratio scale the absolute zero point needs to be determined.A ten-inch rod can be said to be exactly twice as long as five inch one, because both the rods share a common starting point, namely the real zero point.


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Criteria for good measurementIrrespective of the data collection technique used, it is critical that the researcher analyze it for Reliability, validity and practicality.

1. Reliability:The extent to which results are consistent over time and accurate representation of the total population under study is referred to as reliability.In other words, if the results of a study can be reproduced under a similar methodology, then the research instrument is considered to be reliable.


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Should you have a question that can be misunderstood, and therefore is answered differently by respondents, you are dealing with low reliability.The consistence with which questionnaire items are answered can be determined through the test-retest method, whereby a respondent would be asked to answer(s) the same question at two different times.This attribute of the instrument is actually referred to as reliability.If we are dealing with a stable measure, then the result should be similar.A high degree of stability indicates a high degree of reliability, since the results are repeatable.


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It is the degree to which measures are free from error and therefore yield consistent results.Two dimensions underlie the concept of reliability:

Repeatabilityinternal consistency

Test retest method of determining reliability involves administering the same scale or measure to the same respondents at two separate times to test for stability.


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2. Validity:it is the ability of scale or measuring instrument to

measure what is intend to measure.validity is the extent to which differences found with a measuring instrument reflect true differences among those being tested. But the question arises: how can one determine validity without direct confirming knowledge? The answer may be that we seek other relevant evidence that confirms the answers we have found with our measuring tool.What is relevant, evidence often depends upon the nature of the research problem and the judgement of the researcher. But one can certainly consider three types of validity in this connection:


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(i) Content validity; (ii) Criterion-related validity and (iii) Construct validity

(i) Content validity is the extent to which a measuring instrument provides adequate coverage of the topic under study. If the instrument contains a representative sample of the universe, the content validity is good. Its determination is primarily judgemental and intuitive. It can also be determined by using a panel of persons who shall judge how well the measuring instrument meets the standards, but there is no numerical way to express it.


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(ii) Criterion-related validity relates to our ability to predict some outcome or estimate the existence of some current condition. This form of validity reflects the success of measures used for some empirical estimating purpose. The concerned criterion must possess the following qualities: Relevance: (A criterion is relevant if it is defined in terms we judge to be the proper measure.)Freedom from bias: (Freedom from bias is attained when the criterion gives each subject an equal opportunity to score well.)Reliability: (A reliable criterion is stable or reproducible.)Availability: (The information specified by the criterion must be available.)


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In fact, a Criterion-related validity is a broad term that actually refers to (i)Predictive validity and (ii)Concurrent validity.

The former refers to the usefulness of a test in predicting some future performance whereas the latter refers to the usefulness of a test in closely relating to other measures of known validity. Criterion-related validity is expressed as the coefficient of correlation between test scores and some measure of future performance or between test scores and scores on another measure of known validity.


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(iii) Construct validity is the most complex and abstract. A measure is said to possess construct validity to the degree that it confirms to predicted correlations with other theoretical propositions.Construct validity is the degree to which scores on a test can be accounted for by the explanatory constructs of a sound theory. For determining construct validity, we associate a set of other propositions with the results received from using our measurement instrument. If measurements on our devised scale correlate in a predicted way with these other propositions, we can conclude that there is some construct validity.


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3. Test of PracticalityThe practicality characteristic of a measuring instrument can be judged in terms of economy, convenience and interpretability. From the operational point of view, the measuring instrument ought to be practical i.e., it should be economical, convenient and interpretable. Economy consideration suggests that some trade-off is needed between the ideal research project and that which the budget can afford. The length of measuring instrument is an important area where economic pressures are quickly felt. Although more items give greater reliability as stated earlier, but in the interest of limiting the interview or observation time, we have to take only few items for our study purpose. Similarly, data-collection methods to be used are also dependent at times upon economic factors.


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Convenience test suggests that the measuring instrument should be easy to administer.

Although more items give greater reliability as stated earlier, but in the interest of limiting the interview or observation time, we have to take only few items for our study purpose.

Similarly, data-collection methods to be used are also dependent at times upon economic factors.


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For this purpose one should give due attention to the proper layout of the measuring instrument. For instance, a questionnaire, with clear instructions (illustrated by examples), is certainly more effective and easier to complete than one which lacks these features. Interpretability consideration is specially important when persons other than the designers of the test are to interpret the results. The measuring instrument, in order to be interpretable, must be supplemented by (a) detailed instructions for administering the test;(b) scoring keys; (c) evidence about the reliability and (d) guides for using the test and for interpreting results.


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SCALING TECHNIQUES


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1. Comparative Scale


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A comparative Scale asks respondents to rate a concept by comparing it with a benchmark.

Comparative scales involve the direct comparison of stimulus objects.

Comparative scale data must be interpreted in relative terms and have only ordinal or rank order properties.


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Advantages: Small differences between stimulus objects can be

detected. Same known reference points for all respondents. Easily understood and can be applied. Involve fewer theoretical assumptions.

Disadvantages Ordinal nature of data


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Comparative Rating Scale is of 4 types

Paired comparisons

Rank order scale

Constant Sum Scale

The Q Sort technique


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Paired comparisons:Here the respondents are presented with two objects at a time and asked to pick the one they prefer according to some criterion.

The data obtained are ordinal in nature. It is most widely used scale.


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Rank order scaling:Respondents are presented with several objects simultaneously and asked to order or rank them according to some criterion.It is possible that the respondent may dislike the brand ranked 1 in an absolute sense.Rank order scaling also results in ordinal data. Only (n-1) scaling decisions need be made in rank order scaling.Rank the various brands of smart phones in order of preference.Rank the various brands of smart phones in order of preference. Begin by picking out the one brand that you like the most and assign it a number 1. Then find the second most preferred brand and assign it a number 2.


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Continue this process until you have ranked all the brands of smart phones in order of preference.The least preferred brand should be assigned a rank of 10.No two brands should receive the same rank number. The criterion of preference is entirely up to you.There is no wrong or right answer.


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Constant sum scalingRespondents allocate a constant sum of units, such as 100 points to attributes of a product to reflect their importance. If an attribute is unimportant, the respondent assigns it zero points.If an attribute is twice as important as some other attribute, it receives twice as many points.The sum of all the points is 100.Hence name of scale is constant sum scale. The limitations of scale is that


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The Q Sort technique It is used to discriminate among large number of objects quickly. It uses a rank order procedure and the objects are sorted into piles (place (things) one on top of another.) based on similarity with respect to some criteria. The number of objects to be sorted should be between 60-140 approximatelyFor example here we are talking nine brands. On the basis of taste we classify the brands into tasty, moderate and non tasty. We can classify on the basis of price also Low, medium, high. Then we can attain the perception of people that whether they prefer low priced brand, high or moderate.


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We can classify sixty brands or pile it into three piles.So the number of objects is to be placed in three piles low , medium or high.

Thus this technique is an attempt to classify subjects in terms of their similarity to attribute under study.


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2. NON COMPARATIVE RATING SCALES


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Here each object is scaled independently of the others in the stimulus set. The resulting data are generally assumed to be interval or ration scaled. Respondents evaluate only one object at a time, and for this reason non-comparative scales are often referred to as monadic scales. Types of non comparative scales are

Continuous rating scale Itemized rating scale

Likert scale Semantic Differential Scale Stapel’s ScaleMulti Dimensional Scaling Thurston Scales etc..


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1. Continuous Rating Scale2.1


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2.2 Itemized Rating ScaleIt is different from continuous rating scales. They have a number of brief descriptions associated with each category. They are widely used in marketing research.They essentially take the form of multiple category questions.The respondents are provided with a scale that has a number or brief description associated with each category.The categories are ordered in terms of scale position, and the respondents are required to select the specified category that best describes the object being rated.


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2.2.1 Likert ScaleIt was developed by Rensis Likert.Here the respondents are asked to indicate a degree of agreement and disagreement with each of a series of statement.Each scale item has 5 response categories ranging from strongly agree and strongly disagree.

5Strongly agree

4 Agree

3Indifferent

2Disagree

1Strongly disagree


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For the likert scale, various opinion statement are collected, edited and then given to a group of subjects to rate the statement on a five point continuum:

1 = Strongly agree; 2 = agree; 3 = undecided; 4 = disagree; 5 = strongly disagree.

The subjects express the degree the (one to five) of their personal agreement or disagreement with each of the statements. Only those items which in the analysis best differentiate the high scores and the low scorers of the sample subjects are retained and the scale is ready for use.


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To measure the attitude of a given group of respondents, this scale is given to them and every respondent indicates whether s/he strongly agrees, agrees, is undecided, or strongly disagrees with each statement.The respondent’s attitude score is the sum of her/his ratings of all the statements. For this reason, the Likert scale is known as the scale of Summated Ratings.


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Likert scales are of ordinal type, they enable one to rank attitudes, but not to measure the difference between attitudes.By and large, a greater majority of researcher prefer the Likert technique.In many research studies we come across seven-point scales being used, which bear the appearance of the Likert Scale.It must be noted that the typical Likert technique requires an item analysis to establish that all the items in the scale measure the same attitude – no matter whether the scale has five or more points.


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A typical Likert scale has 20 – 30 statements. While designing a good Likert scale, first a large pool of statements relevant to the measurement of attitude has to be generated and then from the pool statements, the statements which are vague(unclear) and non-discriminating have to be eliminated.


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2.2 Stapel's ScaleIt was developed by Jan stapel.Modern versions of the Stapel scale place a single adjective as a substitute for the semantic differential when it is difficult to create pairs of bipolar adjectives.This scale has some features:1. Each item has only one word/phrase indicating the dimension it represents2. Each item has ten response categories.


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For example, in the following items, suppose for quality of ice-cream, we ask respondents to rank from +5 to -5.Select a plus number for words which best describe the ice cream accurately.Select a minus number for words you think do not describe the ice-cream quality accurately. Thus, we can select any number from +5 to -5.+5 for more accurate and -5 for very inaccurate.


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This scale is presented vertically+5+4+3+2+1High Quality-1-2-3-4-5

This is unipolar rating scale.


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2.3 Semantic Differential Scale

It is developed by Osgood, Suci and Tannenbaum, can be used to measure attitudes from the meaning (semantic = meaning or psychological significance) which people give to a word or concept that is related to an attitude object.This instrument consists of a series of bipolar adjectives such as fair – unfair, pleasant – unpleasant, good – bad, clean-dirty, valuable-worthless etc. Each pair constitutes a continnum of seven points, the end point begin the opposites of the adjetive pairs and the mid point being neutral position.


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In this scale, the thing being evaluated is presented once at the top of the page. The scale consist of pairs of adjectives located at the two endpoints of a standard response format.

I think Al Gore is

Smart

Bad

Beautiful

Stupid

Good

Ugly


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When Semantic Differential Scale is used to develop an image profile, it provides a good basis for comparing images of two or more items.The big advantage of this scale is its simplicity, while producing results compared with those of the more complex scaling methods.The method is easy and fast to administer, but it is also sensitive to small differences in attitude, highly versatile, reliable and generally valid.


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2.4 Multi dimensional scalingIt consists of a group of analytical techniques which are used to study consumer attitudes related to perceptions and preferences. It is used to study the major attributes of a given class of products perceived by the consumers in considering the product and by which they compare the different ranks. To study which brand competes most directly with each other. To find out whether the consumers would like a new brand with a combination of characteristics not found in market. What would be the consumers ideal combination of product attributes. What sales and advertising messages are compatible with consumers brand perceptions.


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SAMPLING


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“The selection of some part of an aggregate or totality on the basis of which a judgement or inference about the aggregate or totality is made.”

it is the process of obtaining information about an entire population by examining only a part of it.


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In most of the research work and surveys, the usual approach happens to be to make generalisations or to draw inferences based on samples about the parameters of population from which the samples are taken.

The researcher quite often selects only a few items from the universe for his study purposes.

All this is done on the assumption that the sample data will enable him to estimate the population parameters.


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The items so selected constitute what is technically called a sample, their selection process or technique is called sample design and the survey conducted on the basis of sample is described as sample survey. Sample should be truly representative of population characteristics without any bias so that it may result in valid and reliable conclusions.


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NEED FOR SAMPLINGSampling is used in practice for a variety of reasons such as:1.Sampling can save time and money. A sample study is usually less expensive than a census study and produces results at a relatively faster speed.

2. Sampling may enable more accurate measurements for a sample study is generally conducted by trained and experienced investigators.

3. Sampling remains the only way when population contains infinitely many members.


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4. Sampling remains the only choice when a test involves the destruction of the item under study.

5. Sampling usually enables to estimate the sampling errors and, thus, assists in obtaining information concerning some characteristic of the population.


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STEPS IN

SAMPLE DESIGN


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POPULATION


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Population is any complete group.For example. People

Sales territoriesStores

Census is investigation of all individual elements that make up a population.For example, in the study of agriculture yields, all the cultivated farms will be population.

In the study of socio-economic conditions of a particular village, all families or house in the village will be the population.


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According to the size of population there are two types of population:

Finite population:When number of units in the population is finite, it

is called finite population. For example, the population of student enrolled in a year in a college is a finite population as the number of student is finite number.

Infinite population:When the number of units in a population is very

large, that is practically infinite population. For example, the number of units produced of a product in a continuous process is an infinite population


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The target population is the collection of elements or objects that posses the information sought by the researcher and about which inferences are to be made.

It is a relevant population and operationally defined.The target population should be defined in terms of elements, sampling units, extent and time


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Sampling Frame


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Sampling Frame known as ‘Source list’ from which sample is to be drawn.

It contains the names of all items of a universe (in case of finite universe only).

If source list is not available, researcher has to prepare it.

Such a list should be comprehensive, correct, reliable and appropriate.

It is extremely important for the source list to be as representative of the population as possible.


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Sample is subset of a larger population.

Sample unit is an element, or a unit containing the element, that is available for selection at some stage of the sampling process. There are three types of sampling units:

Primary Sampling Units (PSU)

Secondary Sampling Units

Tertiary Sampling Units


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Sampling element is the object about which or from which the information is desired, e.g. the respondent.

Extent refers to the geographical boundaries.

Time is the time period under consideration.

Sampling is always subject to error.

Sampling error is the difference between the sample results and the result of a census conducted using identical procedures.

It is the statistical fluctuations due to chance variations.


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Errors associated with sampling are as follows.

Sampling frame errorsRandom sampling errorNon response error


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SAMPLING METHODS \ TECHNIQUES


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PROBABILITY TECHNIQUES


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Probability sampling techniqueHere, the sample is selected in such a way that each unit within the population has chance of being selected.Most estimates tend to cluster around the true population or universe mean.When plotted on a graph, these means form what is called the normal or bell curve.

There are four main types of probability or random sampling .

Random samplingStratified samplingSystematic samplingCluster sampling


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Simple random sampling

Here, each element in the population has a known and equal probability of selection. Each possible sample of a given size (n) has a known and equal probability of being the sample actually selected.This implies that every element is selected independently of every other element.

A sampling procedure that assures that each element in the population has an chance of being selected is referred to as simple random sampling.


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Let us assume that you had a school with a 1000 students, divided equally into boys and girls, and you wanted to select 100 of them for further study.You might pull up all their names in a drum and pull 100 names out.Here each person have equal chance of being selected, we can also easily calculate the probability of a given person being chosen, since we know sample size(n) and the population (N) and it becomes a simple matter of division:

n/N*100 OR(100/1000)*100 = 10%

This means that every student in the school as a 10% chance of being selected using this method.


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Many statistics books include a table of random numbers, which are predetermined set of random numbers.It is possible to start at any point on the table and move in any direction to choose the numbers required for sample size.

However, technology has given us a number of other alternatives.


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Procedure for simple random sampling

1.Select a suitable sampling frame.2.Each element is assigned a number from 1 to N (population size)3.Generate n (sample size)4.The numbers generated denote the elements that should be include in the sample.


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Advantages:

1.No partiality is done.2.Units have the characteristics of universe, hence units are representative.3.Simplicity of methods makes no possibility of error.4.It saves money, time and labor.

Disadvantages:1.The selector has no control over the selection of units.2.Researcher may not prepare the whole field when the universal is vast.3.No homogeneous not possible4.No question of alternatives, no replacement of selected units


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Stratified SamplingIt is a two step process in which the population is partitioned into subpopulation, or strata. The strata should be mutually exclusive and collectively exhaustive in that every population element should be assigned to one and only one stratum and no population elements should be omitted.Next, elements are selected from each stratum by a random procedure.A major objective of stratified sampling is to increase precision without increasing cost.


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Strata 1 Strata 2 Strata 3


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The elements within a stratum should be as homogeneous as possible, but the elements in the different strata should be as heterogeneous as possible.

The stratification variables should also be closely related to the characteristic of interest.

Finally, the variables should decrease the cost of the stratification process by being easy to measure and apply.There are two types of stratified sampling methods.

1. proportioned stratified sampling2. disproportioned stratified sampling


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In proportionate stratified sampling, the size of the sample drawn from each stratum is proportionate to the relative size of that stratum in the total population.

In disproportionate stratified sampling, the size of the sample fro each stratum is proportionate to the relative size of that stratum and to the standard deviation of the distribution of the characteristic of interest among all the elements in that stratum.

In this random sampling technique, the whole population is first into mutually exclusive subgroups or strata and then units are selected randomly for each stratum.


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The segments are based on some predetermined criteria such as geographic location, size or demographic characteristic.It is important that the seg/ments be as heterogeneous as possible.


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Procedure for stratified sampling1. Select a suitable frame.2. Select the stratification variable(s) and the number of

strata, H.3. Divide the entire population in to H strata. Based on

the classification variable, each element of the population is assigned to one of the H strata.

4. In each stratum, number the elements form 1 to Nh.(the population size of h)

5. Determine the sample size of each stratum, nh based on proportionate or disproportionate stratified sampling.

6. In each stratum, select a simple random simple size nh.


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Advantages

•Neither group or class of importance is totally neglected as units of each are represented in the sample.•If different classes are divided properly, selection of few units represents the whole group.•On the classification of regional basis, units are not in contact easily. This leads to economy of time and money.•There is a facility in substitution of units. If someone is not contacted easily, the other person of the same class can be substituted for him. Such inclusion result will not show any contradicting.


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Disadvantages•The sample does not become representative if selected sample has more or less units of a class.

•If the size of different group are different, no equal proportional quality can be viewed.

•Non-proportional selection leads to more emphasis in the end. During such time researcher can be biased, hence samples will not representative.

•If group is not expressed properly, the difficulty is seen about the unit to be kept under which group or class.


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Systematic SamplingIf a systematic pattern is introduced into random sampling, it is referred to as “systematic sampling”.In some instances, the most practical way of sampling is to select every ith item on a list. Sampling of this type is known as systematic sampling. An element of randomness is introduced into this kind of sampling by using random numbers to pick up the unit with which to start. For instance, if a 4 per cent sample is desired, the first item would be selected randomly from the first twenty-five and thereafter every 25th item would automatically be included in the sample.


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System Every 3rd house


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Thus, in systematic sampling only the first unit is selected randomly and the remaining units of the sample are selected at fixed intervals. Although a systematic sample is not a random sample in the strict sense of the term, but it is often considered reasonable to treat systematic sample as if it were a random sample.Systematic sampling has certain plus points. It can be taken as an improvement over a simple random sample in as much as the systematic sample is spread more evenly over the entire population.It is an easier and less costlier method of sampling and can be conveniently used even in case of large populations. But there are certain dangers too in using this type of sampling. If there is a hidden periodicity in the population, systematic sampling will prove to be an inefficient method of sampling.


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•Procedure for systematic sampling:1.Select suitable sampling frame.2.Each element is assigned a number 1 to N(population size)3.Determine the sampling interval i.

i = N/n. If I is a fraction, round to the nearest integer.

4.Select a random number, r, between 1 to i , as explained in simple random sampling.For example, there are 10000 elements in the population and a sample of 100 is desired. In this case the sampling interval, I, is 10. A random number between 1 and 10 is selected. If, for example, this number is 9, the sample consists of elements 9,19,29,39,49 and so on..


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Advantages It is more straight-forward than random samplingA grid doesn’t necessarily have to be used, sampling just has to be at uniform intervalsA good coverage of the study area can be more easily achieved than using random sampling

Disadvantages It is more biased, as all members or points have equal chance of being selected.It may therefore lead to over or under representation of a particular pattern.


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Cluster SamplingIf the total area of interest happens to be a big one, a convenient way in which a sample can be taken is to divide the area into a number of smaller non-overlapping areas and then to randomly select a number of these smaller areas (usually called clusters), with the ultimate sample consisting of all (or samples of) units in these small areas or clusters.Thus in cluster sampling the total population is divided into a number of relatively small subdivisions which are themselves clusters of still smaller units and then some of these clusters are randomly selected for inclusion in the overall sample.


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Suppose we want to estimate the proportion of machine parts in an inventory which are defective. Also assume that there are 20000 machine parts in the inventory at a given point of time, stored in 400 cases of 50 each. Now using a cluster sampling, we would consider the 400 cases as clusters and randomly select ‘n’ cases and examine all the machine parts in each randomly selected case.


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Cluster sampling, no doubt, reduces cost by concentrating surveys in selected clusters. But certainly it is less precise than random sampling. There is also not as much information in ‘n’ observations within a cluster as there happens to be in ‘n’ randomly drawn observations. Cluster sampling is used only because of the economic advantage it possesses; estimates based on cluster samples are usually more reliable per unit cost.


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Multi-stage sampling is a further development of the principle of cluster sampling. Suppose we want to investigate the working efficiency of nationalised banks in India and we want to take a sample of few banks for this purpose. The first stage is to select large primary sampling unit such as states in a country. Then we may select certain districts and interview all banks in the chosen districts. This would represent a two-stage sampling design with the ultimate sampling units being clusters of districts.


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If instead of taking a census of all banks within the selected districts, we select certain towns and interview all banks in the chosen towns. This would represent a three-stage sampling design. If instead of taking a census of all banks within the selected towns, we randomly sample banks from each selected town, then it is a case of using a four-stage sampling plan. If we select randomly at all stages, we will have what is known as ‘multi-stage random sampling design’.


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Ordinarily multi-stage sampling is applied in big inquires extending to a considerable large geographical area, say, the entire country. There are two advantages of this sampling design viz.,(a)It is easier to administer than most single stage designs mainly because of the fact that sampling frame under multi-stage sampling is developed in partial units. (b)A large number of units can be sampled for a given cost under multistage sampling because of sequential clustering, whereas this is not possible in most of the simple designs.


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Advantages It is a cheap, quick and easy. Instead of sampling an entire country when using simple random sampling, the researcher can allocate his limited resources to the few randomly selected cluster or area when using cluster samples.

Related to the first advantage, the researcher can also increase his sample size with this technique. Considering that the researcher will only have to take the sample from a number of areas or clusters, he can then select more subjects since they are more accessible.


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Disadvantages It is the least representative of the population.

Here, the degree of error is high.


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NON PROBABILITY TECHNIQUES


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Here, the sampling is selected in such a way that the chance of being selected of each unit within the population of universe is unknown.Indeed, the selection of the subjects is arbitrary, the researcher relies on his\her experience and judgment.As a result there are no statistical techniques that allow for the measurement of sampling error, and therefore it is not appropriate to project the sample characteristics to the population.In spite of this significant shortcoming, its is very popular in hospitality and tourism research.Almost all qualitative research methods rely on non probability sampling techniques.


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There are four main types.

Convenience Sampling

Quota Sampling

Judgment Sampling

Snowball sampling


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Convenience Sampling It attempts to obtain a sample of convenient elements.

Often, respondents are selects because they happen to be in the right place at the tight time.

Examples are.. Use of students, and members of social

organizations Mall intercept interviews without qualifying the

respondents People on the street interviews


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Here, the selection of units from the population is based in easy availability and\or accessibility.

The major disadvantage of this technique is that we have no idea how representative the information collected about the sample is to the population as a whole.

But the information could still provide some fairly significant insights, and be a good source of data in exploratory research.


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Judgement sampling It is a form of convenience sampling in which the population

elements are selected based on judgement of the researcher.Examples.. Test marks Expert witness used in court

Here, the researcher or some other expert uses his\her judgement in selecting the units from the population for study based on the population’s parameters.

It might be the most appropriate if the population to be studied is difficult to locate or if some members are thought to be better then others to interview. This determination is often made on the advice and with the assistance of the client.


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Snowball Sampling Here, an initial group of respondent is selected, usually

at random. After being interviewed, these respondents are asked to

identify others who belong to the target population of interest.

Subsequent respondents are selected based on the referrals.

A variety of procedures are there for snowball sampling. Initial respondents are selected by probability methods. Additional respondents are obtained from information provided by the initial respondents.

It is used when the members of the population are those who are less known


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Quota sampling It may be viewed as two stage judgmental sampling. The first stage consists of developing control

categories, or quotas, of population elements. In the second stage, sample elements are selected

based on convenience or judgement. In quota sampling, the population is first segmented

into mutually exclusive sub-groups, just as in stratified sampling.

Then judgement is used to select the subjects or units from each segment based on a specified proportion.

In this second step which makes the technique one of non-probability sampling.


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Advantages of quota sampling are the speed with which information can be collected, the lower cost of doing so and the convenience it represents.


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SAMPLE DESIGN


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It is a definite plane for obtaining a sample from a given population is called ‘ sample design’.

It is a technique of selecting items for the sample.

It lay down the number of items to be included in the sample.

It should be reliable and appropriate for the research study of the researcher.

It is determined before data are collected.

While developing a sample design, the following points must be taken into consideration.


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Type of universe: In developing any sample design, the first step is to define the universe i.e the set of objects to be studied. The universe may be finite or infinite.

Sample Frame: It contains the names of all items of a universe. It should be representative of all population and should be appropriate, reliable, correct and comprehensive.

Sample Unit: It is to be decided before selecting the sample. Sampling units may be geographical, constructional, social and individual.

Sample Size: It refers to he number of items to be selected from a universe to form a sample. Sample size should not be very large or too small.


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Parameters of interest: While determining a sample design, the specific population parameters, which of interest, must be taken into account by the research.

Budgetary constraints: The size as well as the type of sample depends upon the cost consideration.

Sampling procedure: Finally the researcher must decide about techniques to be used in selecting the items for the sample i.e. he must decide the type of sample. This technique stands for the sample design itself. He should select the sample design in such a way that for a given sample size and for a given cost, the sample design has a smaller sampling error.


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Sample size characteristics: It should be such, so that systematic bias can be

controlled in better way. It should result in a truly representative sample. It should ne viable in the context of funds available for

the research study. It should be such that the result of sample study can be

applied, in general, for the universe with a reasonable level of confidence.

It should result small sampling error.


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Important factors in determining appropriate sample design are

Degree of accuracy Resources Time Advanced knowledge of the population National versus local Need for statistical analysis


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SAMPLE SIZE


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The sample size if dependent on the appropriate sample design.

It is frequently a matter as to the size of a sample drawn, and the notation is that if the sample size is “not large”, the sampling results are likely to be inaccurate.

The sample size decision must be made on a case by case basis, considering the variety of goals to be achieved by a particular study and taking into account numerous other aspects of the research design.

The size of a sample depends upon the basic characteristics of the population.

If there is complete homogeneity, a sample size of 1 would be sufficient, while a larger sample is obviously required where there is a heterogeneity.


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One way of dealing with heterogeneity is to break the population into sub groups or strata, which displays homogeneity among the sample units. This is know as stratified (random) sampling, Which is statistically more efficient than simple random sampling.

Here we need sample frame such as a list of all students in a college from which to drawn a sample.

Where we are sampling from a very much larger population, as in say, a city, we require a complete list of all the households in the city from which to randomly select a given sample, subject to certain characteristics such as age, income etc.., which might be set as “quotas”.


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It is also necessary to ensure that the smallest sub-group or stratum should contain “sufficient” sampling units so that accurate and reliable estimates can be found of the population stratum. Sample size is a balance act between precision and cost survey. Daniel and Terrel have suggested a formula for calculation of ample size when we have a fixed budget for a sample study. The budget represents the total cost C for a sampling study, which can be broken into two parts

the fixed cost CfThe variable cost per sampling unit Cu


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The sample size n is given by the formula:

n = C – Cf / Cu

Let us assume that the budget available for a sample survey is Rs 8,00,000; the cost per questionnaire charged by the Market Research is Rs. 150, and the fixed cost associate with the study are Rs. 1,50,000. Then we have

n = 8,00,000 – 1,50,000 / 150From which we find that the required sample sizen = 4,333


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Important qualitative factors in determining the sample size are:

The important of the decision The nature of the research The number of variables Confidence level Administrative concerns Sample sizes used in similar studies Cost constraints Resource constraints


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SAMPLING PLAN AND

SAMPLE SELECTION


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Sampling plan is a detailed outline of which measurements will be taken at what times, on which element, in what manner, and by whom.

Sampling plans should be designed in such a way that the resulting data will contain a representative sample of the parameters of interest and allow for all questions, as stated in the goals, to be answered.


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The step involved in developing a sampling plan are:

Identify the parameters to be measured, the range of possible values, and the required resolution

Design a sampling scheme that details how and when samples will be taken

Select sample sizes Design data storage formats Assign roles and responsibilities


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Sampling plan must include target population, sampling frame, sampling element, sampling unit, sampling methodology to be adopted, method adopted for determining sample size and procedure for actual sample is selection in order to minimize sample error.

Once the sampling plan has been developed it can be verified and then passed on to the responsible parties for execution.


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Sample Selection It is very important to actually select the sample as

per sampling plan. Otherwise it results in sample selection error. Sample selection error is an administrative error

caused by improper selection of a sample during a survey, resulting in accidental bias in the results.

Sample Selection Error occurs in experiments when a bias is introduced into the way in which experimental units are assigned to groups.

Scaling and Measurement techniques

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