POPULATION AND SAMPLING.pptx

POPULATION AND
SAMPLING
BY: MART NIKKI LOU M. MANTILLA
Methods of Research- Population and Sampling

OUTLINE OF PRESENTATION:
• POPULATION
• POPULATION PARAMETERS
a. Average
b. Mean
c. Median
d. Mode
e. Range
f. Standard Deviation (SD)
• ALL ABOUT SAMPLING

POPULATION
 The entire aggregation of items from which a
samples can be drawn is known as population.
 In sampling, the population may refer to the units,
from which the sample is drawn.
 A population of interest may be the universe of
nation or cities.
 The target group to which the findings (of a
study) would ultimately apply or;
 Is the term statisticians use to describe a large set
or collection of items that have something in
common.
 “N” represents the size of the population

POPULATION PARAMETERS
Statistics such as average and standard
deviations, mean, mode are some population
parameters

Mean : (average)
O The "Mean" is computed by adding all of
the numbers in the data together and
dividing by the number elements
contained in the data set.

Example :
O Data Set = 2, 5, 9, 3, 5, 4, 7
O Number of Elements in Data Set = 7
O Mean = ( 2 + 5 + 9 + 7 + 5 + 4 + 3 ) / 7 = 5

O Median : (middle)
O The "Median" of a data set is dependent on
whether the number of elements in the data set
is odd or even.
O First reorder the data set from the smallest to
the largest
O Mark off high and low values until you reach the
middle.
O If there 2 middles, add them and divide by 2.

O Examples : Odd Number of Elements
O Data Set = 2, 5, 9, 3, 5, 4, 7
O Reordered = 2, 3, 4, 5, 5, 7, 9
^
O Median= 5

O Examples : Even Number of Elements
O Data Set = 2, 5, 9, 3, 5, 4
O Reordered = 2, 3, 4, 5, 5, 9
^ ^
O Median = ( 4 + 5 ) / 2 = 4.5

O Mode : (most often)
O The "Mode" for a data set is the element
that occurs the most often.
O It is not uncommon for a data set to have
more than one mode.
O This happens when two or more elements
occur with equal frequency in the data set.

O Example :
O Data Set = 2, 5, 9, 3, 5, 4, 7
O Mode = 5
O Example:
O Data Set = 2, 5, 2, 3, 5, 4, 7
O Modes = 2 and 5

O Range :
O The "Range" for a data set is the
difference between the largest value and
smallest value contained in the data set.
O First reorder the data set from smallest to
largest then subtract the first element
from the last element.

Examples :
O Data Set = 2, 5, 9, 3, 5, 4, 7
O Reordered = 2, 3, 4, 5, 5, 7, 9
O Range = ( 9 - 2 ) = 7

SAMPLE
Sample: is that part of the target population
which is actually enquired upon or investigated1.
Or
Sample: is a subset of population, selected in
such a way that itis representative of the larger
population2

Sampling: is the process of selecting a small
number of
elements from a larger defined target group of
elements such that the information gathered from the
small group will allow judgments to be made about
the larger groups.
conclusions based on the sample results may be
attributed only to the population sampled*.

• Sampling unit: is the unit of selection
• Unit of study or element: is the subject on which information is
obtained.
• Sampling frame: list of all sampling units in the target population
is called a sampling frame.
• Sample size: the number of units or subjects sampled for inclusion
in the study is called sample size.
• Sampling technique: Method of selecting sampling units from
sampling frame

NEED FOR SAMPLING
1. Complete enumeration may not be possible.
2. Resources: Lower cost, Lesser demand on
personnel.
3. Speed: Faster results due to lesser coverage.
4. Reliable information: Due to small size - better
trained
personnel, more accurate methods, better
supervision.

To draw conclusions about population from sample, there
are
two major requirements for a sample.
a) Firstly, the sample size should be large.
b) Secondly, the sample has to be selected appropriately
so that
it is representative of the population. Sample should
have all
the characteristics of the population.

DISADVANTAGE OF SAMPLING
1. Sampling entails an argument from the fraction to the
whole. Validity depends on representativeness of the
sample.
2. Fails to provide precise information in case of small
segments containing few individuals.
3. Not necessary in studies where complete enumeration is
needed.
4. May cause a feeling of discrimination among the subjects
who are not included in the study.

TYPES OF SAMPLES

SIMPLE RANDOM SAMPLES
Equal probability of selection of units for inclusion in the study
 Requires a list of all sampling units (sampling frame)
 Each individual is chosen randomly.
 Methods:
a. Lottery method (possible for finite population)
b. Random number tables
c. Software that generate random numbers

 Simple random method
• With replacement
• Without replacement
 Advantage
• Very scientific method
• Equal chance of all subjects for selection
 Disadvantage
• Requires sampling frame

SYSTEMATIC RANDOM SAMPLING
 Systematic sampling is a commonly employed
technique,
when complete and up to date list of sampling units is
available.
 A systematic random sample is obtained by
• Selecting the first unit on a random basis
• Then others are included on the basis of sampling
interval
I = N/n.

For example, if there are 100 patients (N) in a hospital and to select a
sample of 20 patients (n) by systematic random sampling procedure,
• Step 1: write the names of 100 patients in alphabetical order or their
roll numbers one below the other.
• Step 2: sampling fraction: divide N by n to get the sampling fraction
(k).In the example k=100/20 = 5.
• Step 3: randomly select any number between 1 to k i.e. between 1 to
5. Suppose the number we select is 4.
• Step 4: patient number 4 is selected in the sample.
• Step 5: Thereafter every 4+k th patient is selected in the sample until
we reach the last one.

 Advantage:
• easy to draw, simplicity.
• assurance that the population will
be evenly sampled.
 Disadvantage:
• Requires sampling frame.

STRATIFIED RANDOM SAMPLING
• Preferred method when the population is heterogeneous with
respect to characteristic under study.
• Population is divided into groups or strata on the basis of
certain characteristics.
• A simple random sample is selected from each strata.
• Ensures representation of different strata/ groups in the study
population.
• Can be done by selecting individuals from different strata in
certain fixed predetermined proportions.

• For example, if we draw a simple random sample from a
population, a sample of 100 may contain
• 10 to 15 from high socioeconomic group
• 20 to 25 from middle socioeconomic group
• 70 to 75 from low socioeconomic group
• To get adequately large representation for all the three
socio
economic structures, we can stratify on socioeconomic class
and select simple random samples from each of the three
strata.

 Advantage:
• All groups, however small are equally represented.
• When we want to highlight a specific subgroup within the population.
Ensures presence of the subgroup.
• Observe existing relationships between two or more subgroups.
• Can representatively sample even the smallest and most inaccessible
subgroups in the population. To sample the rare extremes of the given
population.
• Higher statistical precision compared to simple random
sampling. (d/t lesser variability). So less time and money.
 Disadvantage:
• Requires a sampling frame for each stratum separately.
• Requires accurate information on proportions of each stratum

MULTISTAGE RANDOM SAMPLING
 Multistage sampling refers to sampling plans where the sampling is
carried out in stages using smaller and smaller sampling units at each
stage.
 As the name suggest, multistage sampling is carried out in steps.
This Method is regularly use in conducting national surveys on large
scale. It is an economical and time saving method of selecting a
sample out of widely spread population.
 In this method first the population will be divided on the state basis,
then districts, then cities, then locality, wards, individuals who are
sampled at different stages until a final sample unit.

MULTIPHASE SAMPLING
Is slightly different from multi-stage sampling. With multi-
phase sampling, the sampling unit at each phase is the
same, but some f them are interviewed in detail or asked
more questions than others ask. In other words, all the
members of the sample provided basic information and
some of them provided more and detailed information.

CLUSTER SAMPLING
 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.
 Cluster sampling is used when the population is heterogeneous.
 Clusters are formed by grouping units on the basis of their
geographical locations.
 Cluster sampling is a very useful method for the field epidemiological
research and for health administrators.

 Types:
• One stage – when all units in the selected cluster are selected.
• Two stage – only some units from a selected cluster are taken using
simple random or systematic random sampling.
 Advantages
• Simple as complete list of sampling units within population not required
• Low cost
• Can estimate characteristics of both cluster and population
• Less travel/resources required
 Disadvantages
• Potential problem is that cluster members are more likely to be
alike, than those in another cluster (homogenous).
• Each stage in cluster sampling introduces sampling error—
the more stages there are, the more error there tends to be

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POPULATION AND SAMPLING.pptx

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