Stat 3203 -sampling errors and non-sampling errors
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This document discusses various types of errors that can occur in sampling techniques, including sampling errors and non-sampling errors. It defines sampling errors as errors that arise from using a sample rather than the entire population. Non-sampling errors occur due to issues in data collection, processing, and analysis. Some key points made are that sampling error decreases with larger sample sizes, while non-sampling error does not necessarily decrease, and that important surveys conducted in Bangladesh include demographic, health, and nutrition surveys.
![Biases and variables errors
• Relation between biases and variables errors
𝐸(𝑡 − 𝜃)2= 𝑉 𝑡 + (𝐵(𝑡))2
• Total error can be writen as
𝑇𝑜𝑡𝑎𝑙 𝑒𝑟𝑟𝑜𝑟 = [𝑉 𝑡 + (𝐵(𝑡))2
]
1
2
• It has been seen that sample values are
subject to both sampling and non-sampling
error.](https://image.slidesharecdn.com/stat-3203samplingerrorsandnon-samplingerrors-180923173921/85/Stat-3203-sampling-errors-and-non-sampling-errors-16-320.jpg)
![Biases and variables errors
• 𝜃: true value
• 𝜃 𝑝 : Expected survey value
• 𝜃′: estimated parametric value
• Thus the total errorcan be written as
𝑡 − 𝜃 = 𝑡 − 𝐸 𝑡 + 𝐸 𝑡 − 𝜃 𝑝 + 𝜃 𝑝 − 𝜃′ + [𝜃′ − 𝜃]
– Sampling error
– Non-sampling error
• Both variable errors and biases can arise
either from sampling or non sampling
operations](https://image.slidesharecdn.com/stat-3203samplingerrorsandnon-samplingerrors-180923173921/85/Stat-3203-sampling-errors-and-non-sampling-errors-17-320.jpg)
![Adjustment for Non-response
• Variance:
𝑉( 𝑦 𝑤) = 𝑉1 𝐸2 𝑦 𝑤 + 𝐸1 𝑉2( 𝑦 𝑤)
= 𝑉1 𝑦 + 𝐸1[𝑉2 𝑦 𝑤 𝑛1, 𝑛2 ]
• Here 𝑉1 𝑦 = 1 − 𝑓
𝑆2
𝑛
• And 𝐸1[𝑉2 𝑦 𝑤 𝑛1, 𝑛2 ] =
1−𝑘
𝑛
𝑊2 𝑆2
2
• Combine them
(Proved)](https://image.slidesharecdn.com/stat-3203samplingerrorsandnon-samplingerrors-180923173921/85/Stat-3203-sampling-errors-and-non-sampling-errors-28-320.jpg)
Stat 3203 -sampling errors and non-sampling errors
- 1. Stat-3203: Sampling Technique-II (Chapter-4: Sampling Errors and Non-sampling Errors) (Section-B) Md. Menhazul Abedin Lecturer Statistics Discipline Khulna University, Khulna-9208 Email: [email protected]
- 2. Why have to know errors? • Sample estimate will always be subject to deviation from parameter. • 𝑦 is the unbiased estimate of 𝑌 with Standard deviation (Standard error) 𝑁−𝑛 𝑁𝑛 𝑆 (in case of Simple random sampling) • This error mainly appeared from two sources – Due to sample – Other than sample • It is imprtant to understand common sources and types of errors so you can avoid them.
- 3. Sampling Errors and Non-sampling Errors • The errors involved in collection, processing and analysis of the data in syrvey may be classified – Sampling error – Non-sampling error
- 4. Sampling Errors • Sampling Errors(1): The error which arises due to only a sample being used to estimate the population parameter is termed sampling error or sampling fluctuation. • Sampling Errors(2): Sampling error is the error that arises in a data collection process as a result of taking a sample from a population rather than using the whole population.
- 5. Sources of Sampling Errors • Population specification error • Sample frame error • Selection error • Non-response • Sampling errors Please visit https://www.qualtrics.com/blog/frequent- sampling-errors/
- 6. • If the sample size 𝑛 is equal to 𝑁 we expect that sampling error will be zero. • The decrease in sampling error is inversely proportional to the square root of the sample size. Sampling Errors Sample Size SamplingError
- 7. Sampling Errors • The amount of sampling error decreases with increase in the samle size but surprisingly it becomes otherwise in case of non-sampling error. • The sampling errors are assigned to an estimate because it is based on a ‘part’ from the ‘whole’ while non-sampling errors are assinged because there is departure from the prescribed rules of the survey, such as survey design, field work, tabulation andanalysis of data , etc.
- 8. How to remove? • There is only one way to eliminate this error. This solution is to eliminate the concept of sample, and to test the entire population. • In most cases this is not possible; consequently, what a researcher must to do is to minimize sampling process error. This can be achieved by a proper and unbiased probability sampling and by using a large sample size.
- 9. Non-sampling error • Non-sampling error can occur at any one or more stages of a survey i.e. planning, field work, and tabulation of survey data
- 10. Non-sampling error • Besides sampling error, the sample estimate may be subject to other error which, grouped toghther, are termed non-sampling errors. • Non-sampling error is the error that arises in a data collection process as a result of factors other than taking a sample.
- 11. Sources of Non-sampling error • Non sampling errors broadly grouped are in three number – Group A: Errors resulting from inadequete preparation (Non-response errors) – Group B: Errors resulting in the stage of data collection or taking observation (Response error). – Group C: Errors resulting from data processing (Tabulation errors)
- 12. Sources of Non-sampling error • Group A: Due to faulty sampling frame, biased method of selection units, inadequate schedule. – Ommision of duplication of units due to ambiguous definition of locale, units. – Inaccurate methods of interview and schedules – Difficulties arising due to unawarness on the part of respondents or faulty methods of enumeration/ data collection.
- 13. Sources of Non-sampling error • Group B: These errors refer, the difference between the individual true value and the corresponding sample value irrespsective of the reasons for discrepancy. • Landholder says 10 hactors • Cadastral says 11 hactors • Response error occur… • Main sources of these errors – Inadequate supervission and inspection of field staff – Inadequate trained and experienced field staff – Problems involved in data collection and other type of errors on the part of respondents.
- 14. Sources of Non-sampling error • Group C: These errors can be assinged to a number of defective methods of editing, coding puncing, tabulation, etc. • Main sources – Inadequate scrutiny of basic data – Errors in data processing operations such as editing, coding, punching, listing,verification etc – Others errors commited or admited during publication/ presentation of results.
- 15. Sources of Non-sampling error • These are not exhaustive,appear may large number of errors in a survey • It is difficult to ensure which of these errors are admitted, what is the frequncy of their occurance, and what are their effects on results? • Need subtle investigation at every step of survey.
- 16. Biases and variables errors • Relation between biases and variables errors 𝐸(𝑡 − 𝜃)2= 𝑉 𝑡 + (𝐵(𝑡))2 • Total error can be writen as 𝑇𝑜𝑡𝑎𝑙 𝑒𝑟𝑟𝑜𝑟 = [𝑉 𝑡 + (𝐵(𝑡))2 ] 1 2 • It has been seen that sample values are subject to both sampling and non-sampling error.
- 17. Biases and variables errors • 𝜃: true value • 𝜃 𝑝 : Expected survey value • 𝜃′: estimated parametric value • Thus the total errorcan be written as 𝑡 − 𝜃 = 𝑡 − 𝐸 𝑡 + 𝐸 𝑡 − 𝜃 𝑝 + 𝜃 𝑝 − 𝜃′ + [𝜃′ − 𝜃] – Sampling error – Non-sampling error • Both variable errors and biases can arise either from sampling or non sampling operations
- 18. Biases and variables errors Biases Variances Sampling Biasses Non-sampling Biases Sampling Variances Non-sampling Variances
- 19. Biases and variables errors • Generalization form of biases and variables errors 𝐸(𝑡 − 𝜃)2= ( 𝑖 𝐵𝑖) 2 + 𝑖 𝑆𝑖 2 /𝑛𝑖 𝑎𝑗 Where – 𝐵𝑖 stands for the bias – 𝑆𝑖 stands for varince – 𝑛𝑖 stands for sample size – 𝑎𝑗 Stands for the term for the sampling design used in the survey
- 20. Error decomposition Variance Error Non-response (B) Response(A) Component- I Component-II Non-sampling Sampling Biases
- 21. Non-response errors • Non response errors arises due to variaous causes – Not-at-home – Refusal – Lost schedule
- 22. Adjustment for Non-response • Population 𝑁 size divided into two parts – 𝑁1 (Response classs) and – 𝑁2 (Non-response classs) • Response classs mean= 𝑌1 • Non-response classs mean= 𝑌2 • Poulation mean 𝑌 = 𝑁1 𝑌1+𝑁2 𝑌2 𝑁 = 𝑊1 𝑌1 + 𝑊2 𝑌2 • 𝑊1 + 𝑊2 = 1
- 23. Adjustment for Non-response • Response classs sample size= 𝑛1 • Non-response classs sample size = 𝑛2 • Response classs sample mean= 𝑦1 • Non-response classs sample mean= 𝑦2 • 𝑦1 is a biased estimator of population mean= 𝑌 • Amount of bias 𝐵( 𝑦1) = 𝐸( 𝑦1) − 𝑌 = 𝑌1 − 𝑌 = 𝑊2( 𝑌1 − 𝑌2)
- 24. Adjustment for Non-response • 𝑦2 ′ mean of subsample of size 𝑛2 ′ (𝑛2 > 𝑛2 ′ ) • Since the population mean 𝑌 is expressed in terms of unknown parameters 𝑁1, 𝑁2, 𝑌1 and 𝑌2. • Find unbiased estimator of 𝑁1 and 𝑁2 • 𝑁1 = 𝑛1 𝑛 𝑁 and 𝑁2 = 𝑛2 𝑛 𝑁
- 25. Adjustment for Non-response • Hansen and Hurwitz technique – Take a random sample, wor, of n respondent and mail a schedule to all of them. – When the dead line of reply calculate non rsponse – Select a subsample 𝑛2 ′ from 𝑛2 and collect information from personal interview. – Pool the results from both the clases to estimate the population values.
- 26. Adjustment for Non-response • Pooled estimator of the population mean 𝑌2 is 𝑦 𝑤 = 1 𝑛 (𝑛1 𝑦1 + 𝑛2 𝑦2 ′ ) and variance is 𝑉 𝑦 𝑤 = 1 − 𝑓 𝑆2 𝑛 + 1 − 𝑘 𝑛 𝑊2 𝑆2 2 Where 𝑘 = 𝑛2 𝑛2 ′ , 𝑆2 is as usual 𝑆2 2 is the mean square in the non-response class. (Theorem 13.7.1)
- 27. Adjustment for Non-response • Proof: 𝐸( 𝑦 𝑤) = 𝐸1 𝐸2 𝑦 𝑤 𝑛1, 𝑛2 = 𝐸1 𝐸2 𝑛1 𝑦1 𝑛 𝑛1 + 𝐸1 𝐸2 𝑛2 𝑦2 ′ 𝑛 𝑛2 Again 𝐸1 𝐸2 𝑛1 𝑦2 𝑛 𝑛1 = 𝑁1 𝑁 𝑌1 And 𝐸1 𝐸2 𝑛2 𝑦2 ′ 𝑛 𝑛2 = 𝑁2 𝑁 𝑌2 Thus 𝐸( 𝑦 𝑤) = 𝑌 (unbiased)
- 28. Adjustment for Non-response • Variance: 𝑉( 𝑦 𝑤) = 𝑉1 𝐸2 𝑦 𝑤 + 𝐸1 𝑉2( 𝑦 𝑤) = 𝑉1 𝑦 + 𝐸1[𝑉2 𝑦 𝑤 𝑛1, 𝑛2 ] • Here 𝑉1 𝑦 = 1 − 𝑓 𝑆2 𝑛 • And 𝐸1[𝑉2 𝑦 𝑤 𝑛1, 𝑛2 ] = 1−𝑘 𝑛 𝑊2 𝑆2 2 • Combine them (Proved)
- 29. Adjustment for Non-response • Politz- Simmons’ techique. – Study yourself
- 30. Imporant surveys in Bangladesh • First census 1872 • 2nd census 1881 • Since then regular interval of 10 years • Occational sample surveys are also being conducted alongside to suppliment the short- time needs between censuses.
- 31. Imporant Surveys in Bangladesh • Surveys are divided in four broad categories – Contraceptive prevalence survey (CPS) – Demographic survey – Demographic and health survey (DHS) – Nutrition and health survey including goiter and (iodine deficiency disorder) IDD prevalence survey
- 32. Contraceptive prevalence survey (CPS) • Beginning 1979 funded USAID as apart of USAID’s global CPS project • Agreement BD gov and World Health System • Designed to provide rapid feedback to improve family planning programe performance by collecting information on contraceptive use. • CPSs became an important management tool for monitoring levels and trends of family planning program performance for quite a long time in Bangladesh. • 3rd Stage Cluster sampling and PPS
- 33. Demographic survey • Demographic data at the national level were lacking both in quality and coverage in Bangladesh. • Absecne of demographer • A number of demographic survey were conducted
- 34. Demographic survey • A number of demographic survey were conducted – Demographic Survey in East pakistan:1961-1962 – Population Growth Estimation(PGE):1962-65 – National Impact Survey (NIS): 1968-69 – Population Growth Survey(PGS):1968-70 – Bangladesh Retrospective Survey of Fertility and Mortality (BRSFM):1974 – Bangladesh Fertility Survey (BFS):1975 and 1989
- 35. Demographic and health survey (DHS) • Demographic and health survey (DHS) is the first of this kind in Bangladesh. • It is part of the worldwide Demographic and Health Survey(DHS). • Designed to collect data on fertility, mortality, family planning and maternal and child health. • Conducted by Mittra and Associates under the authority of the National Institute Research and Trainning, Under the Minstry of Health and Family Wealfare, Government of Bangladeh.
- 36. Demographic and health survey (DHS) • The BDHS: 1993-94 • The BDHS: 1996-97 • The BDHS: 1999-2000 • The BDHS: 2004 • The BDHS: 2007 • The BDHS: 2011 • The BDHS: 2014
- 37. Demographic and health survey (DHS)
- 38. Nutrition and health survey • East pakistan Nutrition Survey:1962-64 • Nutrition Survey of Rural Bangladesh:1975-1976 • Natinal Goiter Prevalence Survey:1981-82 • Bangladesh National Nutrition Survey: 1995-96 • Natinal Iodine Deficiency Disorder Survey – 1993 – 1999
- 39. Bangladesh Child Nutrition Survey • The BBS (Bangladesh Bureau of Statistics ) has been periodically conducting Child Nutrition Survey (CNS) as part of its regular activities since 1985 • Funding UNICEF ( United Nations International Children's Emergency Fund) • First conducted 1985-86 • 1989-90, 1995-96, 2000 • Objective: Nutritional status of pre school children aged 6-71 month