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

• 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

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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.