Unit IV--- Sampling and Basic Concepts in Chemical Analysis:

Transcription

1 Unit IV--- Sampling and Basic Concepts in Chemical Analysis: Definition A sampling procedure defines the rules that specify how the system calculates the sample size and it contains information about the valuation of an inspection characteristic during results recording (attributive, variable, manual, etc.). Use Sampling procedures are usually used at characteristic level of a task list or material specification. You can however determine the sample size, without reference to task lists. To do this, you define a sampling procedure for the inspection type in the inspection setup (Quality Management view of the material master). Structure The rules for determining the sample are stored in the sampling type. The sampling type and valuation mode are combined for the inspection characteristics. This combination forms the structure of the sampling procedure. Sampling Type The sampling type defines how a sample is calculated (for example, fixed sample, 100% inspection, use sampling scheme, percentage sample). Together with the valuation mode, the sampling type defines the parameters for sample determination. Using the sampling type, the system proposes a list of rules for sample determination. If there is only one rule available, this is automatically chosen. Valuation Mode The valuation mode (for example, attributive inspection on the basis of nonconforming units, variable inspection according to s-method [one limit], without valuation parameters) defines the rules for accepting or rejecting a characteristic or sample. The sampling type and the valuation mode specify which parameters the system uses to determine a sample size. Inspection Points If you want to use inspection points in the sampling procedure, you need to set an indicator for the corresponding application area. This indicator specifies how many inspection points are to be created for each inspection lot. Usage Indicator

2 To prevent the sampling procedure from being referenced in a task list, you set the indicator No use in insp.plan. The system automatically sets the indicator Use in insp. plan, if the sampling procedure is referenced in a task list. Control Chart Type If you want to use quality control charts in a sampling procedure, you must enter a quality control chart type. The control chart type specifies: The characteristics for which the control chart is suited The control variables a chart contains How the control limits are calculated Basic Concepts of Sampling With a single grain of rice, an Asian housewife tests if all the rice in the pot has boiled; from a cup of tea, a tea-taster determines the quality of the brand of tea; and a sample of moon rocks provides scientists with information on the origin of the moon. This process of testing some data based on a small sample is called sampling. Definition : Sampling is the process by which inference is made to the whole by examining a part. Purpose of Sampling The purpose of sampling is to provide various types of statistical information of a qualitative or quantitative nature about the whole by examining a few selected units. The sampling method is the scientific procedure of selecting those sampling units which would provide the required estimates with associated margins of uncertainity, arising from examining only a part and not the whole. Simple Random Sampling Methods of Sample Selection In this method each item of the data ( population) has the same probability of being selected in the sample. The selection is usually made with the help of random numbers. Suppose there are N=850 students in a school from which a sample of n=10 students is to be taken. The students are numbered from 1 to 850. Since our data runs into three digits

3 we use random numbers that contain three digits. All numbers exceeding 850 are ignored because they do not correspond to any serial numbres in the data. In case the same number occurs again, the repetition is skipped. Systematic Sampling In this method first we have to number the data items from 1 to N. Suppose the sample size be n, then we have to calculate the sampling interval by dividing N by n. And generate a number between 1 and N/n and select that data item to be in the sample. Other items in the sample are obtained by adding the sampling interval N/n successively to the random number. Advantage of this method is that the sample is evenly distributed over the entire data. The town of Fairfax is divided up into N = 576 blocks which are numbered consecutively. A 10 percent sample of blocks is to be taken, which gives a sampling interval of k = 10. If the random number between 1 and 10 is 3, the blocks with the numbers 03, 13, 23, 33, 43,...,573 are in the sample. Sampling with unequal probabilities When the data items vary considerably in size, a simple random or a systematic random sample of items does not produce a good estimate due to high variability. In such a situation we get a better estimate by giving higher probability of selection to the larger data items. Applications of sampling techniques Major TV networks rely on surveys to tell them how many and what types of people are watching their programs. The U.S. Bureau of Census conducts a suvey every month to obtain information on employment and unemployment in the nation. Local housing authorities make surveys to ascertain satisfaction of people in public housing with their living accomodations. Local transportation authorities conduct surveys to acquire information on people's commuting and travel habits. Magazines and trade journals utilize surveys to find out what their subscribers are reading. Surveys are used to ascertain what sort of people use our national parks and other recreation facilities. Auto manufacturers use surveys to find out how satisfied people are with their cars.

4 Advantages of Sampling Greater economy : The total cost of a sample will be much less than that of the whole lot. Shorter time-lag : With smaller number of observations it is possible to provide results much faster as compared to the total number of observations. Greater scope :Sampling has a greater scope regarding the variety of information by virtue of its flexibility and adaptability. Actual appraisal of reliability Limitations of sampling Errors due to sampling may be high for small administrative areas. Sampling may not be feasible for problems that require very high accuracy. Sampling Procedures and Static of Sampling There are many sampling procedures that have been developed to ensure that a sample adequately represents the target population. A few of the most common are described below. Simple Random Sampling In simple random sampling, every individual in the target population has an equal chance of being part of the sample. This requires two steps: 1. Obtain a complete list of the population. 2. Randomly select individuals from that list for the sample. Recall that the sampling procedure must reflect the unit of analysis. In a study where the unit of analysis is the student, the researcher must obtain a complete list of every student in the target population to achieve simple random sampling. This is rarely possible, so very few, if any, educational studies use simple random sampling. Another factor to consider is the word random. Random is a technical term in social science research that means that selection was made without aim, reason, or patterns. If any study uses the word random, it means that specific scientific procedures were used to ensure that the sample was selected purely by chance. Scientists have developed a few procedures that must be followed for a study to achieve random, such as the hat-and-draw method or a random number table. To be random, participants cannot be chosen because of their intelligence, gender, social class, convenience, or any other factor besides scientifically-agreed upon random procedures. Using the word random when the unit of analysis was not selected by the hat-and-draw method or a random number table is either irresponsible or flat-out untruthful.

5 Stratified Random Sampling In stratified random sampling, the researcher first divides the population into groups based on a relevant characteristic and then selects participants within those groups. In educational research, stratified random sampling is typically used when the researcher wants to ensure that specific subgroups of people are adequately represented within the sample. For example, a research study examining the effect of computerized instruction on maths achievement needs to adequately sample both male and female pupils. Stratified random sampling will be used to ensure adequate representation of both males and females. Stratified random sampling requires four steps: Determine the strata that the population will be divided into. The strata are the characteristics that the population is divided into, perhaps gender, age, urban/rural, etc. Determine the number of participants necessary for each stratum. Perhaps the researcher wants equal representation within the strata: half male, half female; 20 children age 5, 20 children age 6, and 20 age 7; etc. Other times (e.g., large survey research), the researcher might want to use proportionate random sampling. This requires that the researcher first knows the proportion of the group in the entire population and then match that proportion within the sample. For example, a researcher might find the most recent Nigerian census to determine that females represent 53% of the population in Nigeria, so the sample will then include 53% females. Split the units of analysis into the respective strata. In other words, if the target population is students and the researcher wants to stratify based on gender, then the researcher will need two lists of the target population: one list of the male students and another list of the female students. Randomly sample participants from within the group. Using either the hat-and-draw method or a random number table, randomly select the requisite number of males and do the same for the females.

6 Purposive Sampling In purposive sampling, the researcher uses their expert judgment to select participants that are representative of the population. To do this, the researcher should consider factors that might influence the population: perhaps socio-economic status, intelligence, access to education, etc. Then the researcher purposefully selects a sample that adequately represents the target population on these variables. Multi-Stage Sampling More frequently, educational researchers use multi-stage sampling. In multi-stage sampling, the sample is selected in multiple steps, or stages. For example, in the first stage, geographical regions, such as local government areas, are selected. In the second stage, perhaps schools may be selected. In the third stage, the unit of analysis - perhaps teachers or students, are sampled. If the unit of analysis is not selected in the first step, then the sampling procedure is multi-stage sampling. In multi-stage sampling, other sampling techniques may be used at the different stages. For example, the first stage may use random sampling, the second stage may use purposive sampling, and the third stage may use stratified sampling. The steps in multi-stage sampling are as follows: Organize the sampling process into stages where the unit of analysis is systematically grouped. Select a sampling technique for each stage. Systematically apply the sampling technique to each stage until the unit of analysis has been selected.

7 Hazards in Sampling A couple of us were arguing about the differences between random, haphazard, and judgmental sampling. One person said that picking samples here and there manually was random sampling. I argued the method described was actually haphazard sampling. Another said that haphazard sampling was not appropriate and that audit judgment was valued, not haphazard sampling. First, true random sampling requires the use of a pseudo-random generator, which can be a simple program, or in the case of ACL, you can use the Sample Records option. Second, the difference in haphazard and judgmental sampling is huge. My colleague insisted that when you select a sample with no explicit method, that is judgmental sampling, and should be noted as such. I disagreed and explained the difference this way: haphazard sampling was selecting samples from a population by merely picking one here and there without any criteria; judgmental sampling is selecting a sample based on some criteria. For example, assume user access to SOX systems is being tested, and the population includes all users in the company. If users are selected haphazardly, the selection would most likely include users with no access to any systems (janitors), users with access only to (mailroom clerks), and users with access to various SOX systems (IT, manufacturing, and marketing staff). If users are selected judgmentally (the criteria being users most likely to have access to SOX systems), then the selections would be made from the IT, finance, management, and similar functions; janitors, mailroom clerks, and the like who have no such access would not be selected. Speaking of haphazard selections, this article notes that haphazard sampling tends to be subconsciously biased, based on various studies conducted. People tend to select items that will reduce the workload (file folders in the top drawer) or are more attractive (such as items from the brightest colored bins). Originally I thought this bias would occur more often on the financial side than the IT side, but I can see how familiarity with the items sampled could impact

8 sampling. In the case of selecting servers, one may subconsciously remember certain servers are located where controls are not as strong, administrators are more lazy, run more applications, or had multiple issues in years past. What do you think? The article includes this guidance: Auditors that continue to use haphazard selection should employ multiple debiasing procedures and carefully document these procedures in their workpapers. Such procedures might include a combination of: 1) stratification by time period, location, and dollar value; 2) use of a high-value top stratum where all items are audited; and 3) an increase in overall sample size. But auditors should understand that even these procedures will not correct for bias that results from biasinducing factors that are not well controlled by stratification and practical increases in sample size (e.g., biases due to physical size, color, and number of adjacent neighbors). Ultimately, using random selection may be the more efficient way to avoid the cost and effort of debiasing procedures.