Click to edit Master text styles Second level Third level Fourth level Fifth level Quantitative Analysis.

Presentación del tema: "Click to edit Master text styles Second level Third level Fourth level Fifth level Quantitative Analysis."— Transcripción de la presentación:

1 Click to edit Master text styles Second level Third level Fourth level Fifth level Quantitative Analysis

2 Population Sample Sample Size Sampling Technique Data Collection Methods

3 What we are interested in as a whole All students of KMUTNB Students of faculty of IT Depend on in the study Finite population Countable, possible to count Infinite population Uncountable, impossible to count

4 A part of population selected for study as it is not possible to study the whole population due to cost and time If study the whole population, then it is census Sample should have all the properties of the population be of proper size and scope correspond to the research properly selected (more of this later) – bad sample leads to error between the statistic obtained from sample and parameter of population e.g.

5 Sampling error Random error – error from sampling process Sampling bias – error from sample being bias to certain thing Sampling Unit The element in the sample e.g. each student in the sample from all the students in the university

6 Define population Population should correspond to the study Proper scope Determine sample size Select sampling method Select sample

7 Larger sample size usually yields less error Define sampling error Usually at 1% or 5% (0.01 or 0.05) In sensitive study, such as those in medical field, error should be set as low as possible e.g. 1% Confidence interval That the sample is not different from population Confidence level 95% means that 95 out of 100 samples will behave similarly to the population

8 Calculate sample size from population size, sampling error and confidence interval Criterion-based Calculation Taro Yamane Cochran Krejcie and Morgan “Cohen's d” – current accepted method Tables also available for Taro Yamane and Krejcie and Morgan http://en.wikipedia.org/wiki/Cohen%27s_d#Cohen.27s_d

9 Population size of 100: take 15-30% as sample Population size of 1,000: take 10-15% as sample Population size of 10,000: take 5-10% as sample Population size of 100,000: take 1-5% as sample Not reliable

10 Unknown population size To estimate population proportion To estimate population mean (to achieve certain margin of error) Known population size …

11 Estimate proportion - W.G. Cochran (1953) n = sample size p = proportion (if not known, use 0.5) z = represents confidence; the value is from z-score table If confidence at 95%, z = 1.96 If confidence at 99%, z = 2.58 d = acceptable error

12 Defining proportion of 0.1, with confidence at 99% and acceptable error of 5%

13 Estimate mean - W.G. Cochran n = sample size σ = standard deviation of population z = represents confidence; the value is from z-score table If confidence at 95%, z = 1.96 If confidence at 99%, z = 2.58 e = acceptable random error (if σ is not known, e can defined as a percentage of σ e.g. 10% of σ (e = 0.10σ)

14 A study of students’ score in mathematics with confidence at 95%, acceptable error of +- 5 marks. Previous study revealed the average of 70 marks, with standard deviation (SD) of 15 marks

15 Taro Yamane Krejcie and Morgan To estimate population proportion To estimate population mean (to achieve certain margin of error)

16 Was popular but outdated n = sample size N = population size e = acceptable sampling error

17 Population of 2000 allowing 5% error

18 n = sample size N = population size e = acceptable sampling error χ 2 = chi-square of degree of freedom 1 and confidence 95% = 3.841 p = proportion of population (if unknown, 0.5)

19 Population of 2000, allowing 5% error at confidence 95% and population proportion of 0.5

20 n = sample size N = population size e = acceptable sampling error z = represents confidence; the value is from z-score table If confidence at 95%, z = 1.96 If confidence at 99%, z = 2.58 p = proportion of population (if unknown, 0.5)

21 Population of 2000, allowing 5% error at confidence 95% and population proportion of 0.5

22 n = sample size N = population size σ = standard deviation of population e = acceptable random error (if σ is not known, e can defined as a percentage of σ e.g. 10% of σ (e = 0.10σ) z = represents confidence; the value is from z-score table If confidence at 95%, z = 1.96 If confidence at 99%, z = 2.58

23 A study of 400 students’ scores in mathematics with confidence at 95%, acceptable error of +- 5 marks. Previous study revealed the average of 70 marks, with standard deviation (SD) of 15 marks

24 Assume population proportion of 0.5 and confidence 95% Error (e) Pop. Size

25 Error (e) Pop. Size

26 Assume population proportion of 0.5 and confidence 95% and error 5% Population Size Population Size Population Size Sample Size Sample Size Sample Size

27 Population Size Population Size Population Size Sample Size Sample Size Sample Size

28 Probability Sampling Each unit in population has the same chance to be selected as sample Non-probability Sampling Each unit in population has different chance to be selected as sample – some unit might never be selected

29 Simple Random Sampling Systematic Random Sampling Stratified Random Sampling Cluster Sampling Multi-stage Sampling

30 Randomly select a unit from population until we have the according to the sample size The method must ensure that each unit has the same chance to be selected Population must be listed and then Random from number associated with each unit (for smaller population) Use table of random number (for larger population) which is now replaced by random number generation in computer

31 Easy to do but should only be used on the population that is homogeneous A complete list of population must be present Not suitable for very large population

32 Systematic sampling arranges the target population according to non-bias ordering scheme and then selecting elements at regular intervals Systematic sampling involves a random start and then proceeds with the selection of every k th element from then onwards. k=(population size/sample size). It is important that the starting point is not automatically the first in the list, but is instead randomly chosen from within the first to the k th element in the list Example would be to select every 10th name from the telephone directory (an 'every 10th' sample, also referred to as 'sampling with a skip of 10').

33 Easy to do but The selection of sample after the first element is dependent on the first element

34 Divide population into subgroups, or strata The members of the same strata should be homogeneous (all elements should be similar with respect to the variables being studied) The size of each stratum is decided by its proportion in the population Each stratum is then sampled as an independent sub- population using Simple or Systematic Random Sampling

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36 Population of 1000 students in 5 faculties: Engineering 200, Science 300, IT 150, Business 150, and Education 200 Grouped into 5 strata based on faculty Using Taro Yamane yields sample size of 286 Engineering = (286/1000) x 200 = 57 Science = (286/1000) x 300 = 86 IT = (286/1000) x 150= 43 Business = (286/1000) x 150 = 43 Education = (286/1000) x 200 = 57 Then use simple/systematic sampling to obtain the sample

37 Samples are selected from all kinds in the population, thus Sample may best represent the population Each stratum must be different from other (unique enough) Do not divide into too many strata

38 It might not be possible to select sample from very large population. Select from existing grouping called cluster Clusters should be homogenous The size of each cluster should be relatively equal The number of clusters is decided by researcher depending on each study

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40 Save time and cost of study Cannot ensure that the sample can properly represent the population Example A study on Asian countries: assuming every country is similar (homogeneous) then select only Thailand, Malaysia and Vietnam as sample

41 A mix of the first 4 methods Usually start with Stratified Sampling or Cluster Sampling End with Simple or Systematic random sampling Used when strata or clusters are still too large or too complex to study

42 Accidental Sampling Quota Sampling Purposing Sampling Convenience Sampling Snowball Sampling

43 No rules, only set the sampling condition to match the research objective Worst method as it cannot guarantee that the sample can represent the population

44 Similar to Stratified Random Sampling Except that the member of each stratum is NOT selected using the probability sampling method

45 AKA Judgment Sampling Researcher select sample based on the objective of the study Cannot guarantee that the samples will maintain the status as time changes Example Study the attitude of director of successful companies

46 Use the method convenient to researching to gather data Example Phone Letter The sample is like to NOT being able to represent the population Bias

47 Randomly select a unit (i.e. a person) from population Then that person suggests the next sample Repeat until meet the sample size “Throw a snowball”

48 Cannot appropriate represent the population unless the sample is carefully selected The sample is dependent on the sample selector (researcher) therefore cannot determine sampling error