Systematic, Stratified & Multistage Sampling

Stratified Sampling

• Stratified random sampling is one of the restricted random methods which, by using available information concerning the data attempts to design a more efficient sample than that obtained by the homogeneous groups or classes called strata.
• Then a sample may be taken from each group by simple random method, and result sample is called a stratified sample.
• Under this sampling design, the entire population (universe) is divided into strata (groups), which are mutually exclusive and collectively exhaustive.
• By mutually exclusive, it is meant that if an element belongs to one stratum, it cannot belong to any other stratum.
• Strata are completely exclusive if all the elements of various strata put together completely cover all the elements of the population.

Limitations

• Utmost care must be exercised in dividing the population into various strata.
• The items from each strata should be selected at random.

Types

Systematic Sampling

• In Proportionate stratified sampling, the size of the sample in each stratum is proportional to the size of the population of the stratum.
• In Disproportionate stratified sampling, the sample would be considered as an example as there is no proportion in the sample of the universe. Disproportionate stratified sampling also includes procedures of taking an equal number of items from stratum irrespective of its size.

Merits

• Stratified sampling is regarded as the most efficient system of sampling.
• Stratified sampling ensures greater accuracy.
• As compared to random sample, stratified samples can be more concentrated geographically.

Multistage sampling

• A type of probability sampling method
• In which sample members from a larger population are selected according to a random starting point and a fixed, periodic interval.
• This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.
• Despite the sample population being selected in advance, systematic sampling is still thought of as being random, provided the periodic interval is determined beforehand and the starting point is random.

Limitations

Merits

• There is the possibility of losing vital information from the population.
• It may not be possible to select the required sample size if the population is too small.
• It may not be good for periodic data.

• It is very convenient to adopt.
• It involves less time and work than other methods.
• Satisfactory Results

• A complex form of cluster sampling. A multi-stage sample is one in which sampling is done sequentially across two or more hierarchical levels.
• Used frequently when a complete list of all members of the population not exists and is inappropriate.
• Although multi stage sampling and stratified sampling bear some superficial similarities, they are substantially different.
• In stratified sampling, a random sample is drawn from all the strata, where in cluster sampling only the selected clusters are studied, either in single or multi-stage.

TYPES OF SAMPLING

ADVANTAGES

• Sampling frames are available at higher stages but not for the ultimate sampling units. Construction of sampling frames at each lower stage becomes less costly.
• Cost efficiency with use of clusters at higher stages of selection
• Flexibility in choice of sampling units and methods of selection at different stages
• Normally more accurate than cluster sampling for the same size sample

Stages in Multi stage Sampling

DISADVANTAGES

• First-stage sampling units are called primary sampling units or PSUs.
• Second-stage sampling units are called secondary sampling units or SSUs.
• Last-stage sampling units are called ultimate sampling units or USUs.
• Example

• Less accurate than SRS of same size (but more accurate for same cost)
• Further analysis is difficult as the matter so collected is bulky

RECAP

&

CASE STUDIES

Introduction

Stratified Sampling

Multi stage Sampling

Systematic Sampling

• There is a need for adequate and credible data which is essential in different fields of human activity and business.

• There are two ways to obtain such an information :

(i) Census Method and

(ii) Sampling Method

• Census Method – Data is collected from each and every unit belonging to the population or universe.

• Sampling Method- Data is collected from a subset or a part of the population or universe.

• A random sample
• Members of the population are first divided into strata
• Then are randomly selected to be a part of the sample
• The representation of strata in sample size can be proportionate or disproportionate.

• A complex form of cluster sampling
• Cluster sampling is a type of sampling which involves dividing the population into clusters. Then, one or more clusters are chosen at random and everyone within the chosen cluster is sampled.
• In multistage Sampling, Instead of using all the elements contained in the selected clusters, the researcher randomly selects elements from each cluster.

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• Statistical method 
• Involves random selection of elements from an ordered sampling frame
• Each element in the population has a known and equal probability of selection
• There should no hidden pattern because of the threat to randomness.

Study of whatsapp addiction in SY BBA LLB Students

Sampling

Strata C

S.No. Name of the Student

Below 3.0

Strata B

3.3 - 3.0

Strata A

• Sampling is the concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population.

• Purpose of Sampling is to draw inference about the population.

• It is a tool which helps to know the characteristics of the population by examining only a smart part of it.

Above 3.3

Study of whatsapp addiction in LLB Students

• Population Size - 26
• Sampling Fraction- ½
• Final Sample Size - 13
• Sample possibilities- Simran, Jahnavi, Mansi, Suyash, Prajakta, Shikha, Sushant, Isha Kakkad, Vedant, Chirayu, Rishabh, Sakshi, Ankita, Suman, Meghna, Harshita, Nisha, Smiti, Raghav, Karan, Nupur, Kruti, Mahi, Sagar, Niyati, Jaineel

• Population Size - 7
• Sampling Fraction- ½
• Final Sample Size - 4 (round off)
• Sample possibilities- Garima Agrawal, Raina Varma, Nishita Banka, Aayesh Gandhi, Gaurav Matta, Hetvi Doshi, Vyoma Mehta

Study of whatsapp addiction in SY BBA LLB Students

• Population Size - 4
• Sampling Fraction- ½
• Final Sample Size - 2
• Sample possibilities- Arshia Saraf, Abhilipsa Panda, Isha Singh, Mohak Rana

For this study the sample size can be broke into following possible clusters

• Sample Size- 9 students out of 36
• Sampling Interval - 36/9 = 4
• Every 4th student after a random start point between 1 to 4
• Random starting point
• Selected sample

1. Garima Agrawal

2. Jahnavi Agrawal

3. Raghav Bhatia

4. Chirayu Biyani

5. Harshita Choudhary

6. Rishabh Dhanuka

7. Shikha Dharia

8. Hetvi Doshi

9. Aayesh Gandhi

10. Mansi Jain

11. Nupur Jain

12. Suyash Jain

13. Vedant Jalan

14. Prajakta Joshi

15. Isha Kakkad

16. Sakshi Kansal

17. Karan Kapoor

18. Gaurav Matta

19. Mahi Mehta

20. Vyoma Mehta

21. Abhilipsa Panda

22. Suman Praharaj

23. Kruti Kamdar

24. Sushant Ramakrishna

25. Ankita Rath

26. Arshia Saraf

27. Niyati Shah

28. Simran Morakhia

29. Meghna Sharma

30. Isha Singh

31. Raina Varma

32. Nisha Fariya

33. Nishita Banka

34. Jaineel Vashi

35. Smiti Singrodia

36. Sagar Shrivastava

• Country
• State
• City
• Block/ Wards
• College
• Course
• Year

Systematic, Stratified & Multistage Sampling

BY:- Rishabh Dhanuka (09)

Kruti Kamdar (32)

Mansi Jain (13)

Mohak Rana (34)