3. Important statistical terms
Population:
a set which includes all
measurements of interest
to the researcher
(The collection of all responses,
measurements,
or counts that are of interest)
Sample:
A subset of the population
4. Population -hg;+Vof _
• 'Population refers to all the individuals
or objects on which we have to make
some study.'
cg';Gwfgsf] nflu 5gf]6 ul/Psf ;Dk"0f{ dflg;Pjd
j:t'x¿sf] ;d"xnfO{ ;du|jf hg;+VofelgG5.
• Finite Population l;ldt hg;+Vof
• Infinite Population cl;ldt hg;+Vof
5. Sample-gd'gf_
The representative proportion of the population is
called a sample. 7"nf] hg;+Vofaf6 5gf]6 ul/Psf] k|ltlglwd"ns
;d"xnfO{ g} gd"gf elgG5 .
Koul (2009: 111) sf cg';f/ æhg;ªVofsf] k|ltlglwd"nsc+znfO{ g}
gd'gf elgG5 .Æ (The respresentative portion of the
population is called sample).
Best & Khan (1998: 13) sf cg';f/ ægd'gfPp6f cjnf]sg /
ljZn]if0fsf nflu hg;ªVofaf6 5gf]6 ul/Psf] ;fgf] cg'kftxf] .Æ (A
sample is a small proportion of a population
selected for observation and analysis.)
6. Characteristics of a good sample
• A true representative of the population
• Free from error due to bias
• Adequate in size for being reliable
• Units of sample should be complete
precise and up to date
• free from random sampling error
7. Sampling gd"gf 5gf]6
• Sampling is the process of selecting a
representative part of a population for
the purpose of determining the
characteristics of the whole population.
• Gfd"gf 5gf]6 To:tf] k|lqmof xf] h;4f/f Jolqm, j:t' /
36gfx¿sf] ;fgf] ;+Vof 5gf]6 ul/G5 / ;Dk"0f{ hg;+Vofsf]
af/]dfslx s'/f kQfnufpgljZn]if0ful/G5.
8. Definitions of Sampling
• Kerlinger (1986:110) sf cg';f/ æhg;ªVof jf ;du|tfsf] k|ltlglwTj x'g] u/L
hg;ªVofsf] s]xL efu 5gf]6 ul/g] k|lj|mofnfO{ gd'gf 5gf]6 (sampling)
elgG5 . (sampling is process of selecting any portion of a
population or universe as representative of the
population or universe).
• Koul (2009: 111) sf cg';f/ ægd'gf 5gf]6 To:tf] k|lj|mof xf] h;åf/f JolQm,
j:t' / 36gfx¿sf] ;fk]lIft ¿kdf ;fgf] ;ªVof 5gf]6 ul/G5 / ;Dk"0f{ hg;ªVofsf af/]df
s]xLs'/fkQfnufO{ljZn]if0ful/G5 .Æ
• Sampling is the process by which a relatively small
number of individuals, objects or events is selected and
analyzed in order to find out something about the
entire population.
9. Why sampling?
• Get information about large populations
• Less costs
• Less field time
• More accuracy i.e. Can Do A Better Job of Data
Collection
• When it’s impossible to study the whole
population
10. Steps in sampling Method
• Defining the population
hg;+VofnfO{ kl/efliftug]{
• Listing the population (Sampling Frame)
hg;+Vofsf] ;"lr tof/ ug]{
• Selecting the representative sample
hg;+Vofsf] k|ltlgwLd"ns gd'gf 5g]6 ug]{
• Obtaining an adequate sample cfjZos
gd'gf k|fKtug]{
12. Target Population:
The population to be studied/ to which the
investigator wants to generalize his results
Sampling Unit:
smallest unit from which sample can be
selected
Sampling frame
List of all the sampling units from which
sample is drawn
Sampling scheme
Method of selecting sampling units from
sampling frame
19. Advantages
1.Easy to conduct
2.High probability of achieving a representative
sample
3. Meets assumptions of many statistical
procedures
Disadvantages
1.Identification of all members of the population
can be difficult
2. Contacting all members of the sample can be
difficult
20. Systematic Sample
• Every kth member ( for example: every 10th
person) is selected from a list of all population
members.
23. Stratified Random Sample
• The population is divided into two or more groups
called strata, according to some criterion, such as
geographic location, grade level, age, or income, and
subsamples are randomly selected from each strata.
25. Advantages
•More accurate sample
•Can be used for both proportional and non-
proportional samples
•Representation of subgroups in the sample
Disadvantages
•Identification of all members of the population can
be difficult
•Identifying members of all subgroups can be
difficult
26. Cluster Sample
• The population is divided into subgroups
(clusters) like families. A simple random sample
is taken of the subgroups and then all members
of the cluster selected are surveyed.
29. Advantages
•Very useful when populations are large and
spread over a large geographic region
•Convenient and expedient
•Do not need the names of everyone in the
population
Disadvantages
•Representation is likely to become an issue
32. Non-Probability Sampling
• s'g} hg;ªVofaf6cWoogsf nflu5gf]6 ul/g]gd'gf;+of]usf]
cfwf/df geO{ k"j{lgwf{l/t;f]r jf ljrf/sf cfwf/df ul/G5, h;df k|To]s
PsfOx¿ gd'gfsf¿kdf 5gf]6 x'g] ;+efjgfx'Fb}geg] To;nfO{;+efjgf
/lxtgd'gf 5gf]6 (Non-Probability Sampling) elgG5 .
• Pant (2012) sf cg';f/ "Non-Probability sampling
is described as those samples, which are not
determined by chances but rather by personal
convenience or judgment of the researcher."
34. Convenience Sample
• Selection of whichever individuals are easiest to reach
• the process of including whoever happens to be
available at the time
• …called “accidental” or “haphazard” sampling
• It is done at the “convenience” of the researcher
36. Purposive Sample
the process whereby the researcher selects a
sample based on experience or knowledge
of the group to be sampled
…called “judgment” sampling
39. Quota Sample
1. Determine what the population looks like
in terms of specific qualities.
2. Create “quotas” based on those qualities.
3. Select people for each quota.
41. disadvantages…
…people who are less accessible (more
difficult to contact, more reluctant to
participate) are under-represented
42. Snowball Sample
In this method the first members of the sample
are identified.
Subsequent members of the sample come by
recommendation or identification by the first
members.
This does not guarantee a representative sample,
but it can be the best method when the subject of
research is sensitive or relates to a population that is
hard to contact (e.g people engaged in social security
fraud).
46. 46
Ways to Determine Sample Size
• Blind guess
• Available budget
• Bayesian considerations
• Rules of thumb
– Main group n > 100
– Subgroups 20 < n < 100
• Standards for comparable studies
• Statistical precision
47. 47
Statistical Precision
Must know:
• Variability of population and individual
stratum
• Acceptable level of sampling error
• Needed level of confidence
• Type of distribution (if non-normal)
49. 49
Sample Size Formula:
Example #1
Suppose a survey researcher, studying
expenditures on lipstick, wishes to have a 95%
confident level (Z) and a range of error (E) of
less than $2.00. The estimate of the standard
deviation is $29.00.
51. 51
Suppose, in the same example as the one
before, the range of error (E) is acceptable at
$4.00. By how much is sample size is
reduced?
Sample Size Formula:
Example #2
54. 54
2
2
E
pqz
n
Where:
n = number of items in samples
Z2 = square of confidence interval in standard error units
p = estimated proportion of success
q = (1-p) or estimated the proportion of failures
E2 = square of maximum allowance for error between true
proportion and sample proportion, or zsp squared.
55. 55
Ex 1 Calculating Sample Size
at the 95% Confidence Level
753
001225.
922.
001225
)24)(.8416.3(
)035( .
)4)(.6(.)961.(
n
4.q
6.p
2
2