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Sampling Design and Scaling Technique : 

Sampling Design and Scaling Technique .

Census : 

Census A population is the total collection of elements about which we wish to make some inference. A census is a count of all the elements of the population Listing of all the population elements is called a sample frame

When : 

When Feasible when population is small Necessary when the elements are quite different from each other

Why Sample ? : 

Why Sample ? Lower Cost Greater Accuracy of Results Greater Speed of Data Collection Availability of Population elements

How to choose a sample ? : 

How to choose a sample ? Determine the target population(research Q) Determine the sampling frame (telephone directories, automobile registrations, customer lists ...) Select a sampling procedure

A good sample will be… : 

A good sample will be… Accurate Precision ( low sampling error )

. : 

.

Simple Random Sampling : 

Simple Random Sampling Each population element has a known and equal chance of selection Probability of Selection = Sample Size Population Size

Random No. Table (page 679) : 

Random No. Table (page 679)

Systematic Sampling : 

Systematic Sampling Every kth element in the population is sampled, beginning with a random start of an element in the range of 1 to k. k=skip interval = population size sample size

Stratified Sampling : 

Stratified Sampling Population is segregated into various subpopulations or strata Simple random sample taken from each strata Improves statistical efficiency Homogeneous within each strata Heterogeneous between different strata Proportionate stratified sampling Disproportionate Stratified Sampling

Proportionate Stratified Sampling : 

Proportionate Stratified Sampling Sample size drawn from the stratum is proportionate to the stratum’s proportion in the population Otherwise – disproportionate stratified sampling

Example : 

Example

Cluster Sampling / Area Sampling : 

Cluster Sampling / Area Sampling Population subdivided into groups of elements Each group called a cluster Each cluster is heterogeneous Homogeneity between clusters Choose several clusters and study in detail High economic efficiency

Sequential / Double / Multiphase Sampling : 

Sequential / Double / Multiphase Sampling Select a sample – collect information(telephone/ net/ mailers ) Select a subsample Conduct detailed analysis

Non Probability Sampling : 

Non Probability Sampling

Convenience : 

Convenience Easy Inexpensive Convenient Useful to test ideas ( exploratory research ) Least reliable

Purposive Sampling : 

Purposive Sampling

Judgement Sampling : 

Judgement Sampling Researcher selects sample members on some criterion . For eg. : Syllabi revision – faculty/ industry experts Sample size is small biased

Quota Sampling : 

Quota Sampling Gender – male, female Class – Socio Economic Classification – To improve representativeness

Example : 

Example

Snowball Sampling : 

Snowball Sampling Respondents are identified through referral networks Drug cultures, deep sea divers, teenage gang activities, community relations

Criteria for selecting a sampling procedure : 

Criteria for selecting a sampling procedure Ease Speed Accuracy Cost

Size of the Sample : 

Size of the Sample Ad Hoc methods No. of groups / subgroups Cost Variability of the population

Size of the sample - statistical method : 

Size of the sample - statistical method n=σ²Z² D²

A researcher wants to estimate the monthly household expense on deptt store shopping so that the estimate will be within + Rs.5 of the true : 

A researcher wants to estimate the monthly household expense on deptt store shopping so that the estimate will be within + Rs.5 of the true population value . What should be the size of the sample ? SD from previous research = Rs 55 D = + Rs.5 CL = 95 %, SD = 55 n=σ²Z² = 55 * 55 * 2*2 = 484 = 490 D² 5 * 5 Where Z = 1.96 = 2(approx)

Measurement And Scaling Techniques : 

Measurement And Scaling Techniques

Measurement in research : 

Measurement in research Select observable events Develop a set of mapping rules Apply to each observation of that event

Example : ratio of male to female attendees in an auto show : 

Example : ratio of male to female attendees in an auto show M : male F : female

What is your opinion on the styling of the Nano ? : 

What is your opinion on the styling of the Nano ? Excellent 5 4 3 2 1 Poor

Characteristics : 

Characteristics Classification : numbers are used to group or sort responses Order : one number is < , > or = another number. Distance : Differences between numbers are ordered Origin : is zero

Measurement Scales : 

Measurement Scales Nominal Ordinal Interval Ratio

Nominal Scale : 

Nominal Scale Numbers used as labels eg : hindu = 1, muslim = 2; christain = 3 …. Mutually exclusive and collectively exhaustive Demograhic data Mode - the most frequently occurring value Chi square test

Ordinal Scale : 

Ordinal Scale Indication of order a > b > c superior to, inferior to, happier, sadder etc Median Non parametric tests, t test, ANOVA

Interval Scale : 

Interval Scale Equality of interval In a ranking Q, favorable 7 6 5 4 3 2 1 unfavorable distance – equal but rank 6 = 2( rank 3) Median, mean Correlation , t test, F test Likert, Thurstone, Stapel

Ratio Scale : 

Ratio Scale Comparisons of absolute magnitude INR 80,000 = 2( INR 40,000) All statistical measures If salesman A sells 30 units per day and salesman B sells 60 units per day, the Output of B = 2 ( output of A)

Attitude : 

Attitude A way of conceptualizing the intangible Cognitive / knowledge component Affective / Liking Component Intention / Action Component

Attitude Scaling : 

Attitude Scaling The process of assessing an attitudinal disposition using a number that represents a persons score ranging from an extremely favorable to extremely unfavorable disposition. It could measure awareness, feelings, intentions…

Measurement Scaling : 

Measurement Scaling Rating Ranking Categorization Sorting

Rating Scales : 

Rating Scales

Simple category Scale; Nominal : 

Simple category Scale; Nominal I plan to purchase a laptop in the next 10 months ____ Yes ____ No

Multiple choice- single response; nominal : 

Multiple choice- single response; nominal What newspaper do you read most often for financial news ? ____ Business News ____ Times Of India ____ Economic Times ____ Others

Multiple choice- multiple response; nominal : 

Multiple choice- multiple response; nominal What magazines do you read ? ____ India Today ____ Outlook ____ Filmfare ____ Business Today ____ Others

Thurstone Differential : 

Thurstone Differential Between 100 – 200 statements are compiled relating to the attitude to be measured Judges (20 +) sort them into 11 piles First pile is the most unfavorable Neutral in pile 6 Most favorable in pile 11 Ratings for each statement are taken Statements with widely scattered ratings are eliminated

. : 

. Median is computed Dispersion is measured Two statements from each pile are chosen Respondents are asked to indicate their agreement or disagreement(scaled) with each of these statements Mean / median is computed

Example: consumer attitudes towards newspaper ads (1 – favorable, 9- unfavorable) : 

Example: consumer attitudes towards newspaper ads (1 – favorable, 9- unfavorable) All newspaper ads should be banned by law (7.2) Reading newspaper ads is a waste of time(8.6) Newspaper ads are monotonous(2.6) Most of the newspaper ads are bad(7.1) Newspaper ads do not interfere too much with the reading of news(4.0)

. : 

. I have no opinion for or against the newspaper ads(1.8) I like newspaper ads at times(3.0) Most newspaper ads are fairly interesting(2.0) I like to buy products advertised in newspapers whenever possible(6.2) Most newspaper ads help people select the best product available(5.0) Newspaper ads are more fun to read than the regular news(4.3)

. : 

. Suppose Respondent A agrees with statement 3,6,7. average score = 2.47 Suppose Respondent B agrees with statement 3,4,5. average score = 4.2 Attitude A > Attitude B Not widely used

Likert Scale Summated Rating ; Interval : 

Likert Scale Summated Rating ; Interval Amity, Bangalore is helping me build a great future Strongly Agree Neither Disagree Strongly Agree Agree nor Disagree disagree 5 4 3 2 1 Also have 7 and 9 point rating system

Semantic Differential Scale : ordinal/ Interval : 

Semantic Differential Scale : ordinal/ Interval 5 / 7 points Example: feedback of a new snack Low price --- ---- ---- ---- ---- ---- ---- High Price Tangy --- ---- ---- ---- ---- ---- ---- Smooth Bitter --- ---- ---- ---- ---- ---- ---- Not Bitter Attractive packaging --- ---- ---- ---- ---- ---- ---- Unattractive packaging

Numerical Scale : Ordinal / Interval : 

Numerical Scale : Ordinal / Interval Extremely Extremely Favorable 5 4 3 2 1 Unfavorable Students Behaviour In Class _________ Students cooperation in teams _________ Students Interest in Subject _________

Numerical / Multiple Rating List Scales: Interval : 

Numerical / Multiple Rating List Scales: Interval “please indicate how important or unimportant each service characteristic is” IMP UNIMP Speed 7 6 5 4 3 2 1 Reliability 7 6 5 4 3 2 1 Technicians 7 6 5 4 3 2 1 Location of 7 6 5 4 3 2 1 Service Station

Constant Sum Scale : Ratio : 

Constant Sum Scale : Ratio You have 100 points to distribute among the following characteristics of pizza Hut. Indicate the relative importance of each attribute : ______ Food Quality ______ Atmosphere ______ Ambience ______ Value for Money 100 TOTAL

Stapel Scale : Ordinal / Interval : 

Stapel Scale : Ordinal / Interval +5 +5 +5 +4 +4 +4 +3 +3 +3 +2 +2 +2 +1 +1 +1 Technology value for after sales Leader money service -1 - 1 - 1 -2 - 2 -2 -3 - 3 -3 -4 - 4 -4 -5 - 5 -5

Graphic Rating Scale : 

Graphic Rating Scale Do you enjoy coming to work ? Place an X along the line which best reflects your feelings Yes ________________________________No Also used for children( visuals/ cartoons)

Ranking Scales : 

Ranking Scales .

Paired Comparison Scale : 

Paired Comparison Scale For each pair of two-seat sports cars listed, place a check beside the one you would most prefer if you had to choose between the two ____ BMW ____ Chevrolet ____ Porsche ____ Porsche ____ BMW ____ Chevrolet

Forced Ranking Scale: Ordinal : 

Forced Ranking Scale: Ordinal Rank these institutes in your order of preference on a scale of 1-5 where 1 is the best ____ Amity, Bangalore ____ Allianz, Bangalore ____ Christ College, Bangalore ____ Amity, NOIDA ____ NMIMS, Bangalore

Comparative Scale: Ordinal : 

Comparative Scale: Ordinal Compared to your previous bike, the new one is: Superior about the same inferior ____ ____ _____ ____ _____

Sorting : 

Sorting Q Sorts- conceptual representation of sorters attitude towards the attitude

Cards(60 – 120) with various responses are created : 

Cards(60 – 120) with various responses are created Sorting of a deck of cards(60 – 120) into piles (7-11)along a continuum by the respondent Left - most favorable Right – least favorable Centre – neutral

Example : 

Example Divide the 100 items on the cards into 10 groups so that they will describe your view of an ideal cake mix. Those items that most closely describe your ideal cake mix should be placed in the groups to the left and those that are least liked be placed in the groups to the right.

. : 

. Most like Least like My ideal My ideal Cake mix Cake mix _______________________________________ 4 8 12 14 20 14 12 8 4 2 Cards per group

Cumulative Scale / Scalogram Analysis : 

Cumulative Scale / Scalogram Analysis Total scores have the same meaning Given a persons total score, it is possible to estimate which items were answered positively or negatively Useful for assessing social distance , organizational hierarchies, and evolutionary product stages Not widely used

Example : 

Example We are surveying a opinions on a new style of running shoe. Preference scale is of 4 items : Reebok is good looking I will insist on Reebok next time as it is great looking The appearance of Reebok is acceptable I prefer Reebok to others

. : 

.

MULTI DIMENSIONAL SCALING : 

MULTI DIMENSIONAL SCALING Disaggregative scaling method – single number cannot describe complex nature of attitudes

Example – cigarette brands : 

Example – cigarette brands India Kings Wills navycut Wills gold flake Four Square Red and White Classic Capstan Gold leaf Charminar Chinar 555

. : 

. Wills gold flake is closest to the ideal point Can measure distances between different brands

Slide 70: 

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