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STANDARD ERROR
• Standard error is the standard deviation of
the means of different samples of
population.
• Standard error of the mean
• S.E. is a measure which enables to judge
whether a mean of a given sample is
within the set of confidence limits or not, in
a population.
• S.E= SD/√n
SAMPLING
• Not possible to include each & every
member
• Not possible to examine all people of
country
• To test efficacy of drug to all patients
• Cooking of rice
• Costly collection & Time consuming
• Blood test
POPULATION
• Population
• Sample
• Parameter: a value calculated from a
population
– Mean (μ)
– Standard Deviation(σ)
• Sample
– Mean (X)
– Standard deviation ( s)
SAMPLING
• Sample is a part of population
• Estimation of population parameters
• To test the hypothesis about the
population from which the sample was
drawn.
• Inferences are applied to the whole
population but generalization are valid if
sample size is sufficiently large & must be
representative of the population-unbiased.
SAMPLING
• Sampling units are break down of
population into smaller parts which are
distinct and non overlapping so that each
member / element of the population
belongs to one and only one sampling
unit.
• When a list of all individuals , households,
schools and industries are drawn, it is
called sampling frame.
Sample
• A representative sample is the one with
which we can draw valid inference
regarding the population parameters.
• It is representative of the population under
study
• Is large enough but not too large
• The selected elements must be properly
approached, included and interviewed.
SAMPLING
• Selected by proper sampling from the
universe
• Differs from the universe in composition
solely by chance
• Each member has the equal chance to be
selected
• Sample mean is very close to the
population mean when bias has been
ruled out.
SAMPLING TECHNIQUES
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SIMPLE RANDOM SAMPLING
SYSTEMATIC SAMPLING
STRATIFIED SAMPLING
MULTISTAGE SAMPLING
CLUSTER SAMPLING
MULTIPHASE SAMPLING
CONVENIENT SAMPLING
QUOTA SAMPLING
SNOW BALL SAMPLING
SIMPLE RANDOM SAMPLING
• Every unit has an equal chance to be
included in the study
• This is done by assigning a no. to each
unit in the sampling frame.
• It is a haphazard collection of no. arranged
in a cunning manner to eliminate personal
selection or bias.
SYSTEMATIC RANDOM SAMPLING
• Sample is selected according to a
predetermined periodicity out of the total no. in
the series
• Systematic R Sampling selects every Kth
element in the population for the sample, with
the starting point determined randomly from the
first k elements.
• Easy to obtain, simple to design
• Time and labour are relatively small
• When population is large---results accurate
result.
• Sample values spread to entire population
STRATIFIED RANDOM SAMPLING
• It simply selects simple random samples from
mutually exclusive subpopulations or strata of
the population.
• Population is first divided into groups or strata
then sample is drawn according to size of the
strata---proportional allocation
• Reduced variability within the stratum yields
more precise estimate of the population.
• Stratification of a population results in strata of
various sizes
MULTISTAGE SAMPLING
• It refers to the sampling procedures
carried out in different stages using simple
random sampling technique.
• It introduces flexibility in sampling
• It enables use of exiting divisions & sub
divisions which saves extra labour.
CLUSTER SAMPLING
• A cluster is a selected group
• When units of population are natural groups or
clusters e.g. villages, wards, factories
• It allows small no. of target population to be
sampled.
• From the cluster chosen, the entire population is
surveyed.
• E.g. vaccination coverage
• Cost effective when population is scattered.
MULTIPHASE SAMPLING
• Part of the information is collected from
the whole sample and part from the
subsample
Non probability sampling
• Convenient sampling
– The probability that a subject is selected is
unknown
– It reflects selection bias of a person
• Quote sampling
TARGET POPULATION
• Is the population to which the investigator
wishes to generalize
• SAMPLE POPULATION
• Is the population from which the sample
was actually drawn
CONFIDENCE INTERVAL
• It is the interval or range of values which most
likely encompasses the true population value.
• It is the extent that a particular sample value
deviates from the population
• A range or an interval around the sample value
• Range or interval is called confidence interval.
• Upper & lower limits are called confidence limits.
C.I
• Random sample of 11 three years children
were taken, sample mean was 16 Kg and
standard deviation is 2 Kg. standard error
is 0.6 Kg. find C.I.
TESTING THE STATISTICAL
HYPOTHESIS
• Null hypothesis or hypothesis of no
difference (Ho)
• Alternative hypothesis of significant
difference (H‫)׀‬
• Test of significance to accept or reject
hypothesis
• A zone of acceptance
• A zone of rejection
Testing of hypothesis
• Z- test when sample is more than 30
• T-test when sample is less than 30
• Chi square test when the data is in
proportions
Sample size
• L= 2 σ
√n
√n= 2 σ
L
n= 4 σ²
L²
Example:
1.mean pulse rate=70
Pop. Standard deviation(σ)=8 beats
Calculate sample size?
2. Mean SBP=120,SD=10, calculate n?
Sample size
• Qualitative data
• N=4pq
L²
e.g.