Sampling methodsను మాత్రమే తెలుసుకోవడం competitive examinationsకు సరిపోదు. Census, Sample Survey, Sampling Frame, Sampling Error, Non-Sampling Errors, Bias, Sampling Fraction వంటి conceptsపై కూడా direct మరియు statement-based questions వచ్చే అవకాశం ఉంటుంది.
Census vs Sample Survey
Target Population
Sampling Frame
Representative Sample
Sampling Fraction
Sampling with / without Replacement
Stratified vs Quota Sampling
Stratified vs Cluster Sampling
Sampling Error
Non-Sampling Errors
Selection Error
Non-response Error
Response Error
Voluntary Response Error
Numerical Problems & Shortcuts
Populationలోని ప్రతి element లేదా unitను investigationలో include చేసి information collect చేసే surveyను Census అంటారు.
Census = A survey conducted by including every element of the population.
ఒక collegeలో 2,000 students ఉన్నారు.
అందరి 2,000 students నుండి information collect చేస్తే → Census
Census → Complete Enumeration
Sample Survey → Partial Enumeration
Population మొత్తాన్ని study చేయకుండా, populationలోని ఒక sampleను మాత్రమే select చేసి information collect చేసే surveyను Sample Survey అంటారు.
Sample Survey = A survey that includes the elements of a sample rather than every element of the population.
Population = 10,000 households
Surveyed = 500 households
→ Sample Survey
| Basis | Census | Sample Survey |
|---|---|---|
| Coverage | Every population unit | Only selected units |
| Nature | Complete enumeration | Partial enumeration |
| Time | Generally requires more time | Generally faster |
| Cost | Usually more costly | Usually economical |
| Sampling Error | Does not occur | Can occur |
| Non-Sampling Error | Can occur | Can occur |
Censusలో Sampling Error ఉండదు.
కానీ Censusలో కూడా Non-Sampling Error రావచ్చు.
Researcherకు information కావలసిన complete collection of subjects or unitsను Target Population అంటారు.
Andhra Pradeshలో government college students యొక్క study చేస్తే, studyకి సంబంధించిన all eligible government college students → Target Population.
Sampleను select చేయడానికి ఉపయోగించే target population members యొక్క listను Sampling Frame అంటారు.
The list of members of the target population used to select a sample.
College students నుండి sample select చేయడానికి official student register ఉపయోగిస్తే:
Student Register → Sampling Frame
Questionలో
“List from which sample is drawn”
లేదా
“List used to select a sample”
అంటే → Sampling Frame
Population characteristicsను సాధ్యమైనంత closely reflect చేసే sampleను Representative Sample అంటారు.
A sample that contains the characteristics of the population as closely as possible.
Random Sample మరియు Representative Sample ఒకే definition కాదు.
Random Sample → Selection procedureకు సంబంధించిన concept.
Representative Sample → Population characteristics sampleలో ఎంతవరకు reflect అయ్యాయనే concept.
Populationలో ఎంత proportion sampleగా తీసుకున్నామో తెలియజేసే ratioను Sampling Fraction అంటారు.
ఇక్కడ:
n = Sample Size
N = Population Size
Percentage రూపంలో:
Population = 5,000
Sample = 500
Find the sampling fraction and sampling percentage.
Sampling Fraction = 0.10 = 1/10
Sampling Percentage = 10%
Sample ÷ Population × 100
500 / 5000 × 100
= 1/10 × 100
= 10%
Population = 4,000
Sampling Percentage = 5%
Find the required sample size.
5% = 1/20
4000 ÷ 20 = 200
| Percentage | Fraction | Fast Method |
|---|---|---|
| 50% | 1/2 | Divide by 2 |
| 25% | 1/4 | Divide by 4 |
| 20% | 1/5 | Divide by 5 |
| 10% | 1/10 | Divide by 10 |
| 5% | 1/20 | Divide by 20 |
| 2% | 1/50 | Divide by 50 |
| 1% | 1/100 | Divide by 100 |
ఒక unitను population నుండి select చేసిన తరువాత, next selectionకు ముందు దానిని తిరిగి populationలో place చేస్తే దానిని Sampling With Replacement అంటారు.
With Replacementలో ఒకే unit more than once select అయ్యే అవకాశం ఉంటుంది.
Selected unitను populationలోకి తిరిగి place చేయకుండా next unitను select చేస్తే దానిని Sampling Without Replacement అంటారు.
Without Replacementలో already selected unit మళ్లీ select కాదు.
| With Replacement | Without Replacement |
|---|---|
| Selected unit is returned | Selected unit is not returned |
| Same unit may appear again | Same unit cannot be selected again |
| Population size remains unchanged for each draw | Available population decreases after each draw |
ఈ రెండు methodsలో population groupsకు representation కనిపించడం వల్ల objective questionsలో confusion రావచ్చు.
| Basis | Stratified Sampling | Quota Sampling |
|---|---|---|
| Type | Random Sampling | Non-Random Sampling |
| Groups | Population divided into strata | Population divided into categories/groups |
| Selection | Random selection within strata | Units selected to fulfil predetermined quota |
| Main Idea | Representation + Random Selection | Fixed Representation / Quota |
Groups + Random Selection → STRATIFIED
Groups + Fixed Quota → QUOTA
| Stratified Sampling | Cluster Sampling |
|---|---|
| Population divided into strata | Population divided into clusters |
| Sample taken from each stratum | One or a few clusters selected |
| Every stratum gets representation | Not every cluster must be selected |
| Some units from all groups | Some groups are selected |
STRATIFIED → Some from ALL
CLUSTER → ALL / units from SOME groups
Sample survey result మరియు entire populationను survey చేసి ఉంటే లభించే result మధ్య chance వల్ల వచ్చే differenceను Sampling Error అంటారు.
Mean విషయంలో:
Sampling Error → Chance Error
Sampling Error → Sample Surveyలో మాత్రమే వస్తుంది
Population Mean = 75
Sample Mean = 78
Find Sampling Error.
Always remember:
Sample − Population
x̄ − μ
Sample Mean = 49.5
Find Sampling Error.
Sample mean population meanను 2.5 units underestimate చేసింది.
Positive Error → Sample estimate is higher
Negative Error → Sample estimate is lower
Dataను collect, record, process లేదా tabulate చేసే సమయంలో chance కాకుండా human లేదా procedural reasons వల్ల వచ్చే errorsను Non-Sampling Errors అంటారు.
Non-Sampling Errors → Censusలో కూడా రావచ్చు
Non-Sampling Errors → Sample Surveyలో కూడా రావచ్చు
Sample select చేయడానికి ఉపయోగించిన Sampling Frame target populationను properly represent చేయకపోవడం వల్ల వచ్చే errorను Selection Error అంటారు.
Telephone directoryను sampling frameగా ఉపయోగిస్తే telephone directoryలో లేని persons automatically excluded అవుతారు.
అందువల్ల sample target populationను పూర్తిగా represent చేయకపోవచ్చు.
Defective / Incomplete Sampling Frame → Selection Error
Sampleలో select చేసిన personsలో కొంతమంది surveyకు response ఇవ్వకపోతే దాని వల్ల వచ్చే errorను Non-Response Error అంటారు.
1,000 personsకు questionnaire పంపారు.
600 persons మాత్రమే respond చేశారు.
Non-respondents characteristics respondentsతో systematically differentగా ఉంటే survey results distorted కావచ్చు.
Selected → Contacted → No Reply
= Non-Response Error
Respondent surveyలో incorrect information ఇవ్వడం వల్ల వచ్చే errorను Response Error అంటారు.
Questionను misunderstand చేయడం
Correct information గుర్తు లేకపోవడం
Sensitive questionకు intentionally wrong answer ఇవ్వడం
Reply వచ్చింది కానీ answer wrong
= Response Error
Randomly selected sampleకు బదులుగా people తమంతట తామే surveyలో participate చేయాలని decide చేసేటప్పుడు వచ్చే biasను Voluntary Response Error అంటారు.
Newspaper లేదా magazineలో ఒక questionnaire publish చేసి “Interested readers respond చేయండి” అని అడగడం.
Strong opinions ఉన్న people ఎక్కువగా voluntarily respond చేసే అవకాశం ఉండటం వల్ల sample populationను represent చేయకపోవచ్చు.
People choose themselves to participate
= Voluntary Response Error
| Basis | Sampling Error | Non-Sampling Error |
|---|---|---|
| Cause | Chance | Human / procedural causes |
| Occurs in Sample Survey? | Yes | Yes |
| Occurs in Census? | No | Yes |
| Examples | Difference between sample statistic and population parameter | Selection, Non-response, Response, Recording errors etc. |
| Nature | Chance Error | Systematic / other survey errors |
| Question Clue | Identify |
|---|---|
| Sample result differs from population result due to chance | Sampling Error |
| Sampling list does not represent population | Selection Error |
| Selected respondent does not answer | Non-Response Error |
| Respondent gives incorrect answer | Response Error |
| People themselves decide whether to participate | Voluntary Response Error |
| Wrong recording / coding / tabulation | Non-Sampling Error |
Sampling procedure systematically certain population membersను favour లేదా exclude చేస్తే sample populationను properly represent చేయకపోవచ్చు. ఇటువంటి systematic tendencyను generally Biasతో associate చేస్తారు.
Large Sample ≠ Automatically Unbiased Sample
Wrong selection methodతో very large sample తీసుకున్నా bias ఉండవచ్చు.
Less Time
Lower Cost
Less Manpower
Quicker Results
Large Populationsను study చేయడం practical అవుతుంది
Detailed investigationకు అవకాశం ఉంటుంది
Sampling Error ఉండవచ్చు
Unrepresentative sample వచ్చే అవకాశం ఉంది
Improper sampling method biasకు దారితీయవచ్చు
Small or highly heterogeneous populationsలో careful design అవసరం
Wrong sample → Wrong Generalisation
Required Sample = 400
Find sampling interval.
Cancel two zeros:
80/4 = 20
Random starting unit = 12.
Find first five sample units.
Start at 12 → keep adding 25.
Group A = 600
Group B = 300
Group C = 100
Total sample required = 200.
Find proportionate sample allocation.
Population Ratio:
Total ratio = 10
A = 6 × 20 = 120
B = 3 × 20 = 60
C = 1 × 20 = 20
A = 120
B = 60
C = 20
When group numbers have an easy common factor:
Simplify to Ratio → Divide Sample by Total Ratio → Multiply.
A) Sample Survey
B) Census
C) Quota Survey
D) Cluster Survey
A) Sampling Error
B) Sampling Frame
C) Sampling Fraction
D) Sample Statistic
A) Response Error
B) Recording Error
C) Sampling Error
D) Non-Sampling Error
A) Sampling Error only
B) Non-Sampling Error
C) Sampling Fraction
D) Standard Error only
A) Selection Error
B) Response Error
C) Sampling Fraction
D) Randomisation
A) Response Error
B) Non-Response Error
C) Sampling Error only
D) Cluster Error
A) Response Error
B) Sampling Error
C) Sampling Fraction
D) Cluster Sampling
A) Voluntary Response Error
B) Systematic Sampling
C) Stratified Sampling
D) Census Error
A) Every random sample must perfectly represent the population
B) A representative sample reflects population characteristics closely
C) Census always contains sampling error
D) Quota sampling is simple random sampling
A) Stratified sampling involves random selection within strata
B) Quota sampling is always a census
C) Stratified sampling has no groups
D) Both are identical
A) 0.5
B) 0.05
C) 5
D) 50
A) 0.5%
B) 5%
C) 50%
D) 500%
A) 60
B) 600
C) 1,000
D) 6,000
6000/10 = 600
A) 10
B) 20
C) 40
D) 80
A) +3
B) −3
C) 125
D) 3%
A) Both Assertion and Reason are true and Reason correctly explains Assertion.
B) Both are true but Reason is not the correct explanation.
C) Assertion is true but Reason is false.
D) Assertion is false but Reason is true.
Reason: Census includes every element of the population.
Reason: Errors may occur during collection, recording and tabulation of data.
Reason: Response Error occurs when respondents provide incorrect answers.
Reason: Stratified Random Sampling involves random selection from strata.
| Clue | Correct Concept |
|---|---|
| Every population unit included | Census |
| Only part of population included | Sample Survey |
| List from which sample is selected | Sampling Frame |
| Population characteristics closely represented | Representative Sample |
| Every kth unit | Systematic Sampling |
| Random sample from every group | Stratified Sampling |
| One/few groups selected | Cluster Sampling |
| Fixed group targets | Quota Sampling |
| Easy-to-reach persons | Convenience Sampling |
| Expert selects units | Judgment Sampling |
| Difference due to chance | Sampling Error |
| Defective sampling frame | Selection Error |
| Selected person does not reply | Non-Response Error |
| Respondent gives wrong answer | Response Error |
| Respondents choose themselves | Voluntary Response Error |
n/N
Sampling Percentage:
(n/N) × 100
Sample Size from Percentage:
n = N × Percentage/100
Systematic Sampling Interval:
k = N/n
Systematic Sample:
r, r+k, r+2k, r+3k, ...
Proportionate Stratified Allocation:
nh = (Nh/N) × n
Sampling Error of Mean:
x̄ − μ
→ Every population element
Sample Survey
→ Part of population
Sampling Frame
→ List used to select sample
Representative Sample
→ Closely reflects population characteristics
Sampling Fraction
→ n/N
Systematic Interval
→ N/n
Stratified
→ Some units from EVERY stratum
Cluster
→ One/Few clusters selected
Quota
→ Predetermined group quota
Sampling Error
→ Due to Chance
→ Sample Survey only
Non-Sampling Error
→ Human / Procedural Causes
→ Census + Sample Survey
Selection Error
→ Sampling Frame problem
Non-Response Error
→ No reply
Response Error
→ Wrong reply
Voluntary Response Error
→ Respondents select themselves
Golden APPSC Memory:
Every unit → Census
Part of population → Sample
Every kth → Systematic
Some from ALL → Stratified
SOME groups → Cluster
Fixed target → Quota
Easy availability → Convenience
Expert choice → Judgment
Chance difference → Sampling Error
No reply → Non-Response Error
Wrong reply → Response Error
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