...Variables Sampling 689 I have edited a portion of Module G from your textbook so that it more closely follows my lecture. I need to acknowledge that this is not my original work and much of it is taken word for word from the 2nd edition of Auditing & Assurance Services by Louwers, Ramsay, Sinason and Strawser. Tad Miller Classical Variables Sampling LEARNING OBJECTIVE Understand the basic process underlying classical variables sampling in an audit examination. When performing substantive procedures, one approach is classical variables sampling. Classical variables sampling methods use normal distribution theory and the Central Limit Theorem to provide a range estimate of the account balance. The auditor uses the sample estimates to determine whether the account balance is fairly stated. The Central Limit Theorem indicates larger sample sizes provide a sampling distribution that more closely reflects a normal distribution. Therefore, larger sample sizes will yield a lower level of sampling risk. In this section, we briefly illustrate mean-per-unit classical variables sampling. We illustrate the manual calculations necessary to determine sample size and evaluate sample results. However, if clients maintain records in electronic format, auditors typically use computer software to perform these tasks. Classical Variables Sampling: Planning In the planning stages of classical variables sampling, the auditor determines the objective of sampling, defines the attribute...
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...Sampling Sampling Third Edition STEVEN K. THOMPSON Simon Fraser University A JOHN WILEY & SONS, INC., PUBLICATION Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or...
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...SAMPLING Definition: the act, process, or technique of selecting a representative part of a population for the purpose of determining parameters or characteristics of the whole population. TYPES OF SAMPLING TECHNIQUES: Cluster sampling Cluster sampling is a sampling technique where the entire population is divided into groups, or clusters and a random sample of these clusters are selected. All observations in the selected clusters are included in the sample. Cluster sampling is typically used when the researcher cannot get a complete list of the members of a population they wish to study but can get a complete list of groups or 'clusters' of the population. It is also used when a random sample would produce a list of subjects so widely scattered that surveying them would prove to be far too expensive, for example, people who live in different counties in the Country. Advantages One advantage of cluster sampling is that it is cheap, quick, and easy. Instead of sampling the entire country when using simple random sampling, the research can instead allocate resources to the few randomly selected clusters when using cluster sampling. A second advantage to cluster sampling is that the researcher can have a larger sample size than if he or she was using simple random sampling. Because the researcher will only have to take the sample from a number of clusters, he or she can select more subjects since they are more accessible. Disadvantages One main disadvantage of cluster...
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...SAMPLING: In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population. The three main advantages of sampling are that the cost is lower, data collection is faster, and since the data set is smaller it is possible to ensure homogeneity and to improve the accuracy and quality of the data. The sampling process comprises several stages: * Defining the population of concern * Specifying a sampling frame, a set of items or events possible to measure * Specifying a sampling method for selecting items or events from the frame * Determining the sample size * Implementing the sampling plan * Sampling and data collecting PROBABILITY AND NON-PROBABILITY SAMPLING: A probability sampling scheme is one in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined. The combination of these traits makes it possible to produce unbiased estimates of population totals, by weighting sampled units according to their probability of selection. Non-probability sampling is any sampling method where some elements of the population have no chance of selection (these are sometimes referred to as 'out of coverage'/'under covered'), or where the probability of selection can't be accurately determined. It involves the selection of elements based on assumptions regarding...
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...Sampling Techniques Psychology 341 August 11, 2013 ABSTRACT The present research paper was designed to discuss the different types of sampling methods used to conduct research in the field of Psychology. The sampling techniques included in this paper are probability sampling, non probability sampling, surveys and questionnaires. The use of examples for each type of technique is given to further the understanding of each specific type. Furthermore, some the most important aspects that should considered before selecting a method are outlined in detail. Sampling Techniques When conducting research, it is almost impossible to study the entire population that we are interested in looking at more in depth. For example, if we were interested in comparing the level of romantic satisfaction among college students in the United States, it would be practically impossible to survey every single person who is attending college in the country. Not only would it take an extremely long time to do so, but it would also be very expensive. That is why researchers will use small samples from the population to gather their data instead. A sample is particularly useful because it allows the researcher to make inferences about a specific population without having to actually survey the entire population (Trochim, 2006). There are several sampling techniques used to gather information about a sample. Some of these include probability sampling, non probability sampling, surveys, and questionnaires...
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...Sampling techniques: Advantages and disadvantages Technique | Descriptions | Advantages | Disadvantages | Simple random | Random sample from whole population | Highly representative if all subjects participate; the ideal | Not possible without complete list of population members; potentially uneconomical to achieve; can be disruptive to isolate members from a group; time-scale may be too long, data/sample could change | Stratified random | Random sample from identifiable groups (strata), subgroups, etc. | Can ensure that specific groups are represented, even proportionally, in the sample(s) (e.g., by gender), by selecting individuals from strata list | More complex, requires greater effort than simple random; strata must be carefully defined | Cluster | Random samples of successive clusters of subjects (e.g., by institution) until small groups are chosen as units | Possible to select randomly when no single list of population members exists, but local lists do; data collected on groups may avoid introduction of confounding by isolating members | Clusters in a level must be equivalent and some natural ones are not for essential characteristics (e.g., geographic: numbers equal, but unemployment rates differ) | Stage | Combination of cluster (randomly selecting clusters) and random or stratified random sampling of individuals | Can make up probability sample by random at stages and within groups; possible to select random sample when population lists are very localized...
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...When is Random Sampling not the best approach to sample selection? Provide an example A random sample is one in which every member of the population has an equal chance of being selected to be part of the sample. For example, you could obtain a random sample by having everyone in a population roll a die and choosing those people who roll a 6. In contrast, the sample would not be random if you chose everyone taller than 6 feet, because not everyone would have an equal chance of being selected ( Bennett, Briggs, Triola, 2009). Example: Telephone Book Sampling If you want to conduct an opinion poll in which the population is all the residents in a town. Could you choose a random sample from selecting names from the local telephone book? A sample drawn from a telephone book is not a random sample of the town population because phone books are missing a lot of names, and anyone whose name is missing has no chance of being selected. The phone book will be missing names and if two or more people share the same phone number the listing could be under one name. The people who choose to have an unlisted phone number or who only use a cell phone do not have the same chance of being polled as the one whom are listed ( Bennett, Briggs, Triola, 2009) Bennett, J. O., Briggs, W. L., Triola, M. F., (2009). Statistical Reasoning for everyday life. (3rd ed.). Retrieved from University of Phoenix eBook. Angela...
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...THE SAMPLING PROCESS Step 1: Define the Population A population must be defined in terms of elements, sampling units, extent and time. IN relation to these constituent parts, the population of purchasing agent is. (element) purchasing agents in (sampling unit) companies and governmental agencies that have (extent) bought any of our products (time) in the last three years Step 2: Specify the Sampling Frame If a probability sample is to be taken, a sampling frame is required. A sampling frame is a means of representing the elements of the population. A sampling frame maybe a telephone book, a city directory, an employee roster, a listing of all students attending a university, or a list of all possible phone numbers. Maps also serve frequently as sampling frames. A sample of areas within a city may be taken and another sample of households may then be taken within each area. City blocks are sometimes sampled and all households on each sample block given instructions as to how to take “random walks” from the intersection and select the households to be interviewed. A perfect sampling frame is one in which every element of the population is represented once but only once. Step 3: Specify Sampling Unit The sampling unit is the basic unit containing the elements of the population to be sampled. It may be the element itself or a unit in which the element is contained. For example, if one wanted a sample of males over 13 years of age, it might be possible to sample them...
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...Sampling Frame Advanced Cell technologies are constantly conducting hundreds of clinical trials in order to gain more knowledge on stem cell research. When dealing with the ethical barriers derived from stem cell research Advanced Cell Technologies spare no resources to maintain a healthy line so crossing of moral barriers occur. In order to conduct and proceed with research, a set of specific sampling frames must first be created. In statistics, a sampling frame is the source material or device from which a sample is drawn. [1] It is a list of all those within a population who can be sampled, and may include individuals, households or institutions. In many practical situations the frame is a matter of choice to the survey planner, and sometimes a critical one. [...] Some very worthwhile investigations are not undertaken at all because of the lack of an apparent frame; others, because of faulty frames, have ended in a disaster or in cloud of doubt.—Raymond James Jessen Within an ideal sampling frame the following elements must be achieved. First, all units have a logical, numerical identifier. Second all units can be found - their contact information, map location or other relevant information is present. Thirdly, the frame is organized in a logical, systematic fashion. Next the frame has additional information about the units that allow the use of more advanced sampling frames. Next every element of the population of interest is present in the frame. Finally, every element...
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...Richmond Housing Market Case 2 Surveys and Sampling A. Identify the population and variables. Population is the whole group of Richmond buyers interested to buy a house. Variables are: location, price, bedrooms, bathrooms, sq.ft, and realtor B. Identify variables as categorical or quantitative. * Location is categorical variable * Price is quantitative variable * Bedrooms are quantitative variable * Baths are quantitative variable * Sq.Ft is quantitative variable * Realtor is categorical variable C. What are some possible population parameters of interest? The parameter in this case is the 182 listing in Richmond, some other options to be considered are: average house price ($310,381), house size, how many bedrooms and bathrooms, location of the house, who is it listed by and the city zone. D. What are some possible sample statistics that could be calculated from this data? It is not necessary to calculate the statistics, just identify them. Average price for houses based on the county location, average household income, preferable characteristic and taste of the house buyers E. What is the sampling frame for the sample? The sampling frame is randomly selected from the single-dwelling properties for sale in the Greater Richmond area shown on the website realestate.aol.com. F. What is the sampling design? Systematic Random sampling (SRS) G. Are there any sources of bias in the sample? Yes – based on the data we have the direction...
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...CHAPTER 9 Audit Sampling Review Questions 9-1 Nonstatistical sampling is an audit sampling technique in which the risk of sampling error is estimated by the auditors using professional judgment rather than by the laws of probability. Statistical sampling involves the quantification of the risk of sampling error through the use of mathematics and laws of probability. 9-2 Sampling risk is the possibility that the auditors will make an erroneous decision based on a sample result. To control sampling risk the auditors increase the size of their samples. Nonsampling risk is the risk of erroneous conclusions by the auditors based on any factor other then sampling. For example, the auditors may perform inappropriate tests, or they may not recognize errors in the sample items examined. Nonsampling risk may be controlled by adequate planning and supervision of engagements, and the establishment of effective quality control policies and procedures. 9-3 The physical representation of the actual population is the recorded value that represents the population. For example, if the auditors use a computer printout of recorded accounts payable from which to sample, they must attempt to determine that it properly includes all accounts payable. 9-4 All three of the methods of selecting items for examination (random number table selection, systematic selection, random number generator selection) will produce a random sample if properly applied. However...
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...Summary Audit sampling is necessary and helps improve an audit engagement because examining all items are rather very timely, requires more effort, and of course, at higher cost. Audit risks such as inherent, control and detection risk are first assessed when doing audit sampling. Low control risk means auditors rely extensively on the entity's internal control, and vice versa. The process for determining risks and gathering evidences to provide reasonable assurance are done through other audit procedures such as tests of controls and tests of details. These procedures are done by sampling. Using sampling, when auditors do not obtain sufficient and appropriate evidences, there is a risk of not identifying material errors and therefore result in a wrong conclusion. The use of either non-statistical sampling techniques or statistical ones does not directly affect application of audit procedures, appropriateness of audit evidences or courses of actions that could be taken. Even though the procedures in non-statistical sampling is less formal, they are still rigorous. Non-statistical sampling method involves eight steps namely establish objective test, defining the population, determining distortions, determining the appropriate sample size, determination of the right method for the sample selection, proper testing of the selected sample, extrapolating results, risk assessment. Firms include in their policies the techniques which they use to implement auditing procedures....
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...Logic of Sampling Name Institution The sampling of a given data especially population is very important in analysing information. This depends on the method used to sample a given set of data. The methods include random sampling, stratified sampling, and systematic sampling. Every sampling method uses logic in sampling of data. This involves the procedure in sampling of a given set of information. Random sampling The random numbers used from the random tables include 11168, 36318, 75064, 21215, 91791, 76831, 10468, 44482, 66558, and 12032. The data in the table provide is labelled in terms of two digits. 11168- 01, 11, 64 36318- 03, 63, 18 75064- 07, 50, 64 21215- 02, 12, 15 91791- 09, 17, 91 76831- 07, 68, 31 10468- 01, 04, 68 44482- 04, 44, 82 66538- 06, 65, 38 12032- 01, 20, 32 The first ten numbers from the random table within the boundaries of the data are selected. This does not include the repeating entry. The selected random numbers are from the list of random table numbers include 01, 11, 64, 03, 63, 18, 07, 50, 02, and 12. Names of the selected ten random numbers 1. Lauren Aaronson 2. Andrew Abbot 3. James Abbot 4. Saleha Abedin 5. Christopher Abells 6. Marjorie Abend-Wein 7. Jill Abood 8. Reed Adams 9. Evan Adelson 10. Francis Adeola Procedure in random sampling The procedure in random sampling uses random tables to determine the values to sample. Before selecting the values, each value of the data provided...
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...BSHS/435 Sampling A sample is drawn from a population, which refers to all possible cases of what the researcher is interested in studying. A sample consists of one or two elements selected from a population. To select a good sample we have to clearly define the population from which we will be drawing a sample. Failure to do so can result in inaccurate conclusions. In probability sampling each element has an equal chance of inclusion. The simplest technique for probability samples is Simple Random Sampling. Simple random sampling treats the target population as a unitary whole. We might start off with a sampling frame which has a list of the whole population—or as much information as we can obtain. Next we would number the elements in the sampling frame sequentially and select elements from the list randomly. We would not know what the outcome would be, but each has an equal shot at being chosen. We can also program the computer to choose a random sample. Researchers may also use non probability sampling. In this type of sampling the researcher does not know the probability of each population’s elements inclusion in the sample (Dejong, 2011). Data Collection There are many different ways to collect data for research. Measures differ from one another in terms called levels of measurement. Nominal measures classify observations into mutually exclusive and exhaustive categories. They represent nominal variables such as sex, ethnicity, religion...
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...Sampling Designs • 1. Simple random sampling (SRS) Steps: – (1) Assign a single number to each element in the sampling frame. – (2) Use random numbers to select elements into the sample until the desired number of cases is obtained. • The method is not very different from winning a lottery. 2. Systematic Sampling • Steps: – (1) Calculate the sampling interval as the ratio between population size and sample size, I = N/n. – (2) Arrange all elements in the population in an order. – (3) Select a case in the first interval randomly. – (4) Select every ith case from this point. 2. Systematic Sampling (continued) I I 1st element, randomly chosen I I I I – Systematic Sampling is easier and simpler than SRS – The text warns of a danger to this method. What is it? 3. Stratified Sampling • Stratified sampling is more complicated than SRS. The advantage is the guaranteed representativeness in some important characteristics. • For example, say that we want to select a sample of 100 individuals. Sex ratio in the sample is up to chance if we do SRS. We can guarantee the 50-50 split if we do stratified sampling: Stratified Sampling, Graphic Representation Population SRS SRS Sample • Stratified sampling is often used to reduce the variability of a sample. Oversampling, Graphic Representation Population SRS SRS Sample • Increasing the representation of a group in a sample. This is often done when groups are very different in size...
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