welcome

MAJOR CREDIT SEMINAR

ON

- STRATIFIED RANDOM SAMPLING
- By -Shashank kshandakar

M.V.Sc(1st year)

Division

of lesit

Content....

- Definitions and concepts in sampling
- Principles of sampling
- Advantages of sampling
- Types of sampling
- Stratified random sampling its properties

Important definitions

- Population population is an aggregates of

object under study. - Sample- A finite sub-set of statistical

individual in a population is called a sample. - Sampling Unit Sets of units considered for

selection in some stage of sampling. - Sampling scheme-Method of selecting sampling

units from population

Important definitions.

- Census-The process of complete enumeration of

all the elements or units in the population - Sample size-The number of elements or units in a

sample is known as sample size. - Accuracy-The amount of deviation of the

estimate from the true value. - Precision-The deviation of the estimate from the

average value. It is reciprocal of the variance

Sampling Frame

- Sampling Frame- A complete list, map or other

acceptable materials which serve as a guide to

the population to be covered is known as frame. - A sampling frame which has the property that we

can identify every single element and include any

in our sample - The sampling frame must be representative of the

population - A sampling frame must be up-to-date.

Important definitions

- Sampling fraction- Ratio of sample size(n) to

the population size(n) i.e. (n/N) - Finite population correction-1- (Sampling

fraction) - Sample space-A space consisting of all possible

sample is called sample space - Relation between cost (per unit of sample

selection) precision

Important definitions

- Sampling distribution-The aggregates of the

various value of the statistic under

consideration so obtained(one from each sample)

may be grouped into a frequency distribution

which is known as sampling distribution of the

statistic. - Standard error-The standard deviation of the

sampling distribution of a statistic is known as

standard error.

Important definitions

- Parameter-A descriptive measure computed from

the data of a population is called as parameter. - Statistic-A descriptive measure computed from a

sample data is called as statistic. - Estimator-An estimator is a rule, function or

formula of variates for estimating the population

parameter. - Estimates -A particular value of an estimator

from a fixed set of value of a random sample is

known as estimate.

It is very easy and convenient to draw the

sample from homogenous population

The population having significant variations

(Heterogeneous), observation of multiple

individual needed to find all possible

characteristics that may exist

When sampling is not necessary?

- When population is very small.
- When we have extensive resources.
- When we dont expect a very high response.

Sampling

- Sampling is the process of selecting units or

elements from the study population in such a way

that the units or elements selected represent the

whole population

Principles of Sampling Theory

- Principle of Statistical Regularities.
- Principle of Inertia of large number.
- Principle of Validity.
- Principle of Optimization.

Principal Steps in a Sample Survey

- Statement of objectives.
- Definition of population to be studied.
- Determination of sampling frame and sampling

units. - Selection of proper sampling design.
- Organization of field work.
- Summary and analysis of data.

The Sampling Process

Plan procedure for selecting sampling units

4

Determine if a probability or non-probability

sampling method will be chosen

Determine sample size

3

5

Select actual sampling units

Select a Sampling Frame

2

6

Define the Target population

Conduct fieldwork

1

7

Advantage of sampling

- 1. Reduced cost of survey.
- 2. Greater speed of getting results.
- 3. Greater accuracy of results.
- 4. Greater scope.(When its impossible to study

the whole population) - 5. Adaptability.

Type of sampling method

- Probability sampling
- Non-probability sampling.

Probability sampling

- The term probability sampling is used when the

selection of the sample is purely based

on chance. - Every unit of the population has known nonzero

probability of being selected for the sample. The

probability of selection may be equal or unequal

but it should be non-zero and should be

known. The probability sampling is also called

the random sampling

Types Probability sampling

- Probability sampling includes
- Simple Random Sampling,
- Systematic Sampling,
- Stratified Random Sampling,
- Cluster Sampling
- Multistage Sampling.
- Multiphase sampling

Simple random sampling

- Applicable when population is small, homogeneous

readily available but there is no guarantee

that all segment of population will be

represented in SRS - All unit within the frame have an equal

probability. - It provides for greatest number of possible

samples. - Simplest common method of sampling
- Every sample are drawn unit by unit with equal

probability of selection on the basis of sample

drawn SRS may be divide into two group

Simple random sampling with replacement

- Simple random sampling with replacement
- If a unit is selected noted then

returned back to the population before the next

selection is made this procedure is repeated n

times is known as Simple random sampling with

replacement - Number of sample required Z2a pq

/(S.E)2 - Var(yn)

Simple random sampling without replacement

- If a unit is selected noted not returned back

to the population (selected unit is not available

for further selection) this procedure is known as

Simple random sampling with replacement - Number of sample requiredn0/1( n0-1)/N
- Var(yn)

Advantage of SRS

- Minimal knowledge of population needed
- Economical required less time.
- Easy to analyze data
- Disadvantage of SRS
- High cost low frequency of use
- Requires sampling frame
- Does not use researchers expertise
- Larger risk of random error than stratified

STEPS IN COMPUTING THE SIZE OF A SAMPLE

- Determine the size of the target population.
- Decide on the margin of error. As much as

possible the margin of error should not be higher

than 5. - Use the formula
- n N
- 1 Ne2 (Pagoso , et

al.) - n sample size
- N the size of the population
- e the margin of error
- Compute the sample proportion by dividing the

result in number 3 by the population.

STEPS IN COMPUTING THE SIZE OF A SAMPLE

- Population is 5,346
- Margin of error is 3
- Using the formula
- n ___5,346_
- 1 5346(.03)2
- n 920
- Sample proportion () 920 / 5346
- 17

Procedure of selection of a random sample

- Lottery method
- Use of random number table
- Tippets random number table
- Fisher Yates random number table
- Kendall smith random number table
- A million random digit number table.

Test for randomness of selected random number

- Frequency test
- Serial test
- Gap test
- Poker test.

Stratified random sampling

- Most commonly used sampling technique
- Stratum (Strata.pl) - Clear division into which

some thing is separated - The population (N) unit is divided into K group

or sub-population called strata - The sample is drawn by first dividing the

population into homogeneous sub-populations

(strata) and then drawing samples from each of

the sub-population (stratum). - It ensures proportionate representation of

character under study when drawing a sample from

a heterogeneous population and hence increases

the quantity of information for a given cost.

How to Stratify and How Many Strata?

- Strata should be homogeneous to increase

efficiency - Usually 5-10 Strata are taken. If too many strata

then the sample size within strata is too low.

Principle of stratification

- Strata should be non-overlapping should

together comprise the whole population. - Strata are homogenous themselves with respect to

characters under study. - Population are divided into strata on the basis

of sex , age, purpose ( milch, drought, dual )

breed, land holding capacity of livestock owners,

or any auxiliary information.

Auxiliary information

- Past data or some other information related

to the character on which we divide the

population into strata such that - Within strata -Variable are homogenous.

Between strata -Variable

are heterogeneous.

Sampling technique Use of auxiliary information

Stratified sampling technique Construction of strata

PPS Sample selection, to get more efficient estimator of the population parameter

Ratio regression estimation For estimation purpose.

Advantage of stratification

- Administrative convenience
- Improving sampling design
- Stratification makes it possible to use different

sampling design in different strata - Provide better cross section of population i.e.

adequate representation from various group of the

population - Gain in precision in the estimation of population

parameter.

Main problem in stratification

- What should be the number of strata?
- How to allocate n sample from different strata
- How we distribute population into various strata
- How to determine the boundary of the strata.

Allocation of sample size in different strata

- Allocation of the sample to different strata is

done by considering of 3 factors - Total no. of unit in the strata
- Variability within the stratum
- The cost of taking observation per sampling unit

in the stratum - (N.B-a good allocation is one where maximum

precision is obtained with minimum recourses)

Method of allocation

- Equal allocation
- Proportional allocation
- Neyman allocation
- Optimum allocation.

Equal allocation

- Most convenience
- Equal no. of sample are drawn from each stratum.
- Not usually sensible unless all strata are equal

size in terms of overall estimates precision.

However, maybe good if you want to compare

stratum means as your primary focus

Proportional allocation

- Given by Bowley (1926)
- Very common in practice
- Sampling fraction of each stratum is same

Proportional allocation

Allocate proportional to the size of the

strata-very widely used

Neyman allocation

- Also known as minimum variance allocation
- 1st discovered by Tschuprow (1923), but

rediscovered by J.Neyman (1934)

(Assumption sampling cost per unit

among different strata is same size of the

sample is fixed) - Allocation of sample among different strata is

based on joint consideration of stratum size

stratum variation

Optimum allocation

- Optimum allocation is mean to choose sample so as

to - Minimise the variance(maximise the precision) of

the estimate for fixed sample size(n). - Minimise the variance(maximise the precision) of

the estimate at fixed cost. - Minimise the total cost for fixed desired

precision

Cluster Sample

- A Cluster Sample is obtained by first grouping

the elements of the population into clusters and

then simple random sampling or other type of

sampling is used to select the clusters. - This type of sampling is used when a sampling

frame cannot be prepared for individual units in

the population but can be prepared for some

cluster of them or when substantial time or

expense can be saved by collecting data from a

modest number of clusters.

.

- When drawing a cluster sample, the first task is

to specify appropriate clusters. In doing so,

consideration has to be made about the level of

heterogeneity of elements within clusters.

- If clusters are generally heterogeneous, then

few large clusters may be selected to constitute

the sample but if they are homogeneous, then many

small-sized clusters should be used.

Difference between strata cluster

- Although strata and clusters are both

non-overlapping subsets of the population, they

differ in several ways. - All strata are represented in the sample but

only a subset of clusters are in the sample. - With stratified sampling, the best survey results

occur when elements within strata are internally

homogeneous. However, with cluster sampling, the

best results occur when elements within clusters

are internally heterogeneous.

Difference Between Cluster and Stratified Sampling

Population of L strata, stratum l contains nl

units

Population of C clusters

Take simple random sample in every stratum

Take srs of clusters, sample every unit in chosen

clusters

Drawbacks

- Sampling frame of entire population has to be

prepared separately for each stratum - When examining multiple criteria, stratifying

variables may be related to some, but not to

others, further complicating the design, and

potentially reducing the utility of the strata. - In some cases (such as designs with a large

number of strata, or those with a specified

minimum sample size per group), stratified

sampling can potentially require a larger sample

than would other methods

Post-stratification

- Stratification is sometimes introduced after the

sampling phase in a process called

"poststratification. - This approach is typically implemented due to a

lack of prior knowledge of an appropriate

stratifying variable or when the experimenter

lacks the necessary information to create a

stratifying variable during the sampling phase.

Although the method is susceptible to the

pitfalls of post hoc approaches, it can provide

several benefits in the right situation.

Implementation usually follows a simple random

sample. In addition to allowing for

stratification on an ancillary variable,

poststratification can be used to implement

weighting, which can improve the precision of a

sample's estimates.

Oversampling

- Choice-based sampling is one of the stratified

sampling strategies. In this, data are stratified

on the target and a sample is taken from each

strata so that the rare target class will be more

represented in the sample. The model is then

built on this biased sample. The effects of the

input variables on the target are often estimated

with more precision with the choice-based sample

even when a smaller overall sample size is taken,

compared to a random sample. The results usually

must be adjusted to correct for the oversampling

References

- Cochran, W. G., 1977. Sampling Techniques, Third

Edition. New York John Wiley SonsCochran, W.

G., 1977. Sampling Techniques, Third Edition. New

York John Wiley Sons - Des Raj and Chandhok, P. (1998). Sampling Survey

Theory. Narosa Publishing House, New Delhi - Horvitz, D. G., and D.J. Thompson, 1952. A

generalization of sampling without replacement

from a finite universe. The Journal of the

American Statistical Association 47663-685. - Murthy, M.N. (1977). Sampling Theory and Methods.

Statistical Publishing Society, Calcutta. - Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S and

Ashok, C. (1984). Sampling Theory of Surveys with

Applications. Indian Society of Agricultural

Statistics, New Delhi

Thank you