Question

Probability-proportional-to-size (PPS) sampling is used by internal auditors to reach conclusions  

           regarding monetary amounts.

1. Describe the situation in which the application of PPS sampling is most applicable.

2. Explain how a PPS sample should be selected. Identify the factors that affect PPS sample size.

3. Indicate the effect each factor has on sample size.

4. Discuss the advantages and disadvantages of PPS sampling relative to classical variables sampling that an internal auditor must consider when deciding which of the two approaches is best for a particular sampling application.  

Answer 1

Sampling is a research method where subgroups are selected from a larger group known as a target population. The subgroups or samples are studied. If the sample is correctly chosen the results can be used to represent the target population. Probability proportional to size (PPS) takes varying sample sizes into account. This helps to avoid underrepresenting one subgroup in a study and yields more accurate results.

• 1. SAMPLING BUSINESS STATISTICS ASSIGNMENT INCLUDES VARIOUS METHODS OF SAMPLING, DEMERITS AND MERITS OF SAMPLING DEEPAK YADAV, MBA SEC-A 10/22/2012
• 2. Sampling Sampling is a fundamental aspect of statistics, but unlike the other methods of data collection, sampling involves choosing a method of sampling which further influences the data that you will result with. There are two major categories in sampling: 1. Probability and 2. Non-probability sampling. Probability Sampling Under probability sampling, for a given population, each element of that population has a chance of being picked to part of the sample. In other words, no single element of the population has a zero chance of being picked The odd/chances/probability of picking any element is known or can be calculated. This is possible if we know the total number in the entire population such that we are then able to determine that odds of picking any one element. Probability sampling involves random picking of elements from a population, and that is the reason as to why no element has a zero chance of being picked to be part of a sample.
• 3. Methods of Probability Sampling There are a number of different methods of probability sampling including: Random Sampling Random sampling is the method that most closely defines probability sampling. Each element of the sample is picked at random from the given population such that the probability of picking that element can be calculated by simply dividing the frequency of the element by the total number of elements in the population. In this method, all elements are equally likely to be picked if they have the same frequency. Systematic Sampling Systematic sampling is the method that involves arranging the population in a given order and then picking the nth element from the ordered list of all the elements in the population. The probability of picking any given element can be calculated but is not likely to be the same for all elements in the population regardless of whether they have the same frequency. Stratified Sampling Stratified sampling involves dividing the population into groups and then sampling from those different groups depending on a certain set criteria.
• 4. For example, dividing the population of a certain class into boys and girls and then from those two different groups picking those who fall into the specific category that you intend to study with your sample. Cluster Sampling Cluster sampling involves dividing up the population into clusters and assigning each element to one and only one cluster, in other words, an element can't appear in more than one cluster. Multistage Sampling Multistage sampling involves use of more than one probability sampling method and more than one stage of sampling, for example for using the stratified sampling method in the first stage and then the random sampling method in the second stage and so on until you achieve the sample that you want. Probability Proportional to Size Sampling Under probability proportional to size sampling, the sample is chosen as a proportion to the total size of the population. It is a form of multistage sampling where in stage one you cluster the entire population and then in stage two you randomly select elements from the different clusters, but the number of elements that you select from each cluster is proportional to the size of the population of that cluster. Non-Probability Sampling Unlike probability sampling, under non-probability sampling certain elements of the population might have a zero chance of
• 5. being picked. This is because we can't accurately determine the chances/probability of picking a given element so we do not know whether the odds of picking that element are zero or greater than zero. Non-probability sampling may not always be a consequence of the sampler's ignorance of the total number of elements in the population but may be a result of the sampler's bias in the way he chooses the sample by excluding some elements. Methods of Non-Probability Sampling There are a number of different methods of Non-probability sampling which include: Quota Sampling Quota sampling is similar to stratified sampling only that in this case, after the population is divided into groups, the elements are then sampled from the group using the sampler's judgement and as a consequence the method loses any aspect of being random and can be extremely biased. Accidental or Convenience Sampling Accidental sampling is a method of sampling where by the sampler picks the sample based on the fact that the elements that he/she picks are conveniently close at the moment. For example, if you walked down the street and sampled the first ten people you meet, the fact that they happened to be there is convenient for you but accidental for them which leads to the name of the method.
• 6. Purposive or Judgmental Sampling Purposive or judge mental sampling is a method of sampling where by the sampler picks the sample from the entire population solely based on the his/her judgment. The sampler controls to a very large extend which elements have a chance of being selected to be in the sample and which ones don't. Voluntary Sampling Voluntary sampling, as the name suggests, involves picking the sample based on which elements of the population volunteer to participate in the sample. This is the most common method used in research polls. Snowball Sampling Snowball sampling is a method of sampling that relies on referrals of previously selected elements to pick other elements that will participate in the sample.
• 7. ADVANTAGES AND DISADVANTAGES OF SAMPLING 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 Complex, combines limitations of cluster and stratified random sampling Purposive Hand-pick subjects on the basis of specific characteristics Ensures balance of group sizes when multiple groups are to be selected Samples are not easily defensible as being representative of populations due to potential subjectivity of researcher Quota Select individuals as they come to fill a quota by Ensures selection of adequate numbers of Not possible to prove that the sample is representative of
• 8. characteristics proportional to populations subjects with appropriate characteristics designated population Snowball Subjects with desired traits or characteristics give names of further appropriate subjects Possible to include members of groups where no lists or identifiable clusters even exist (e.g., drug abusers, criminals) No way of knowing whether the sample is representative of the population Volunteer, accidental, convenience Either asking for volunteers, or the consequence of not all those selected finally participating, or a set of subjects who just happen to be available Inexpensive way of ensuring sufficient numbers of a study Can be highly unrepresentative