SAMPLING TECHNIQUES

Dr. Narasimha B. C Post Graduate

 

11111

CONTENTS

Introduction

Definitions

Need for sampling

Major requirements for a sample

• Sample size

Reliable sample

SAMPLING TECHNIQUES

CONTENTS

Sampling techniques

Sampling errors

Advantages & limitations of sampling

Conclusion

References

SAMPLING TECHNIQUES

Introduction

A major reason for having an insight into the science

of epidemiology & research methodology is that we

always study a ‘sample’

Concerned with the selection of representative sample,

especially for the purposes of statistical inference.

Idea of sampling is very old & people have used it in

day-to-day life. For example:

SAMPLING TECHNIQUES

Introduction

On the basis of a sample study, we can predict

& generalise the behaviour of the population.

Most researchers come to a conclusion of their

study by studying a small sample from the

huge population or universe.

Census VS sampling

SAMPLING TECHNIQUES

DEFINITIONS

Population- aggregate of units of observations either animate

or inanimate about which certain information is required.

Sample-word used to describe a portion chosen from the

population

For sampling purpose, the population has to be divided into

smaller units - sampling unit

URL:http://www.google.co.in/images?rls=ig&hl=en&source=imghp&biw=1024&bih=651&q=population+and+sample&gbv=2&aq=4&aqi=g1&aql=&oq=population+and+sam&gs_rfai=SAMPLING TECHNIQUES

DEFINITIONS

Sample size-number of units in a sample

Sampling frame - list of each and every individual in

the population

Variable: any quality or quantity liable to show

variation from one individual to the next in the same

population

Variate: individual observations of any variable

SAMPLING TECHNIQUES

DEFINITIONSDistinction Population Sample

Definition Collection of items under consideration.

Part of the population selected for study.

Characteristics Parameter Statistics

Symbols N= populationµ = population meanσ = population standard deviationπ = population percentage

n = sample sizex = sample means = sample standard deviationp = sample percentage

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Need for sampling

Complete enumerations are practically impossible

when the population is infinite.

When the results are required in a short time.

When the area of survey is wide.

When resources for survey are limited particularly

in respect of money and trained persons.

SAMPLING TECHNIQUES

Major requirements for a sample

To draw conclusions about population from

sample, there are two major requirements for a

sample.

• Sample has to be selected appropriately so that it is

representative of the population. It should have all the

characteristics of the population.

• The sample size should be adequately largeSAMPLING TECHNIQUES

Sampling Terminology

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Sample size estimation

Problems with very large sample size:

1) Cost, time and personnel

2) Unethical

Problems with very small sample size:

1) May give unreliable conclusion that cannot be used, so

there is wastage of resources & amounts to unnecessary

exposure to the subjects. SAMPLING TECHNIQUES

Calculating the sample size : depends upon

precision which in turn depends upon significance

level & allowable error.

Depends upon the kind of data:

Qualitative datan= 4pq/ L2

Quantitative datan= 4 σ2

L2

SAMPLING TECHNIQUES

Significance level-5%p - prevalenceq - 100-pL – allowable error (10 or 20%)

σ= SD of populationL= allowable error expressed in confidence limit

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Example:1) Incidence rate in the last influenza epidemic was found to be 50 per 1000 (5%) of the population exposed. What should be the sample size to find incidence rate in the current epidemic if allowable error is 10% & 20%.

P= 5%, q=95%

If L = 10% of p then, it is

5 * 10/100 = 0.5%

At 10% risk

n = 4pq/ L2

= 4 * 5 * 95/ (0.5)2

If L= 20% of p then, it is

20 *5/100 = 1%

At 20% risk

n = 4pq/ L2

= 4 * 5 * 95/ 1*1

= 7600

= 1900

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Example: Mean pulse rate of a population is believed to be 70 per minute with a standard deviation of 8 beats. Calculate the minimum size of the sample to verify this if allowable error L= ± 1 beat at 5% risk.

n= 4 σ2

L2

σ= 8 , L= + 1 beat with 5% riskn= 4* 82 = 256 1

If L = ± 2 beats with 5 % risk then,n= 4* 82 = 64 22

SAMPLING TECHNIQUES

If L is less then n will be more i.e. larger the sample size, lesser will be the error.

= 256 64

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Population

Sampledrawsample

drawsample

generalizeback

generalizeback

Sampling – “A process of selecting a subset/part from a larger group in such a way that information / estimates from the subset can be generalized to the larger group".

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Types of Sampling Methods

Cluster

Sampling

Non-Probability Sampling

Convenience

Probability Sampling

Simple Random

Systematic

Stratified

Purposive

SAMPLING TECHNIQUES

Simple Random Sampling (SRS)

Here each unit in the population has equal chance or

probability to be selected in the sample.

Situations where random sampling can be done:

• Sampling frame is available.

• When the population is small.

• Parameters to be estimated -homogeneously distributed in

population.

• Units should be readily available- ex: patients in wardsSAMPLING TECHNIQUES

Simple Random Sampling (SRS)

The procedure involved in Random Sampling:

• Preparing a sampling frame

• Deciding the size of the sample to be chosen.

• To select the required number of units at random

Random samples can be drawn by:

• lottery method -

• random number tables-

• using calculators or computers-

SAMPLING TECHNIQUES

RANDOM NUMBER TABLE

SOURCE: Training for mid-level managers. 7. The EPI coverage survey. [Serial online] 2008 [Cited 2013 June 6] Available from URL: http://whqlibdoc.who.int/hq/2008/WHO_IVB_08.07_eng.pdf

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Procedure to select a sample using random number table:

Units of the population from which a sample is required are assigned with

equal number of digits.

We may start at any place and may go on in any direction such as column

wise or row- wise in a random number table. But consecutive numbers are

to be used.

On the basis of the size of the population and the random number table

available with us, we proceed according to our convenience.

If any random number is greater than the population size N, then N can be

subtracted from the random number drawn. This can be repeatedly until the

number is less than N or equal to N. SAMPLING TECHNIQUES

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Example 1: In an area there are 500 families. Using the following extract from a table of random numbers select a sample of 15 families to find out the standard of living of those families in that area.

4652 3819 8431 2150 2352 2472 0043 34889031 7617 1220 4129 7148 1943 4890 17492030 2327 7353 6007 9410 9179 2722 84450641 1489 0828 0385 8488 0422 7209 4950

SAMPLING TECHNIQUES

203 023 277 353 600 794 109 179 272 284 450 641 148 908 280

203 023 277 353 100 294 109 179 272 284 450 141 148 408 280

N=500n=15

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1 2 3 4 5 6 7 8 9 10

Simple Random Sampling ex:

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

N =30n = 10

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Merits of using random numbers:

1. Personal bias is eliminated

2. It is in general a representative sample for a

homogenous population.

3. The accuracy of a sample can be tested by examining

another sample from the same universe when the

universe is unknown.

4. This method is also used in other methods of sampling.

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Limitations of SRS:

1. Preparing lots or using random number tables is

tedious when the population is large.

2. It is generally seen that the units of a simple random

sample lie apart geographically. The cost and time of

collection of data are more.

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SYSTEMATIC RANDOM SAMPLING Commonly employed technique, when complete and up to date list of

sampling units is available.

Obtained by selecting 1 unit on a random basis & then choosing additional

units at evenly spaced intervals until the desired no is obtained.

Procedure: 1.Prepare the list of population (sampling units) 1 to N.

2. Decide on the n (sample size) that you want or need.

3. Calculate sampling fraction/ sampling interval (k)

k= N/n where N = population size & n = sample size

4. Randomly select an integer between 1 to kth.

5. Add to this the sampling interval to get required sample. Then take every

kth unit.

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SYSTEMATIC RANDOM SAMPLING

Example: systematic sampling

Ex: in PPI 15 out of 150 houses have to be selected

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SYSTEMATIC RANDOM SAMPLING Merits :

Simple and convenient to adopt.

Time and labour involved in the collection of sample is relatively small.

If the population is sufficiently large, homogenous & each unit is numbered, this

method can yield accurate results.

Limitations:

The sample may exhibit a pattern or periodicity

Systematic sampling may not represent the whole population.

There is a chance of personal bias of the investigators.

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STRATIFIED RANDOM SAMPLING

Preferred when the population is heterogeneous with respect to

characteristic under study.

The complete population is divided into homogenous sub groups

-‘Strata’ & then a stratified sample is obtained by independently

selecting a separate simple random sample from each population

stratum.

Gives equal chance to the units in each stratum to be selected as

sample.

The total sample is the addition of samples of each stratum

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Stratified random sampling: Ex:

STAFF

PG

OTHER

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6

10 2 8 4 1 6 12 8 4 2 1 6

Non-Proportional stratified sampling

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6

10 2 8 4 1 6 12 8 4 2 1 6

Proportional stratified sampling

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STRATIFIED RANDOM SAMPLING

Merits:

1. It is more representative.

2. It ensures greater accuracy

3. It is easy to administer as the universe is sub -

divided.

4. For non – homogeneous population, it may yield

good results.SAMPLING TECHNIQUES

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STRATIFIED RANDOM SAMPLING

Limitations:

1. To divide the population into homogeneous strata,

it requires more money, time and statistical

experience which are a difficult one.

2. Improper stratification leads to bias, if the

different strata overlap such a sample will not be a

representative oneSAMPLING TECHNIQUES

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LOT QUALITY ASSURANCE SAMPLING

Originated in manufacturing industry for quality control purposes

Only outcome - “acceptable” or “not acceptable”

Two types of risk

(i) Risk of accepting a “bad” lot

(ii) Risk of not accepting a “good” lot

The advantage over a traditional stratified sampling design: the

response for each lot is binary (acceptable or not) & therefore

smaller sample sizes can be used

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CLUSTER SAMPLING

Used when the population is heterogeneous & when sampling frame is

not available at individual level

Clusters are formed by grouping units on the basis of their

geographical locations or political boundaries.

Obtained by selecting clusters from population on the basis of SRS

From the selected clusters each and every unit is included for study

Special form of cluster sampling - “30 cluster sampling” for field

studies in assessing vaccination coverage

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CLUSTER SAMPLING

Section 4

Section 5

Section 3

Section 2Section 1

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CLUSTER SAMPLING

Advantages:

- Only need to obtain list of units in the selected clusters.

- Cost-effective.

Disadvantages:

- Not intended for calculation of estimates from

individual clusters.

- Less precise than simple random sample.

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MULTISTAGE SAMPLING

Sampling procedures carries out in several stages using random sampling

techniques.

When the sampling frame is rarely available, or if such a list is available, it

may be too large. To overcome such a problem, multi-stage sampling

procedures are often employed.

Each point of sampling is called a “stage” and the term “multi-stage

sampling procedure” is generally used to refer to a sample selection process

that has at least two stages.

Any of the probability sampling techniques may be used at each stage of a

multi-stage procedure STAGE 1

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NFHS-3, data WAS collected by multistage

sampling.

Rural areas – 2 stage sampling – Villages from list by PPS,

Households from village

Urban areas – 3 stage sampling - Wards (PPS) – CEB*

(PPS) – 30 households from each CEB

* CEB – Census enumeration blocks

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MULTIPHASE SAMPLING

Part of information is collected from the whole

sample & part from the sub sample.

Number in the sub samples in 2nd & 3rd phases

will become successively smaller & smaller.

Survey by such methods will be less costly,

less laborious & more purposeful.

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MULTIPHASE SAMPLING

Ex: In a tuberculosis survey

First phase- physical examination or mantoux test done in all cases of the sample

Second phase-x-ray of the chest done in mantoux positive cases & in those with clinical symptoms

Third phase -sputum may be examined in X-ray positive casesSAMPLING TECHNIQUES

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TABLE: COMPARITIVE PERFORMANCE OF VARIOUS RANDOM SAMPLING METHODSMethod of random sampling

Desired size of target population

Reliability of conclusions for fixed sample size

Economy Remarks

Simple Small Very good Expensive Requires full sampling frame

Systematic Small Good Economical sampling frame not needed but the size of the target population is needed

Stratified Medium Good Expensive Good for non-homogenous population

Cluster Large Poor Very economical

Very convenient for geographically diverse population

Multi stage Very large Medium economical Requires sampling frame only for each nested unit

SOURCE: Indrayan A, Satyanarayana L. Simple biostatistics. `3rd ed. Academia publishers: 2009; Delhi

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NON RANDOM SAMPLING

The sampling is purposive when cases that serve specific

purpose are chosen.

Results based on non-random samples are not generalizable yet

are useful in some situations in providing a clue about the

status of a phenomenon. Non-Probability Sampling

Convenient sampling

•Snowball sampling

•Convenient sampling

Purposive sampling

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Snowball sampling

Each subject refers another subject to the sample

Hard-to-reach, or equivalently hidden populations.

• when the population is small relative to the general population

• geographically dispersed

• when population membership involves stigma

• group has networks that are difficult for outsiders to penetrate

Ex: people exposed to sex workers or those injecting

drugs in the context of HIV.

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Convenient Sampling

A sample is drawn on the basis of opportunity – use

who’s available

many studies are done on medical students just because

they are available in captivity & would generally provide

correct response.

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Purposive sampling

A purposive sample is one which is selected by

the researcher subjectively.

• The researcher attempts to obtain the sample that

appears to him to be representative of the

population.

• Based on intent SAMPLING TECHNIQUES

Characteristics:• Selection is made by human choice than at random

when you are studying particular groups

Example:To study on the vulnerable cases - A sample of people from low socio-economic status

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Differences b/w Non-probability samples & probability samples

SAMPLING TECHNIQUES

URL:http://www.chsbs.cmich.edu/fattah/courses/empirical/22.html

Key terms Non-probability samples

Probability samples

Sampling frame Does not exist or inaccurate

Accurate and up-to-date

Sampling error Cannot be calculated

Can be calculated

Sample size Matter of convenience

Determined by sampling theory

Level of generalizability

Illustrative Representative.

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Errors in sampling

Sampling errors- Size of the sample

-Natural variability of the individual reading

Non sampling errors

Coverage errors

Observational errors

Processing errors

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Advantages of Sampling

There are many advantages of sampling methods over census

method. They are:

1. Saves time and labour.

2. Results in reduction of cost in terms of money and man-hour.

3. Ends up with greater accuracy of results.

4. Has greater scope.

5. Has greater adaptability.

6. If the population is too large, or hypothetical sampling is the only

method to be used.

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Limitation of Sampling

Sampling is to be done by qualified and

experienced persons. Otherwise, the

information will be unbelievable.

Sample method may sometimes give the

extreme values

There is the possibility of sampling errors.

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CONCLUSION

Whenever a scientific study is planned it may not always be

feasible to study the entire population. In such situations we

need to apply some sampling technique to select our

samples and it’s better to select probability sampling

techniques. Selecting a sampling method depends upon:

• Population to be studied ( size & heterogeneity with respect to variables)

• Resources available

• Importance of having a precise estimate of the sampling error

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REFERENCES Park K, Park’s text book of preventive & social medicine, 23rd

ed, 2015.

Bhalwar R, Text book of public health and community medicine.

Pune: Department of Community Medicine Armed Forces

Medical College; 2009.

Murthy NS. Applied statistics in health sciences. 2nd ed. New

Delhi: Jaypee; 2010.

Mahajan BK. Methods in biostatistics. 6th ed. New Delhi:

Jaypee; 2006SAMPLING TECHNIQUES

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REFERENCES

Satguru prasad, Elements of biostatistics, 3rd ed, meerut, Rastogi,

2015.

Antoniswamy, Biostatistics principles and practice, New Delhi,

Mc Graw Hill Education (India) pvt ltd, 2010.

Suryakantha AH, Community Medicine, 3rd ed. New Delhi,

Jaypee, 2014.

World wide web.

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