Stratified Random Sampling. Cluster Sampling. Systematic Sampling. Judgement sampling. Quota Sampling. Convenience Sampling. Sampling Distribution of sample mean. Sampling with Replacement. Sampling Without Replacement. Sample Distribution of Proportions. Sample distribution of difference between two means. Sampling techniques. With Replacement. Without Replacement.

2. SAMPLING THEORY
Types of Sampling and Sampling Techniques
Presented by:
Fahad Farooq
Osama Waheed
Hamza Iltaf
Muhammad Uzair
Huzaifa Ijaz Minhas
Supervisor: Ma’am Dr. Misbah Baloch

3. Contents:
 Stratified Random Sampling.
 Cluster Sampling.
 Systematic Sampling.
 Judgement sampling.
 Quota Sampling.
 Convenience Sampling.
 Sampling Distribution of sample mean.
 Sampling with Replacement.
 Sampling Without Replacement.
 Sample Distribution of Proportions.
 Sample distribution of difference between two means.
 Sampling techniques.
 With Replacement.
 Without Replacement.

4. Types of Random Sampling:

5. Simple Random Sampling:
 A simple random sample is a subset of a statistical population in which each
member of the subset has an equal probability of being chosen.
 Random sampling is used in science to conduct randomized control tests or for
blinded experiments.
 Although simple random sampling is intended to be an unbiased approach to
surveying, sample selection bias can occur.
 When a sample set of the larger population is not inclusive enough, representation
of the full population is skewed and requires additional sampling techniques.

7. Stratified Random Sampling:
 Stratified random sampling is a method of sampling that involves dividing a population into
smaller groups–called strata.
 The groups or strata are organized based on the shared characteristics or attributes of the
members in the group.
 Stratified random sampling is more advantageous when the population varies widely since it
helps to better organize the samples for study.
 Stratified random sampling works well for populations with a variety of attributes but is
otherwise ineffective if subgroups cannot be formed.

9. Cluster Sampling:
 This method is used when there are different subsets of groups present in a larger
population.
 mutually homogeneous yet internally heterogeneous groupings are evident in a statistical
population.
 In this sampling plan, the total population is divided into these groups known as clusters.
 It can be Single-stage, two-stage or multi-stage Cluster Sampling.

11. Systematic Sampling:
 Sampling method in which sample members from a larger population are selected according
to a random starting point but with a fixed, periodic interval.
 This interval, called the sampling interval, is calculated by dividing the population size by the
desired sample size.
 The central assumption, that the results represent the majority of normal populations,
guarantees the entire population is evenly sampled.
 disadvantage is that the population needs to exhibit a natural amount of randomness to it else the
risk of choosing similar instances is increased, defeating the purpose of the sample.

13. Judgement Sampling:
 A non-probability sampling technique in which the sample members are chosen only on the
basis of the researcher’s knowledge and judgment.
 There are chances that the results obtained will be highly accurate with a minimum margin
of error.
 The researcher’s knowledge is primary in this sampling process as the members of the
sample are not randomly chosen.
 If the knowledge of researcher lacks then the result will not be satisfactory.

15. Quota Sampling:
 Sampling method in which researchers create a sample involving individuals that represent
a population.
 Researchers choose these individuals according to specific traits or qualities.
 The final subset will be decided only according to the interviewer’s or researcher’s
knowledge of the population.
 population do not have an equal chance of being selected to be a part of the sample group.

17. Convenience Sampling:
 Sampling in which people are sampled simply because they are "convenient" sources of
data for researchers.
 Convenience sampling is defined as a method adopted by researchers where they collect
market research data from a conveniently available pool of respondents.
 . It is the most commonly used sampling technique as it’s incredibly prompt, uncomplicated,
and economical.
 In many cases, members are readily approachable to be a part of the sample.

19. Sampling Distribution of sample mean:
 The mean of the sampling distribution of the mean is the mean of the population from which
the scores were sampled.
 Therefore, if a population has a mean μ, then the mean of the sampling distribution of the
mean is also μ.
 The symbol μM is used to refer to the mean of the sampling distribution of the mean.
𝜇𝑥 = 𝜇

20.  Variance
 Standard Deviation/Error of Mean

21. Sampling with Replacement:
 In sampling with replacement, the mean of all sample means equals the mean of the
population:
 Variance:
𝜎𝑥
2
=
𝜎2
𝑛
 standard deviation:

22. Sampling Without Replacement:
 Variance:
𝜎𝑥
2
=
𝜎2
𝑛
𝑁 − 𝑛
𝑁 − 1
 Standard deviation/Error:

23. Sample Distribution of Proportions:
 The Sampling Distribution of Proportion measures the proportion of success, i.e. a
chance of occurrence of certain events, by dividing the number of successes i.e. chances by
the sample size ’n’.
 Thus, the sample proportion is defined as: 𝑝 =
𝑥
𝑛
 Sample distribution proportion with replacement:
 Sample distribution proportion without replacement:

24. Sample distribution of difference between two means:
 The sampling distribution of the difference between the two means, i.e. X͞ 1 – X͞ 2.
 X͞ 1 – X͞ 2 is equal to the difference between the Population Means. Symbolically.
 With Replacement:
 Without Replacement:

25. Sampling techniques:
 With Replacement:

29.  Without Replacement: