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Unit VIII · Statistics, operations and operations research
9 min readConcept sheetMCQ · classify the method, match and sequence

Data collection, questionnaire design and sampling

Primary data is collected first-hand; secondary data already exists. A good questionnaire avoids leading and double-barrelled questions. Probability sampling gives every unit a known, non-zero chance of selection.

Primary vs secondary dataPrimary: collected fresh for the study (survey, observation, experiment). Secondary: already published or recorded (Census, RBI bulletins, company records)
Questionnaire vs scheduleA questionnaire is filled in by the respondent; a schedule is filled in by the enumerator
Probability methodsSimple random, systematic, stratified, cluster, multistage
Non-probability methodsConvenience, judgement (purposive), quota, snowball

Methods of collecting primary data

MethodHow it worksStrengthLimitation
ObservationThe researcher watches behaviour, e.g. shoppers in a storeRecords what people do, not what they sayCannot capture motives; observer bias
Personal interviewFace-to-face questions, structured or unstructuredDeep answers; can probe and clarifyCostly and slow; interviewer bias
Telephone or online surveyQuestions by phone, email or web formFast and cheap over wide areasLow response; reaches only connected people
Mailed questionnaireThe respondent fills it in and sends it backCheapest; respondents can take their timeLow response rate; needs literate respondents
ScheduleAn enumerator asks the questions and fills in the formWorks with illiterate respondents; high responseNeeds trained enumerators; costly
Focus groupA small group (typically about 6 to 12 people; sources differ) discusses a topic with a moderatorRich ideas for exploratory researchSmall and not representative; a few may dominate
ExperimentChange one variable and measure the effect, e.g. a price testShows cause and effectArtificial settings; costly

Questionnaire vs schedule

QuestionnaireFilled in by the respondent, usually sent by post or online. Cheap and covers a wide area, but response is low and respondents must be literate.
ScheduleFilled in by an enumerator, who asks the questions face to face. Costlier, but response is higher and it works with illiterate respondents, as in the Census.

NET often asks who fills in the form. That one fact separates the two.

Designing a questionnaire

Textbooks such as Malhotra give a sequence like this one.

  1. 1
    Specify the information needed from the research objectives.
  2. 2
    Decide how it will be administered: in person, by telephone, by mail or online.
  3. 3
    Decide the content of each question: is it needed, and can the respondent answer it?
  4. 4★
    Choose the question form: open-ended, or closed (dichotomous, multiple choice, scales).
  5. 5★
    Word each question simply. Avoid leading, loaded, ambiguous and double-barrelled questions.
    'Rate the price and quality' asks two things at once
  6. 6
    Order the questions: easy openers, general before specific (the funnel), sensitive and classification questions last.
  7. 7
    Design the layout, pre-test (pilot) the draft on a small sample, and revise it.

★ one-way, controls the pace

Scales of measurement (Stevens, 1946) and attitude scales

ScaleKey ideaExample or author
NominalLabels or categories only; the mode is the right averageGender, region
OrdinalRank order; median and percentiles allowedRanking five brands
IntervalEqual intervals but no true zero; mean and SD allowedTemperature in °C
RatioEqual intervals and a true zero; all statistics allowedIncome, sales, age
LikertAgree-disagree statements, usually 5 points, summed into a scoreRensis Likert, 1932
Semantic differentialBipolar adjectives at the two ends of a 7-point scaleOsgood, Suci and Tannenbaum, 1957
ThurstoneStatements placed at equal-appearing intervals by judgesL. L. Thurstone
GuttmanCumulative: agreeing with a strong item implies agreeing with milder onesLouis Guttman
StapelUnipolar, −5 to +5 with no zero, around a single adjectiveJan Stapel

The sampling process

The sampling frame is the list from which the sample is drawn, such as a voter list or a customer database.

Sampling techniques

TechniqueTypeHow it worksExample
Simple randomProbabilityEvery unit has an equal chance; lottery or random numbersDrawing 50 roll numbers by lottery
SystematicProbabilityRandom start, then every kth unit, where k = N ÷ nEvery 20th invoice
StratifiedProbabilitySplit into homogeneous strata; draw a random sample from eachStudents by course, with proportional allocation
ClusterProbabilitySplit into groups (often areas); pick whole clusters at randomPicking 10 wards of a city and surveying every home in them
MultistageProbabilitySampling in stages, from larger to smaller unitsState → district → village → household
ConvenienceNon-probabilityWhoever is easiest to reachMall-intercept survey
Judgement (purposive)Non-probabilityThe researcher picks units thought typical or expertInterviewing chosen industry experts
QuotaNon-probabilityFixed numbers per category, filled non-randomly50 men and 50 women, chosen by the interviewer
SnowballNon-probabilityEach respondent refers othersHard-to-reach groups, such as gig workers

Stratified vs cluster sampling

StratifiedGroups are homogeneous within and differ from each other. A random sample is drawn from every stratum. Improves precision.
ClusterGroups should be heterogeneous within, each like a mini-population. Some whole clusters are picked at random. Cuts cost, but is usually less precise.

Worked example: stratified allocation, systematic interval and standard error

Problem

A college has 1,200 students: 600 in BCom, 400 in BBA and 200 in BSc. (a) Allocate a sample of 60 proportionally. (b) Find the systematic sampling interval for 60 from the full list. (c) The SD of students' daily spending is ₹120. Find the standard error of the mean for n = 36.

Working
  1. (a) Each stratum gets n × stratum size ÷ N. BCom = 60 × 600 ÷ 1,200 = 30; BBA = 60 × 400 ÷ 1,200 = 20; BSc = 60 × 200 ÷ 1,200 = 10. Total = 60.
  2. (b) k = N ÷ n = 1,200 ÷ 60 = 20. With a random start of 7, pick 7, 27, 47, … up to 7 + 59 × 20 = 1,187.
  3. (c) SE = σ ÷ √n = 120 ÷ √36 = 120 ÷ 6 = ₹20.
  4. If n rises to 144, SE = 120 ÷ 12 = ₹10: a sample four times as large halves the error.
Answer

30, 20 and 10 students; k = 20; SE = ₹20 (₹10 with n = 144).

Sampling vs non-sampling error

Sampling errorArises because only part of the population is studied. It falls as n rises (SE = σ ÷ √n) and is zero in a census.
Non-sampling errorArises from faulty frames, non-response, wrong answers, interviewer bias or data entry. A bigger sample does not cure it, and it occurs in a census too.
How NET asks this

NET asks you to classify a method (probability or not, primary or secondary), match techniques with descriptions, sequence the sampling process, and spot faulty questions such as double-barrelled or leading ones.

Exam angle

Typical MCQ: “Is quota sampling a probability method?” No. It looks like stratified sampling, but the interviewer, not chance, picks the units within each quota. Trap: equating quota with stratified sampling.

Typical MCQ: “If the sample size is made four times larger, what happens to the standard error of the mean?” It halves, because SE = σ ÷ √n and √4 = 2. Trap: saying it falls to one-fourth.

Typical MCQ: “Who fills in a schedule?” The enumerator, who asks the questions. A questionnaire is filled in by the respondent. Trap: treating the two as the same.

Remember it

Probability sampling: 'Some Students Study Commerce Methodically': Simple random, Systematic, Stratified, Cluster, Multistage. Non-probability: 'Can't Judge Quality Samples': Convenience, Judgement, Quota, Snowball.