Chapter business research sampling design.pptx

Research

1. Chapter Five Sampling Design

2. Introduction The statistical investigation can take two forms: The researcher studies every unit of the field of study (survey) and drive conclusion by computing the sum of all units. This type of survey is also called census survey In the other type, the researcher study only a unit in the field of survey and this type of survey is called sample survey. In this technique, some units are taken as representative of the whole field of domain and the conclusion of the sample is extended to the whole population.

3. Before going to details and uses of sampling it is appropriate to be familiar with some basic terms. Population: is the total set of units in which a researcher is interested; Can be finite or infinite population. For example, all employees of an organization to study the reasons of employee turnover Sampling: is the process of selecting units into a sample from a larger set of the same units (Population). Sampling frame: a listing of all the elements in the population from which the sample is drawn. For example, the list of employees found in personnel department to get information on employee turnover Sample design: Is a definite plan for obtaining a sample frame. Important Terms

4. Element: Is unit from which information is collected and which provides the basis of analysis. Parameter: is a characteristics of the population about which researchers are interested to find out. Statistic: Is a characteristic of a sample Example, when we work out certain measurement like, mean from a sample they are called statistics. But when such measure describe the characteristic of the population, they are called parameter(s) For example, population mean (  ) is a parameter; where as the sample mean (x) is a statistics. Cont…

5. Unit of analysis: the type of objective whose characteristics the researcher wants to measure and study. For example: If data are collected on employees, the unit of analysis is employee. Sampling unit: a unit or set of units considered for selection at a stage of sampling. Sampling unit may or may not be the same as a unit of analysis. It is possible to include several units of analysis. For example, if the researcher wants to interview senior managers in the public sector, the senior managers become the unit of analysis and the public organisations across the country become sampling unit. Cont…

6. Sampling Process Steps involved in Sampling procedure:

7. The first thing the sample plan must include is a definition of the population to be investigated. Defining the target population implies specifying the subject of the study. Specification of a population involves identifying which elements (items) are included, as well as where and when. If the research problem is not properly defined then defining population will be difficult. 1) Defining the Population

8. Once the population has been defined, the researcher must decide whether the survey is to be conducted among all members of the population or only a subset of the population. That is, a choice must be made between census and sample ADVANTAGES OF CENSUS Reliability: Data derived through census are highly reliable. The only possible errors can be due to computation of the elements. Detailed information: Census data yield much more information. LIMITATION OF CENSUS Expensiveness: Investigating each elements of the population is expensive to any individual researcher Excessive time and energy: Beside cost factor, census survey takes too long time and consumes too much energy . 2) Census Vs. Sample

9. A beginner researcher commonly asks himself when and where sampling technique is appropriate to his/her study. Sampling technique is used under the following conditions. Vast data: When the number of units is very large, sampling technique must be used as it economize money, time and effort When at most accuracy is not required: The sampling technique is very suitable in those situations where 100% accuracy is not required, otherwise census technique is unavoidable. Infinite population: If the population is unlimited, sampling technique is about to happen. When census is impossible: If we want to know the amount of mineral wealth in a country we cannot dig all mines to discover and count. Rather we have to use the sampling technique. Homogeneity: If all units of the population are alike (similar) sampling technique is easy to use . Cont… Need for Sampling

10. An ideal (most suitable) sample should fulfill the following four basic characteristics. Representativeness: An ideal sample must represent adequately the whole population. It should not lack a quality found in the whole population. Independence: Each unit should be free to be included in the sample. Adequacy: The number of units included in the sample should be sufficient to enable derivation of conclusion applicable for the whole population. Homogeneity: The element included in the sample must bear likeness with other element . Cont… Essentials of an Ideal sample

11. Less accuracy: In comparison to census technique the conclusion derived from sample are more liable to error. Therefore, sampling technique is less accurate than the census technique. Misleading conclusion: If the sample is not carefully selected or if samples are arbitrarily /illogical selected, the conclusion derived from them will become misleading if extended to all population. In assessing the monthly expenditure of university students if the selected sample contains more rich students, our result (conclusion) will be erroneous if it extended to all students Need for specialized knowledge: The sample technique can be successful only if a competent and able scientist makes the selection. If it is done by average researcher the selection is liable to error. Cont… Limitations of sampling

12. Sample design must result in a truly representative sample. (b) Sample design must be such which results in a small sampling error . (c) Sample design must be viable in the context of funds available for the research study. (d) Sample design must be such so that systematic bias can be controlled in a better way. (e) Sample should be such that the results of the sample study can be applied, in general, for the universe with a reasonable level of confidence. Cont… Characteristics of Good Sample Design

13. Sampling design/method can be classified in to two broad categories: i ) Probability (random) ii) Non probability ( non random) sampling I) PROBABILITY SAMPLING Probability sampling provides a scientific technique of drawing samples from population according to some laws of chance in which each unit has some definite pre- assigned probability of being chosen in the sample. 3) Sampling Design

14. TYPES OF PROBABILITY SAMPLING There are various types of probability sampling techniques: the most well known are the following: a) Simple random sampling b) Stratified sampling c) Systematic sampling d) Cluster sampling Cont…

15. A) SIMPLE RANDOM SAMPLING Random sampling is more suitable in more homogeneous and comparatively larger groups. Under this sampling design, every item of the universe has an equal chance of inclusion in the sample. The sample is chosen by some methods like flipping a coin (head or tail selection) or lottery method. B) STRATIFIED RANDOM SAMPLING When the population is heterogeneous with respect to the variables or characteristics under study then the technique of stratified sampling is used to obtain more efficient and accurate results. Stratification means division of the universe /study population/ into groups/cluster according to geographical, sociological or economic characteristics. Each cluster has homogenous characteristics. To select the elements from each stratum, apply simple random sampling. Cont…

16. There are two types of stratified random sampling: A. NON-PROPORTIONATE To select the elements= Sample size (n) from each stratum N o of stratum (k) Select the required elements from each stratum using the SRS techniques. B. PROPORTIONATE Percentage (P)= Elements in each stratum Total population size To select the elements = % (P) x sample size from each stratum Select the required elements from each stratum using SRS techniques. Cont…

17. Example : compute sample size under each type of stratified random sampling Stratum A. 10 B. 30 C. 60 N=100 n= 20 ANSWER: Non-proportionate: sample size/ No. of strata= 20/3 = 6.666 Proportionate: A= 10/100 = 0.1 x 20 = 2 B= 30/100 = 0.3 x 20 = 6 C= 60/100 = 0.6 x 20 = 12 Cont…

18. C) SYSTEMATIC SAMPLING Under this method, a sample is taken from a list prepared on a systematic arrangement either on the base of alphabetic order or on house number or any other method. In this method only the first sample unit is selected using the SRS techniques and the remaining units are automatically selected in a definite sequence at equal spacing from one another. D) CLUSTER SAMPLING In cluster sampling the total population is divided into a number of relatively small subdivisions which are themselves clusters of still smaller units and then some of these clusters are randomly selected for inclusion in the overall sample. Cont…

19. II) NON – PROBABILITY SAMPLING Non – probability sampling or judgment sampling is based on the personal Judgment or knowledge. Under this method, a desired number of sample units are selected deliberately or purposely depending upon the object of the enquiry so that only the important items representing the true characteristics of the population are included in the sample. Thus, the researcher takes into accounts other considerations. Cont…

20. These designs are usually applied when the study population is unknown or the individual elements in the sampling population cannot be identified easily. TYPES OF NON-PROBABILITY SAMPLING i ) Quota ii) Convenience iii) Judgmental/Purposive iv) Snowball Cont…

21. I) QUOTA SAMPLING METHOD It is done based on geographic proximity and the elements in the study population have certain visible characteristic/principles criteria such as age, gender, education, occupation, political, religion , race, etc,. II) CONVENIENCE SAMPLING METHOD In this method a sample is selected according to the convenience of the investigator. The selection is unsystematic careless, accidental, thus this method applied under the following circumstances Lack of clarity about the universe Non-availability of source list Cont…

22. III) SNOWBALL SAMPLING METHOD: This design is based on networks. A few individuals in an organization/ community are asked to provide information about the study. After the information is collected from them, you ask them to give you the name of others who have knowledge about the issue. These will be considered as part of the sample and information will be gathered from them and asked further to identify others. This process will continue until the number equals to the required sample size or you reached saturation point in terms of the information required. Cont…

23. IV) JUDGMENTAL/ PURPOSIVE SAMPLING METHOD In this method, the investigator purposively selects certain units as to who will provide the best information for the purpose of the study. It is characterized by Representative character Specific objective Freedom from bias Cont…

24. A researcher is worried about sample size because of the fact that sample size (number of elements in sample) and precision of the study are directly related. The larger the sample size the higher is the accuracy. The sample size determination is purely statistical activity, which needs statistical knowledge. SAMPLE SIZE: the number of elements selected for the sample to represent the population. Sample size determination is influenced by: the purpose of the study, population size, and type the risk of selecting a "bad“ sample The degree of variability in the attributes being measured The level of confidence or risk: The level of precision , 4) Sample Size Determination

25. Three criteria usually will need to be specified to determine the appropriate sample size: 1. The level of precision: sampling error that is mostly expressed in percentage point, example : ±5% 2 . The level of confidence or risk: based on the Central limit theory that states when a population is repeatedly sampled, the average value of the attribute obtained by those samples is equal to the true population value. 3. The degree of variability in the attributes being measured: the more heterogeneous a population, the larger the sample size required to obtain a given level of precision. The less variable (more homogeneous) a population, the smaller the sample size. Cont…

26. 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. Non-sampling error is the error that arises in a data collection process as a result of factors other than taking a sample. Poor sampling methods Questionnaire or measurement error Behavioral effects 26 Sampling and Non-sampling Error

27. There are several approaches to determining the sample size. Using a census for small populations Imitating a sample size of similar studies Using published tables Applying formulas to calculate a sample size Use computer soft ware Sample Size Determination Strategies

28. Using a Census for Small Populations One approach is to use the entire population as the sample; although cost considerations make this impossible for large populations. Attractive for small populations (e.g., 200 or less). Eliminates sampling error and provides data on all the individuals in the population. Some costs such as questionnaire design and developing the sampling frame are “fixed,” that is, they will be the same for samples of 50 or 200. Finally, virtually the entire population would have to be sampled in small populations to achieve a desirable level of precision .

29. Using a Sample Size of a Similar Study Use the same sample size as those of studies similar to the one you plan (Cite reference). Without reviewing the procedures employed in these studies you may run the risk of repeating errors that were made in determining the sample size for another study. However, a review of the literature in your discipline can provide guidance about “typical” sample sizes that are used.

30. Using Published Tables Published tables provide the sample size for a given set of criteria. Necessary for given combinations of precision, confidence levels and variability. The sample sizes presume that the attributes being measured are distributed normally or nearly so. Although tables can provide a useful guide for determining the sample size, you may need to calculate the necessary sample size for a different combination of levels of precision, confidence, and variability.

31. Sample Size for ±5%, ±7% and ±10% Precision Levels where Confidence Level Is 95% and P=.5. Size of Population Sample Size (n) for Precision (e) of: ±5% ±7% ±10% 100 81 67 51 125 96 78 56 150 110 86 61 175 122 94 64 200 134 101 67 225 144 107 70 250 154 112 72 275 163 117 74 300 172 121 76 325 180 125 77 350 187 129 78 375 194 132 80 400 201 135 81 425 207 138 82 450 212 140 82

32. Using Formulas to Calculate a Sample Size Sample size can be determined by the application of one of several mathematical formulae. Formula mostly used for calculating a sample for proportions. For example: For populations that are large, the Cochran (1963:75) equation yields a representative sample for proportions. Fisher equation, Mugenda etc

33. Cont… Cochran Equation Where n is the sample size, Z 2 is the abscissa of the normal curve that cuts off an area α at the tails; (1 – α) equals the desired confidence level, e.g., 95%); e is the desired level of precision, p is the estimated proportion of an attribute that is present in the population,and q is 1-p. The value for Z is found in statistical tables which contain the area under the normal curve. e.g Z = 1.96 for 95 % level of confidence

34. A Simplified Formula For Proportions Yamane Taro (1967:886) provides a simplified formula to calculate sample sizes. Assumptions: 95% confidence level P = .05 Cont… Yamane Equation Where; n is the sample size; N is the population size and e is the level of precision.

35. Finite Population Correction For Proportions With finite populations, correction for proportions is necessary If the population is small then the sample size can be reduced slightly. This is because a given sample size provides proportionately more information for a small population than for a large population. The sample size (n ) can thus be adjusted using the corrected formula. Where; n is the sample size; N is the population size and n o is calculated sample size for infinite population

36. Cont… The sample size formulas provide the number of responses that need to be obtained. Many researchers commonly add 10 % to the sample size to compensate for persons that the researcher is unable to contact. The sample size also is often increased by 30% to compensate for non-response (Example; self administered questionnaires).

37. Use of Software in Sample Size Determination Depending on the type of study and specific software, some information will be required: Population sample size, population standard deviation, population sampling error, confidence level, z –value, power of study etc … Example: 80% power in a clinical trial means that the study has a 80% chance of ending up with a p-value of less than 5% in a statistical test (i.e. a statistically significant treatment effect), if there was really an important difference (e.g. 10% versus 5% mortality) between treatments.

38. Further Considerations The above approaches to determining sample size have assumed that a simple random sample is the sampling design. More complex designs, e.g. case control studies etc , one must take into account the variances of sub-populations, strata, or clusters before an estimate of the variability in the population as a whole can be made.