WEEK4MEASUREMENT, SCALING

QUESTIONNAIRE DESIGN AND SAMPLING

By Dr. Muhammad Ramzanmramzaninfo@gmail.com,

03004487844

Edited by Ahsan Khan Ecoahsankhaneco@yahoo.com

03008046243

Scale

Series of items arranged according to value for the purpose of quantification

A continuous spectrum

7 38

Primary Scales of Measurement

ScaleNominal Numbers

Assigned to Runners

Ordinal Rank Orderof Winners

Interval PerformanceRating on a

0 to 10 Scale

Ratio Time to Finish, in

Seconds

Thirdplace

Secondplace

Firstplace

Finish

Finish

8.2 9.1 9.6

15.2 14.1 13.4

Nominal Scale

The numbers serve only as labels or tags for identifying and classifying objects.

When used for identification, there is a strict one-to-one correspondence between the numbers and the objects.

The numbers do not reflect the amount of the characteristic possessed by the objects.

The only permissible operation on the numbers in a nominal scale is counting.

Social security number, hockey players number. Imn marketing research respondents, brands, attributes, stores and other objects

Ordinal Scale

A ranking scale in which numbers are assigned to objects to indicate the relative extent to which the objects possess some characteristic.

Can determine whether an object has more or less of a characteristic than some other object, but not how much more or less.

Any series of numbers can be assigned that preserves the ordered relationships between the objects. So relative position of objects not the magnitude of difference between the objects.

In addition to the counting operation allowable for nominal scale data, ordinal scales permit the use of statistics based on percentile, quartile, median.

Possess description and order, not distance or origin

Interval Scale

Numerically equal distances on the scale represent equal values in the characteristic being measured.

It permits comparison of the differences between objects.

The difference between 1 & 2 is same as between 2 & 3

The location of the zero point is not fixed. Both the zero point and the units of measurement are arbitrary.

Everyday temperature scale. Attitudinal data obtained on rating scales.

Do not possess origin characteristics (zero and exact measurement)

Ratio Scale

The highest scale that allows to identify objects, rank order of objects, and compare intervals or differences. It is also meaningful to compute ratios of scale values

Possesses all the properties of the nominal, ordinal, and interval scales. It has an absolute zero point.

Height, weight, age, money. Sales, costs, market share and number of customers are variables measured on a ratio scale

All statistical techniques can be applied to ratio data.

Illustration of Primary Scales of Measurement

Nominal Ordinal RatioScale Scale Scale

Preference $ spent last No. Store Rankings 3 months

1. Lord & Taylor2. Macy’s3. Kmart4. Rich’s5. J.C. Penney 6. Neiman Marcus 7. Target 8. Saks Fifth Avenue 9. Sears 10.Wal-Mart

IntervalScale Preference

Ratings

1-7 11-17

7 79 5 15 02 25 7 17 2008 82 4 14 03 30 6 16 1001 10 7 17 2505 53 5 15 359 95 4 14 06 61 5 15 1004 45 6 16 010 115 2 12 10

Primary Scales of Measurement

Scale Basic Characteristics

Common Examples

Marketing Examples

Nominal Numbers identify & classify objects

Social Security nos., numbering of football players

Brand nos., store types

Percentages, mode

Chi-square, binomial test

Ordinal Nos. indicate the relative positions of objects but not the magnitude of differences between them

Quality rankings, rankings of teams in a tournament

Preference rankings, market position, social class

Percentile, median

Rank-order correlation, Friedman ANOVA

Ratio Zero point is fixed, ratios of scale values can be compared

Length, weight Age, sales, income, costs

Geometric mean, harmonic mean

Coefficient of variation

Permissible Statistics Descriptive Inferential

Interval Differences between objects

Temperature (Fahrenheit)

Attitudes, opinions, index

Range, mean, standard

Product-moment

Scale Evaluation

Discriminant NomologicalConvergent

Test/ Retest

Alternative Forms

Internal Consistency

Content Criterion Construct

GeneralizabilityReliability Validity

Scale Evaluation

Reliability

Reliability can be defined as the extent to which measures are free from random error, the measure is perfectly reliable.

In test-retest reliability, respondents are administered identical sets of scale items at two different times and the degree of similarity between the two measurements is determined.

In alternative-forms reliability, two equivalent forms of the scale are constructed and the same respondents are measured at two different times, with a different form being used each time.

Reliability

Internal consistency reliability determines the extent to which different parts of a summated scale are consistent in what they indicate about the characteristic being measured.

In split-half reliability, the items on the scale are divided into two halves and the resulting half scores are correlated.

The coefficient alpha, or Cronbach's alpha, is the average of all possible split-half coefficients resulting from different ways of splitting the scale items. This coefficient varies from 0 to 1, and a value of 0.6 or less generally indicates unsatisfactory internal consistency reliability.

Validity

The validity of a scale may be defined as the extent to which differences in observed scale scores reflect true differences among objects on the characteristic being measured, rather than systematic or random error. Perfect validity requires that there be no measurement error.

Content validity is a subjective but systematic evaluation of how well the content of a scale represents the measurement task at hand.

Criterion validity reflects whether a scale performs as expected in relation to other variables selected (criterion variables) as meaningful criteria.

Validity Construct validity addresses the question of what

construct or characteristic the scale is, in fact, measuring. Researcher tries to answer theoretical questions, why the sale works and what deductions can be made concerning the underlying theory. It requires a sound theory of the nature of construct being measures and how it relates to other construct. Construct validity includes convergent, discriminant, and nomological validity. Convergent validity is the extent to which the scale correlates

positively with other measures of the same construct. Discriminant validity is the extent to which a measure does

not correlate with other constructs from which it is supposed to differ.

Nomological validity is the extent to which the scale correlates in theoretically predicted ways with measures of different but related constructs.

Relationship Between Reliability and Validity

If a measure is perfectly valid, it is also perfectly reliable.

If a measure is unreliable, it cannot be perfectly valid.

Furthermore, systematic error may also be present, Thus, unreliability implies invalidity.

If a measure is perfectly reliable, it may or may not be perfectly valid, because systematic error may still be present.

Reliability is a necessary, but not sufficient, condition for validity.

A Good Questionnaire Appears As easy to compose as a good poem But, it is usually the result of long,

painstaking work

The Major Decisions in Questionnaire Design1. What should be asked?2. How should each question be phrased?3. In what sequence should the questions

be arranged?4. What questionnaire layout will best

serve the research objectives?5. How should the questionnaire be

pretested? Does the questionnaire need to be revised?

• Avoid Complexity: use simple, conversational language

• Avoid leading and loaded questions

• Avoid ambiguity: be as specific as possible

• Avoid double-barreled items

• Avoid making assumptions

• Avoid burdensome questions

1. Do you believe that private citizens have the right toown firearms to defend themselves, their families, and property from violent criminal attack?

Yes No Undecided

2. Do you believe that a ban on the private ownershipof firearms would be significantly reduce the number ofmurders and robberies in your community?

Yes No Undecided

1a. How many years have you been playing tennis on a regular basis? Number of years: __________

b. What is your level of play?

Novice . . . . . . . . . . . . . . . -1 Advanced . . . . . . . -4Lower Intermediate . . . . . -2 Expert . . . . . . . . . -5Upper Intermediate . . . . . -3 Teaching Pro . . . . -6

c. In the last 12 months, has your level of play improved, remained the same or decreased?

Improved. . . . . . . . . . . . . . -1 Decreased. . . . . . . -3Remained the same . . . . . -2

2a. Do you belong to a club with tennis facilities? Yes . . . . . . . -1No . . . . . . . -2

b. How many people in your household - including yourself - play tennis?Number who play tennis ___________

3a. Why do you play tennis? (Please “X” all that apply.)

To have fun . . . . . . . . . . -1To stay fit. . . . . . . . . . . . -2To be with friends. . . . . . -3To improve my game . . . -4To compete. . . . . . . . . . . -5To win. . . . . . . . . . . . . . . -6

b. In the past 12 months, have you purchased any tennis instructional books or video tapes? Yes . . . . . . . -1

No . . . . . . . -2

Dear Passenger:

American Airlines is pleased to have you on board today.

To help us provide the best service possible, we need to know more about you and your opinions of our service. If you are over 11 years old, we would appreciate it if you would complete this questionnaire.

Your flight attendant will pick up your completed questionnaire shortly.

Thank you.

1. Please indicate: Flight number ___________ Date_____________

2a. At the city where you boarded this particular plane, did you make a connection from another flight?

Yes, from American . . . . 1Yes, from Other Airline . . 2No . . . . . . . . . . . . . . . . . . 3

b. Did you board this plane at the airport from which it just took off, or were you a through passenger for which that was an intermediate stop?

Boarded here . . . . . . . . . . 1Through passenger. . . . . . 2

3. How would you rate the overall service from American for this flight, all things considered, from your arrival at the airport terminal until now?

Excellent Good Fair PoorOverall Service . . . . . . . . . . 1 2 3 4

4. Please rate each of the following with regard to this flight, if applicable.

Excellent Good Fair Poor

1 2 3 4Courtesy and Treatment from the: Skycap at airport . . . . . . . . . . . . . . Airport Ticket Counter Agent . . . . . Boarding Point (Gate) Agent . . . . . Flight Attendants . . . . . . . . . . . . . .Your Meal or Snack. . . . . . . . . . . . .Beverage Service . . . . . . . . . . . . . .Seat Comfort. . . . . . . . . . . . . . . . . . Carry-On Stowage Space. . . . . . . .Cabin Cleanliness . . . . . . . . . . . . . Video/Stereo Entertainment . . . . . .On-Time Departure . . . . . . . . . . . .

Questionnaire Design

Question sequence Question layout Pretesting is Important

Sampling Terminology- 1 Population: The aggregate of all the

elements sharing some common set of characteristics that comprises the universe for the purpose of the marketing research problem. The population parameters are typically numbers such as customers loyal to a particular brand of toothpaste. The information about the population parameters may be obtained through a census or sample.

Census involves a complete enumeration of the elements of a population

Sampling Terminology-2 Sample is a subgroup of the elements

of the population selected for participation in the study.

Sample characteristics/statistics are used to make inferences about the population parameters. The inferences that link sample characteristics and population parameters are estimation procedures and test of hypotheses

Conditions for Sample vs. Census Use

Conditions Favoring the Use of

Type of Study

Sample Census

1. Budget

Small

Large

2. Time available

Short Long

3. Population size

Large Small

4. Variance in the characteristic

Small Large

5. Cost of sampling errors

Low High

6. Cost of nonsampling errors

High Low

7. Nature of measurement

Destructive Nondestructive

8. Attention to individual cases Yes No

The Sampling Design Process

Define the Population

Determine the Sampling Frame

Select Sampling Technique(s)

Determine the Sample Size

Execute the Sampling Process

Define the Target Population

The target population is the collection of elements or objects that possess the information sought by the researcher and about which inferences are to be made. The target population should be defined in terms of elements, sampling units, extent, and time.

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

A sampling unit is an element, or a unit containing the element, that is available for selection at some stage of the sampling process.

Extent refers to the geographical boundaries. Time is the time period under consideration.

Define the Target Population

Important qualitative factors in determining the sample size

the importance of the decision the nature of the research the number of variables the nature of the analysis sample sizes used in similar studies incidence rates completion rates resource constraints

Sample Sizes Used in Business Research Studies

Type of Study

Minimum Size Typical Range

Problem identification research (e.g. market potential)

500

1,000-2,500

Problem-solving research (e.g. pricing)

200 300-500

Product tests

200 300-500

Test marketing studies

200 300-500

TV, radio, or print advertising (per commercial or ad tested)

150 200-300

Test-market audits

10 stores 10-20 stores

Focus groups

2 groups 4-12 groups

Classification of Sampling Techniques

Sampling Techniques

NonprobabilitySampling Techniques

ProbabilitySampling Techniques

ConvenienceSampling

JudgmentalSampling

QuotaSampling

SnowballSampling

SystematicSampling

StratifiedSampling

ClusterSampling

Other SamplingTechniques

Simple RandomSampling

Nonprobability sampling relies on personal judgment of the researcher rather than chance to select sample elements. The researcher can arbitrary or consciously decide what elements to include in the sample and may yield good estimates of the population characteristics. The estimates obtained are not statistically projectable to the population.

Probability sampling is a procedure in which each element of the population has a fixed probabilistic chance of being selected for the sample. Sampling units are selected by chance. It requires a precise definition of the target population and general specification of the sampling frame. Confidence intervals which contain the true population value with a given level of certainty, can be calculated. This allows researcher to make inferences and projections about the target population, from which sample was drawn.

Nonprobability: Convenience Sampling

Convenience sampling attempts to obtain a sample of convenient elements. Often, respondents are selected because they happen to be in the right place at the right time.

use of students, and members of social organizations

mall intercept interviews without qualifying the respondents

department stores using charge account lists “people on the street” interviews

Judgmental Sampling

Judgmental sampling is a form of convenience sampling in which the population elements are selected based on the judgment of the researcher.

test markets purchase engineers selected in industrial

marketing research bellwether precincts selected in voting

behavior research expert witnesses used in court

Quota SamplingQuota sampling may be viewed as two-stage restricted 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 judgment.

Population Samplecomposition composition

ControlCharacteristic Percentage Percentage NumberSex Male 48 48 480 Female 52 52 520

____ ____ ____100 100 1000

Snowball Sampling

In snowball sampling, an initial group of respondents 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.

Probability: Simple Random Sampling 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.

Systematic Sampling The sample is chosen by selecting a random starting

point and then picking every ith element in succession from the sampling frame.

The sampling interval, i, is determined by dividing the population size N by the sample size n and rounding to the nearest integer.

When the ordering of the elements is related to the characteristic of interest, systematic sampling increases the representativeness of the sample.

If the ordering of the elements produces a cyclical pattern, systematic sampling may decrease the representativeness of the sample. For example, there are 100,000 elements in the population and a sample of 1,000 is desired. In this case the sampling interval, i, is 100. A random number between 1 and 100 is selected. If, for example, this number is 23, the sample consists of elements 23, 123, 223, 323, 423, 523, and so on.

Stratified Sampling

A two-step process in which the population is partitioned into subpopulations, 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, usually SRS.

A major objective of stratified sampling is to increase precision without increasing cost.

Stratified Sampling The elements within a stratum should be as uniform as

possible, but the elements in different strata should be as mixed 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.

In proportionate(balanced) 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 (unequal) stratified sampling, the size of the sample from 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.

Cluster Sampling The target population is first divided into mutually

exclusive and collectively exhaustive subpopulations, or clusters.

Then a random sample of clusters is selected, based on a probability sampling technique such as SRS.

For each selected cluster, either all the elements are included in the sample (one-stage) or a sample of elements is drawn probabilistically (two-stage).

Elements within a cluster should be as heterogeneous (mixed) as possible, but clusters themselves should be as homogeneous (uniform) as possible. Ideally, each cluster should be a small-scale representation of the population.

In probability proportionate to size sampling, the clusters are sampled with probability proportional to size. In the second stage, the probability of selecting a sampling unit in a selected cluster varies inversely with the size of the cluster.

Non probability Sampling Technique Strengths Weaknesses Convenience Least expensive, least time-

consuming, most convenient Selection bias, sample not representative, not recommended for descriptive or causal research

Judgmental Low cost, convenient, not time-consuming

Does not allow generalization, subjective

Quota Sample can be controlled for certain characteristics

Selection bias, no assurance of representativeness

Snowball Can estimate rare characteristics

Time-consuming

Probability Sampling Simple random (SRS)

Easily understood, results projectable

Difficult to construct sampling frame, expensive, lower precision, no assurance of representativeness

Systematic Can increase repre…tiveness, easier to implement than SRS, sampling frame not necessary

Can decrease repre..iveness if there are cyclical patterns

Stratified Includes all important subpopulations, precision

Difficult to select relevant stratification variables, not feasible to stratify on many variables, expensive

Cluster Easy to implement, Cost -effective

Imprecise, Difficult to compute and interpret results

Procedures for Drawing Probability Samples

Simple Random Sampling

1. Select a suitable sampling frame

2. Each element is assigned a number from 1 to N (pop. size)

3. Generate n (sample size) different random numbers between 1 and N

4. The numbers generated denote the elements that should be included in the sample

Procedures for DrawingProbability Samples

Systematic Sampling

1. Select a suitable sampling frame

2. Each element is assigned a number from 1 to N (pop. 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 and i, as explained in simple random sampling

5. The elements with the following numbers will comprise the systematic random sample: r, r+i,r+2i,r+3i,r+4i,...,r+(n-1)i

1. Select a suitable frame

2. Select the stratification variable(s) and the number of strata, H

3. Divide the entire population into 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 from 1 to Nh (the pop. size of stratum h)

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

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

Procedures for DrawingProbability Samples

nh = nh=1

H

Stratified Sampling

Procedures for DrawingProbability Samples Cluster

Sampling

1. Assign a number from 1 to N to each element in the population

2. Divide the population into C clusters of which c will be included in the sample

3. Calculate the sampling interval i, i=N/c (round to nearest integer)

4. Select a random number r between 1 and i, as explained in simple random sampling

5. Identify elements with the following numbers: r,r+i,r+2i,... r+(c-1)i

6. Select the clusters that contain the identified elements

7. Select sampling units within each selected cluster based on SRS or systematic sampling

8. Remove clusters exceeding sampling interval i. Calculate new population size N*, number of clusters to be selected C*= C-1, and new sampling interval i*.

Procedures for Drawing Probability Samples

Repeat the process until each of the remaining clusters has a population less than the sampling interval. If b clusters have been selected with certainty, select the remaining c-b clusters according to steps 1 through 7. The fraction of units to be sampled with certainty is the overall sampling fraction = n/N. Thus, for clusters selected with certainty, we would select ns=(n/N)(N1+N2+...+Nb) units. The units selected from clusters selected under PPS sampling will therefore be n*=n- ns.

Cluster Sampling

Choosing Nonprobability vs. Probability Sampling

Conditions Favoring the Use of

Factors

Nonprobability sampling

Probability sampling

Nature of research

Exploratory

Conclusive

Relative magnitude of sampling and nonsampling errors

Nonsampling errors are larger

Sampling errors are larger

Variability in the population

Homogeneous (low)

Heterogeneous (high)

Statistical considerations

Unfavorable Favorable

Operational considerations Favorable Unfavorable

Improving Response Rates

PriorNotification

MotivatingRespondents

Incentives Questionnaire Designand Administration

Follow-Up OtherFacilitators

Callbacks

Methods of ImprovingResponse Rates

ReducingRefusals

ReducingNot-at-Homes

You are good studentsBy Dr. Muhammad Ramzanmramzaninfo@gmail.com, 03004487844

Edited by Ahsan Khan Ecoahsankhaneco@yahoo.com03008046243