6.1-*Chapter 7 Sampling Methods by Try Sothearith trysothearith@gmail.com sothearith_t@yahoo.com Tel: 012 585 865 / 016555507NU: Statistics for Manager

6.1-*DefinitionsSampling ConceptsSampling MethodsNU: Statistics for Manager

Sampling Methods6.1-*

Probability SamplesSimple Random SampleUse random numbers to select items from a list (e.g., VISA cardholders).

Systematic SampleSelect every kth item from a list or sequence (e.g., restaurant customers).

Stratified SampleSelect randomly within defined strata (e.g., by age, occupation, gender).

Cluster SampleLike stratified sampling except strata are geographical areas (e.g., zip codes).

Sampling Methods6.1-*

Non-probability SamplesJudgment SampleUse expert knowledge to choose typical items (e.g., which employees to interview).

Convenience SampleUse a sample that happens to be available (e.g., ask co-worker opinions at lunch).

Focus GroupsIn-depth dialog with a representative panel of individuals (e.g. iPod users).

Why Sample the Population?Why sample?The destructive nature of certain tests.The physical impossibility of checking all items in the population.The cost of studying all the items in a population.The adequacy of sample results in most cases.The time-consuming aspect of contacting the whole population.6.1-5

Sampling Methods Simple Random SampleEvery item in the population of N items has the same chance of being chosen in the sample of n items.We rely on random numbers to select a name.6.1-*

Sampling Methods Random Number TablesA table of random digits used to select random numbers between 1 and N.Each digit 0 through 9 is equally likely to be chosen. Setting Up a RuleFor example, NilCo wants to award cash prizes to 10 of its 875 loyal customers.To get 10 three-digit numbers between 001 and 875, we define any consistent rule for moving through the random number table.6.1-*

Sampling Methods Setting Up a RuleRandomly point at the table to choose a starting point.Choose the first three digits of the selected five-digit block, move to the right one column, down one row, and repeat.When we reach the end of a line, wrap around to the other side of the table and continue.Discard any number greater than 875 and any duplicates.6.1-*

Table of 1,000 Random Digits6.1-*

8213414458667165426931928462410305200260323672578307139168297676811913424349196192934182291559502566450564393931188432721133299494193489707695605280101024419093516786346385568700348281123261487946398412940844345008720189580096697205764104213687564964

8443845828403532892511911535022464096880931666840998681678717173564113901393346665312906557544430845432909675318799497133922715955461676385303633199909689385410882332209430605790240179138839855319457675403412270019216814470541681481349922640102829071

7806492111515417656369027677180649971938173541268026246717469401993165967130331675912862091208157817987666731296358213518644831828861137886867243067633789551055119294444315995729359963118190858773130927988811635221225102617982867001358603547401518556

1921653008444981926212196939479016276337126462683828078867296943824235352084895753529762974174154735344556136393711680387596016327957166696428634650155351090412704384593257815751445247261817415624208430658188948820897867307379498518235021783972866398

Sampling Methods With or Without ReplacementIf we allow duplicates when sampling, then we are sampling with replacement.Duplicates are unlikely when n is much smaller than N.If we do not allow duplicates when sampling, then we are sampling without replacement.6.1-*

Sampling Methods Computer MethodsThese are pseudo-random generators because even the best algorithms eventually repeat themselves.6.1-*

Excel - Option AEnter the Excel function =RANDBETWEEN(1,875) into 10 spread-sheet cells. Press F9 to get a new sample.Excel - Option BEnter the function =INT(1+875*RAND()) into 10 spreadsheet cells. Press F9 to get a new sample.InternetThe web site www.random.org will give you many kinds of excellent random numbers (integers, decimals, etc).MinitabUse Minitabs Random Data menu with the Integer option.

Sampling Methods Row Column Data ArraysWhen the data are arranged in a rectangular array, an item can be chosen at random by selecting a row and column.For example, in the 4 x 3 array, select a random column between 1 and 3 and a random row between 1 and 4.This way, each item has an equal chance of being selected.6.1-*

Sampling Methods Row Column Data ArraysUse =RANDBETWEEN function to choose row 3 and column 3 (Target).6.1-*

Dillard'sK-MartSaksDollar GeneralKohl'sSears RoebuckFederated Dept StoresMay Dept StoresTargetJ. C PenneyNordstromWal-Mart Stores

Sampling Methods Randomizing a ListIn Excel, use function =RAND() beside each row to create a column of random numbers between 0 and 1.Copy and paste these numbers into the same column using Paste Special | Values (to paste only the values and not the formulas).Sort the spreadsheet on the random number column.6.1-*

Sampling MethodsThe first n items are a random sample of the entire list (they are as likely as any others). Randomizing a List (Figure 2.6)6.1-*

Sampling Methods Systematic SamplingFor example, starting at item 2, we sample every k = 4 items to obtain a sample of n = 20 items from a list of N = 78 items. Note that N/n = 78/20 4. Sample by choosing every kth item from a list, starting from a randomly chosen entry on the list.6.1-*

Sampling Methods Systematic SamplingA systematic sample of n items from a population of N items requires that periodicity k be approximately N/n.Systematic sampling should yield acceptable results unless patterns in the population happen to recur at periodicity k.Can be used with unlistable or infinite populations.Systematic samples are well-suited to linearly organized physical populations.6.1-*

Sampling Methods Systematic SamplingFor example, out of 501 companies, we want to obtain a sample of 25. What should the periodicity k be? k = N/n = 501/25 20. So, we should choose every 20th company from a random starting point. 6.1-*

Sampling Methods Stratified SamplingUtilizes prior information about the population.Applicable when the population can be divided into relatively homogeneous subgroups of known size (strata).A simple random sample of the desired size is taken within each stratum.For example, from a population containing 55% males and 45% females, randomly sample 120 males and 80 females (n = 200).6.1-*

Sampling Methods Stratified SamplingOr, take a random sample of the entire population and then combine individual strata estimates using appropriate weights.For a population with L strata, the population size N is the sum of the stratum sizes: N = N1 + N2 + ... + NL The weight assigned to stratum j is wj = Nj / nFor example, take a random sample of n = 200 and then weight the responses for males by wM = .55 and for females by wF = .45.6.1-*

Sampling Methods Cluster SampleStrata consist of geographical regions.One-stage cluster sampling sample consists of all elements in each of k randomly chosen sub regions (clusters).Two-stage cluster sampling, first choose k sub regions (clusters), then choose a random sample of elements within each cluster.6.1-*

Here is an example of 4 elements sampled from each of 3 randomly chosen clusters (two-stage cluster sampling).Sampling Methods Cluster Sample (Figure 2.7)6.1-*

Sampling Methods Cluster SampleCluster sampling is useful when - Population frame and stratum characteristics are not readily available - It is too expensive to obtain a simple or stratified sample - The cost of obtaining data increases sharply with distance - Some loss of reliability is acceptable6.1-*

Sampling Methods Judgment SampleA non-probability sampling method that relies on the expertise of the sampler to choose items that are representative of the population.Can be affected by subconscious bias (i.e., non-randomness in the choice).Quota sampling is a special kind of judgment sampling, in which the interviewer chooses a certain number of people in each category.6.1-*

Focus GroupsSampling Methods Convenience SampleTake advantage of whatever sample is available at that moment. A quick way to sample.A panel of individuals chosen to be representative of a wider population, formed for open-ended discussion and idea gathering.6.1-*

*************************