moduule 7-stats-sampling

8/7/2019 moduule 7-stats-sampling

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Module 7

Sampling

and

sampling distribution
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Population

A group ofindividuals oritems that

share one or more characteristics from

which data can be gathered and

analyzed.
http://www.businessdictionary.com/definition/group.htmlhttp://www.businessdictionary.com/definition/individual.htmlhttp://www.businessdictionary.com/definition/item.htmlhttp://www.investorwords.com/4525/share.htmlhttp://www.businessdictionary.com/definition/characteristic.htmlhttp://www.businessdictionary.com/definition/data.htmlhttp://images.google.com/imgres?imgurl=http://static.howstuffworks.com/gif/population-six-billion-1.jpg&imgrefurl=http://people.howstuffworks.com/population-six-billion.htm&usg=__xWZKb-eBJASe2O4SPP_3TRPIiVo=&h=329&w=400&sz=50&hl=en&start=1&tbnid=KLQCap6blHwhOM:&tbnh=102&tbnw=124&prev=/images%3Fq%3Dpopulation%26hl%3Den%26rls%3Dcom.microsoft:en-us:IE-SearchBox%26rlz%3D1I7SPDA_en%26sa%3DGhttp://images.google.com/imgres?imgurl=http://static.howstuffworks.com/gif/population-six-billion-1.jpg&imgrefurl=http://people.howstuffworks.com/population-six-billion.htm&usg=__xWZKb-eBJASe2O4SPP_3TRPIiVo=&h=329&w=400&sz=50&hl=en&start=1&tbnid=KLQCap6blHwhOM:&tbnh=102&tbnw=124&prev=/images%3Fq%3Dpopulation%26hl%3Den%26rls%3Dcom.microsoft:en-us:IE-SearchBox%26rlz%3D1I7SPDA_en%26sa%3DGhttp://www.businessdictionary.com/definition/data.htmlhttp://www.businessdictionary.com/definition/characteristic.htmlhttp://www.investorwords.com/4525/share.htmlhttp://www.businessdictionary.com/definition/item.htmlhttp://www.businessdictionary.com/definition/individual.htmlhttp://www.businessdictionary.com/definition/group.html


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sampling

Sampling is that part ofstatistical practice

concerned with the selection of individualobservations intended to yield some knowledge

about a population of concern, especially for the

purposes ofstatistical inference.

Each observation measures one or moreproperties (weight, location, etc.) of an

observable entity enumerated to distinguish

objects or individuals.
http://en.wikipedia.org/wiki/Statisticalhttp://en.wikipedia.org/wiki/Population_(statistics)http://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Population_(statistics)http://en.wikipedia.org/wiki/Statistical


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The sampling process comprises of

several stages

1. Defining the population ofconcern

2. Specifying a sampling frame, aset of items or events possible tomeasure

3. Specifying a sampling method forselecting items or events from theframe

4. Determining the sample size

5. Implementing the sampling plan

6. Sampling and data collecting

7. Reviewing the sampling process
http://en.wikipedia.org/wiki/Set_(mathematics)http://en.wikipedia.org/wiki/Set_(mathematics)


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Two types of data collection

Census technique In this technique each and every item or unit

constituting the universe is selected for datacollection

Also called 100% enumeration technique

Sample technique Under this technique some representative units, or

informants are selected from a universe


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Methods of sampling

Probability sampling methodNon-probability sampling

method


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Sub classification of

non-probability sampling Quota method

whole universe is dividedfirst into certain parts andthe total sample is allocatedamong these parts

Then judgment is used toselect the subjects or unitsfrom each segment basedon a specified proportion

For example, an interviewermay be told to sample 200

females and 300 malesbetween the age of 45 and60.

Also refer merits and demerits
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Convenience method It is a type of purposive sampling in which the sample units

are selected purposively by the investigator to suit hisconvenience in the matter of location, and contact with theunits

it is the method most commonly employed in many practicalsituations

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Sequential method It is type of purposive sampling in which a number

of sample lots are drawn one after another in order

of a sequence till a satisfactory sample lot isobtained

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Sub classification of

probability sampling

Simple random sampling Is a type of unrestricted random sampling in which

each and every item of the universe is selected by

chance, without interference of any bias orpurpose on the part of the invigilator

In a simple random sample of a given size, all such

subsets of the frame are given an equal

probability. Each element of the frame thus has an equal

probability of selection: the frame is not subdivided

or partitioned
http://images.google.com/imgres?imgurl=http://ccelearn.csus.edu/wasteclass/images/randomSampling.jpg&imgrefurl=http://ccelearn.csus.edu/wasteclass/mod9/mod9_05.html&usg=__SrQbYBnUQ2D4jQ3pkqPl3qM5EQk=&h=334&w=302&sz=12&hl=en&start=1&um=1&tbnid=k9wek8n1ksfXfM:&tbnh=119&tbnw=108&prev=/images%3Fq%3Dsampling%26um%3D1%26hl%3Den%26rls%3Dcom.microsoft:en-us:IE-SearchBox%26rlz%3D1I7SPDA_enhttp://en.wikipedia.org/wiki/Simple_random_samplehttp://images.google.com/imgres?imgurl=http://ccelearn.csus.edu/wasteclass/images/randomSampling.jpg&imgrefurl=http://ccelearn.csus.edu/wasteclass/mod9/mod9_05.html&usg=__SrQbYBnUQ2D4jQ3pkqPl3qM5EQk=&h=334&w=302&sz=12&hl=en&start=1&um=1&tbnid=k9wek8n1ksfXfM:&tbnh=119&tbnw=108&prev=/images%3Fq%3Dsampling%26um%3D1%26hl%3Den%26rls%3Dcom.microsoft:en-us:IE-SearchBox%26rlz%3D1I7SPDA_enhttp://en.wikipedia.org/wiki/Simple_random_sample


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Stratified random sampling In this different number of samples are drawn at

random from different strata, or divisions of the

universe The two main reasons for using a stratified

sampling design are [1] to ensure that particular

groups within a population are adequately

represented in the sample, and [2] to improve efficiency by gaining greater

control on the composition of the sample


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Systematic random sampling or quasirandom sampling

In this the initial unit of the sample is selected at

random from the initial stratum of the universe ,andthe other units are selected at a certain spaceinterval from the universe arranged in a systematicorder like, numerical , alphabetical or geographicalorder

Selecting (say) every 10th name from thetelephone directory is called an every 10thsample, which is an example ofsystematic sampling
http://en.wikipedia.org/wiki/Systematic_samplinghttp://en.wikipedia.org/wiki/Systematic_sampling


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Cluster sampling

In this whole universe is subdivided into certain prominent

subgroups called clusters, and certain such clusters are

selected at random to provide for sample

Sometimes it is cheaper to 'cluster' the sample in some

way e.g. by selecting respondents from certain areas only, or

certain time-periods only

Cluster sampling is an example of '' or '

multistage sampling': in the first stage a sample of areas

is chosen; in the second stage a sample of respondentwithin those areas is selected.
http://en.wikipedia.org/wiki/Cluster_samplinghttp://en.wikipedia.org/wiki/Multistage_samplinghttp://en.wikipedia.org/wiki/Multistage_samplinghttp://en.wikipedia.org/wiki/Cluster_sampling


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Area sampling The total area under investigation is divided into

small sub-areas which are sampled at random or

by some restricted random process. Each of the chosen sub-areas is then fully

inspected and enumerated, and may form a frame

for further sampling if desired.

Suitable for any common problem of population


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Sampling errors

Are those errors whichoccur on account of the

use of sample techniques

in the collection of data

There is always some

difference between the

exact and estimated

values of the parameterswhich is nothing but

sampling error


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Causes of sampling errors

Selection of irrelevant , or unrepresentativeitems as the samples

Improper substitution of the sample items

Bias in the estimating method Variability of the population

Faulty demarcation of the statistical units

Fluctuation of sampling Smallness of the size of the sample


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Relation between sampling errors

and size of the sample

S

ize

of

the

erro

r

Size of the sample

moduule 7-stats-sampling

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