The Process of Obtaining Information About a Whole by Examining Only a Part


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The Process of Obtaining Information About a Whole by Examining Only a Part

  • The Process of Obtaining Information About a Whole by Examining Only a Part

  • Whole = Population Part = Sample

  • Everyday Life Concept

  • Example: Physician makes diagnosis on the basis of the findings of a small sample of blood

  • Auditors use sampling to draw conclusions about large volumes of transactions

  • Market researchers use sample of customers to determine market potential

  • Sample Inspection is done to accept or reject a lot

  • ?



Population too large to be studied in full

  • Population too large to be studied in full

  • Sampling is Cheaper & Quicker as compared to Census

  • Necessary in destructive testing-

  • Census not feasible-testing of medicines



To Estimate Value of a Population Parameter (Mean, Variance, Proportions etc.) on the basis of Value of the Corresponding Sample Statistic.

  • To Estimate Value of a Population Parameter (Mean, Variance, Proportions etc.) on the basis of Value of the Corresponding Sample Statistic.

  • More Representative the Sample, More Accurate is the Estimate.

  • Bigger the Sample, Better the Estimate.

  • Bigger the Sample, Greater is Cost & Time



Population: Entire group of people, events, or objects of interest in context of research

  • Population: Entire group of people, events, or objects of interest in context of research

  • Element: A single member of the population

  • Population Frame: List of all elements in the population from which a sample is drawn

  • Example: List of all students in a college, list of all ent. events in Mumbai in June 2010, list of all songs sung by Lata Mangeshkar

  • Population Parameters: Proportion, Mean & Variance.



Sample: A subset of population selected for data collection in the research study

  • Sample: A subset of population selected for data collection in the research study

  • Subject: A single member of the sample

  • Sampling: Process of selecting sufficient number of elements from the population

  • Sampling saves time & cost of research

  • Sample Statistics: Sample proportion, Sample mean (central tendency) & sample variance (dispersion).



Difference between the Actual Value of the Characteristic of Population and the Value Estimated from the Sample.

  • Difference between the Actual Value of the Characteristic of Population and the Value Estimated from the Sample.

  • The Art & Science of Sampling is to Apply Appropriate Techniques to Minimize this Risk, i.e. Minimizing Sampling Error.



Statistical Assurance About Minimum Sampling Error (Risk) is Provided by Two Parameters:

  • Statistical Assurance About Minimum Sampling Error (Risk) is Provided by Two Parameters:

  • Precision: Quantum of Admissible Error

  • Reliability or Confidence Level: The Probability that the Sample Estimate Will Be In Fact Within the Stipulated Range of Precision



Quantum of Admissible Error. Ideally Zero.

  • Quantum of Admissible Error. Ideally Zero.

  • Cannot be Zero Unless Sample is 100%.

  • Precision Should be as small as possible



Precision (i.e. Error or Risk in Statistics) Decreases as Sample Size Increases.

  • Precision (i.e. Error or Risk in Statistics) Decreases as Sample Size Increases.

  • But, Cost & Time of Estimation Increases as Sample Size Increases.

  • This is an Issue of Resource Allocation.

  • Hence, You as Manager, Strike a Balance and Decide Optimal Level of Precision.

  • Note: Precision is Management Decision.



It is the Probability that the Sample Estimate Will Be In Fact Within the Range of Precision Set by You.

  • It is the Probability that the Sample Estimate Will Be In Fact Within the Range of Precision Set by You.

  • This Prob Has to be Very High: 90%, 95%,99%.

  • 100% Impossible Unless Sample is 100%.

  • In Any Sampling Scenario, You Must First Set Precision and Confidence Level.

  • They will determine Required Sample Size





How Big Should Be My Sample?

  • How Big Should Be My Sample?

  • Sample Size Depends Upon the Sampling Technique Selected for the Purpose.

  • Therefore, First We Must Know About the Various Sampling Techniques.



A Statistical /Probability Sample Should Be:

  • A Statistical /Probability Sample Should Be:

  • Selected Objectively so that Inferences Drawn from it are Reliable,

  • Free from Personal Biases,

  • Giving Equal or Known Chance of Selection to Every Unit of the Population.

  • So, Sample Must Be Drawn Scientifically.



Many Techniques Available.

  • Many Techniques Available.

  • Selection of the Right One Depends Upon:

  • - Nature of the Population,

  • - Cost Budget,

  • - Time Constraint,

  • - Precision & Confidence Required

  • Hence, Selection Falls in Your Domain.



Most Widely Used for Ease and Low Cost

  • Most Widely Used for Ease and Low Cost

  • Equal Probability of Selection to All Units in Population

  • Random Number Tables (RNT) Available

  • Internationally Tested for Randomness





Assign Sequential Numbers to All Units

  • Assign Sequential Numbers to All Units

  • Open Any Page of RNT. Start Anywhere

  • From This Starting Point Proceed Vertically Downwards and Select As Many Numbers As Required





Quality Controller wishes to select a random sample of 25 drums from the lot numbered from 312 to 9233.

  • Quality Controller wishes to select a random sample of 25 drums from the lot numbered from 312 to 9233.

  • Drums are already numbered

  • Largest Number: 9233. Hence 4-digit Nos.

  • Randomly select the starting point: 7383

  • Hence, First Sample is Drum No. 7383

  • Next No. is 6546. feasible. Accept it.

  • Next No. is 9895. Infeasible. Discard it.





Use When Pop is Already Arranged in an Order.

  • Use When Pop is Already Arranged in an Order.

  • Example: Vouchers, Employee No., Batch No.

  • Variation of SRS. Faster. Speeds Up Sampling.

  • Does Not Use Random Number Tables.

  • Compute Skip Interval k = Ratio of Pop Size to Sample Size.

  • Randomly Select a Starting Number < k.

  • Then Systematically Selects Every kth Number.

  • Widely Used for Ease and Lower Cost.



Internal Auditor wishes to select a sample of 50 accounts receivable out of 520 such accounts in a sales office.

  • Internal Auditor wishes to select a sample of 50 accounts receivable out of 520 such accounts in a sales office.

  • She opts for Systematic Sampling.

  • Skip Interval k = 520 / 50 = 10.4

  • Suppose Her Random no. below 10 is 7.

  • Sample: Acct Nos. 7, 17, 27, 37,……, 497



Example: 520 accounts receivable from 4 product divisions: Agro-Chemical (323), Leather (54), Textile(22), Plastic (121).

  • Example: 520 accounts receivable from 4 product divisions: Agro-Chemical (323), Leather (54), Textile(22), Plastic (121).

  • Sample of 50: 32, 5, 2 & 11 respectively

  • Population Discernibly Heterogeneous

  • Divide It into Several Parts (Called Strata)

  • Each Stratum Homogeneous Within Itself

  • Draw a Simple Random or Systematic Sample from Each Stratum.



Example: Hosiery Crates ( Each Crate Contains Full Assortment of Sizes), Bldgs in Apt Complex

  • Example: Hosiery Crates ( Each Crate Contains Full Assortment of Sizes), Bldgs in Apt Complex

  • Population Discernibly Heterogeneous

  • Divide It into Several Clusters

  • Each Cluster Heterogeneous Within Itself

  • Draw SRS or Systematic Sample of Clusters

  • Study Each Sampled Cluster Fully.

  • Use When Population is Inherently Divided into Heterogeneous Clusters.

  • Convenient. Saves Cost & Time.



Samples are Drawn from Samples

  • Samples are Drawn from Samples

  • Example: Select 4 Out of 25 Working Days, and Select Ten Sacks of Finished Product from Each Selected Day’s Output

  • This is 2-Stage Sampling.

  • In Complex Situations, This Process Can Go On for 3, 4 or Even More Stages.



Factors Influencing Sample Size:

  • Factors Influencing Sample Size:

  • Precision (Your Decision)

  • Confidence Level (Your Decision)

  • Sampling Technique (Your Decision)

  • Population Size (Known to You)

  • Pop Parameter to be Estimated (KtY)

  • Dispersion in Population (Known to You)



Effect of Factors Influencing Sample Size

  • Effect of Factors Influencing Sample Size

  • Lower Precision – Bigger Sample

  • Higher Confidence – Bigger Sample

  • Wider Dispersion in Pop – Bigger Sample

  • Ironically, Population Size Affects Sample Size Only Marginally



Example: A sample of 100 TVs to be drawn from 10,000 TVs produced in June 2010

  • Example: A sample of 100 TVs to be drawn from 10,000 TVs produced in June 2010

  • Each TV has 100 ÷ 10,000 = 0.01 i.e. 1% chance of being chosen

  • Sampling Design tells researcher precisely how to pick up 100 TVs



Two lucky numbers to be drawn out of 100 tokens. Put all 100 tokens in a basket. Stir well. Close eyes and pick up two tokens

  • Two lucky numbers to be drawn out of 100 tokens. Put all 100 tokens in a basket. Stir well. Close eyes and pick up two tokens

  • For larger population, assign serial numbers to each element. Use a standard table of random numbers. Select the required number of elements one after other

  • But, enlisting large p pulations is tedious.



HR Director of a software firm with 1926 engineers wants to find out desirability of changing the current 10 – 6 working hours to flexitime along with its benefits & drawbacks perceived by the engineers before the next board meeting

  • HR Director of a software firm with 1926 engineers wants to find out desirability of changing the current 10 – 6 working hours to flexitime along with its benefits & drawbacks perceived by the engineers before the next board meeting

  • She would pick up a few engineers randomly & ask them appropriate questions.



A sample of 50 cars to be selected from 10,000 cars produced in 2009

  • A sample of 50 cars to be selected from 10,000 cars produced in 2009

  • 10,000 ÷ 50 = 200. Select every 200th car

  • More precisely, select a random number between 1 and 200, say 30. Select 30th car

  • Starting from 30th car, select every 200th car: 30, 230, 430, 630, 830, 1030, 1230, 1430…



Maruti Suzuki Ltd. wants to check response of prospective buyers to the new features introduced in its small car segment

  • Maruti Suzuki Ltd. wants to check response of prospective buyers to the new features introduced in its small car segment

  • From the dealers alphabetical list, the Company selects every 50th dealer & sends a senior marketing manager to talk to them.



If population contains identifiable subgroups of elements, researcher must provide proper representation to each subgroup

  • If population contains identifiable subgroups of elements, researcher must provide proper representation to each subgroup

  • Ex.: Population: All students of a college

  • Identifiable Subgroups: males / females; arts/ science / commerce; brilliant / average / poor

  • Lata M. songs: By language, solo / duet etc.



Process: Divide the population into mutually exclusive identifiable subgroups (strata)

  • Process: Divide the population into mutually exclusive identifiable subgroups (strata)

  • Draw a simple random sample (or systematic sample) from each stratum

  • Size of sample from each stratum directly proportional to size of the stratum

  • Homogeneity within each stratum

  • Heterogeneity between strata.





Stratified random sampling involves dividing population into strata

  • Stratified random sampling involves dividing population into strata

  • Hence, it needs higher time and cost

  • But, it provides desired precision with smaller sample than sampling from non-stratified population



Used when population consists of several groups of elements in such a manner that:

  • Used when population consists of several groups of elements in such a manner that:

  • Groups are similar to each other and

  • Each group (CLUSTERS) is heterogeneous

  • So, population has inter-group homogeneity and intra-group heterogeneity

  • Exactly opposite of stratified population

  • Process: Select a few clusters randomly.



Complex of many identical buildings. We can select 5 out of 50 buildings

  • Complex of many identical buildings. We can select 5 out of 50 buildings

  • A Mgmt Inst: 2000 students per year. 50 per batch. 40 batches run concurrently. Each has some active, some ordinary & some passive students, and 75% boys, 25% girls. Choose 4 batches and talk to all 200 students without disturbing other 36 batches.



A truckload of mangoes in 4 dozen boxes. Each box has upper layer of top quality fruits. Quality & size drops layer by layer.

  • A truckload of mangoes in 4 dozen boxes. Each box has upper layer of top quality fruits. Quality & size drops layer by layer.

  • Thus, homogeneity between boxes & heterogeneity within each box.

  • Draw a random or systematic sample of a few boxes, open them and study them.

  • No need to open other boxes from the truck.



Convenient

  • Convenient

  • Sample size smaller

  • Less time and cost

  • But, restrictive in application: You don’t frequently get such populations.



Under a community health program for tribals, it was necessary to discover their current state of nutrition, health & beliefs

  • Under a community health program for tribals, it was necessary to discover their current state of nutrition, health & beliefs

  • Since adivasi padas are located at long distances from each other in tribal areas, a few adivasi padas were selected at random and all residents from infants to old ones were checked.




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