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.

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

• 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 L²Example: 1.mean pulse rate=70

Pop. Standard deviation(σ)=8 beatsCalculate sample size?

2. Mean SBP=120,SD=10, calculate n?

Sample size

• Qualitative data

• N=4pq L²e.g.