Collecting Data to Support Decision Making - Business Decision Making - ثاني ثانوي

Lesson 3 Chapter 9 www.ien.edu.sa QUICK TIP Experiments allow you to test "what if?" questions. Experiments are usually harder to conduct than observational studies, but when done properly can also yield more valuable results. Collecting Data to Support Decision Making 3-1 The Importance of Data Collection Data collection is a particularly important step in the data analysis process. When we set out to collect information, it is important to keep in mind the questions we hope to answer on the basis of the resulting data. Sometimes we are inter- ested in answering questions about the characteristics of a single population or in comparing two or more populations. To accomplish this, we select a sample from each population under consideration and use the sample information to gain insight into characteristics of those populations. For example, an ecologist might be interested in estimating the average shell thickness of eagle eggs. A social scientist studying a rural community may want to determine whether age and attitude toward educational attainment are related. These are examples of studies that are observational in nature. In these studies, we want to observe characteristics of members of an existing population or of several populations, and then use the resulting information to draw conclusions. In observational studies, it is important to obtain samples that are representa- tive of the corresponding populations. Consider data that tells you about the population you are sampling, for instance, by looking at census data for a country or, for a smaller organization, information from a human resources department. Sometimes the questions we are trying to answer deal with the effect of certain variables on some response and cannot be answered using data from an observa- tional study. These questions are often of the form, "What happens when...?" or, "What is the effect of...?". For example, an educator may wonder what would happen to test scores if the required lab time for a chemistry course was increased from three hours to six hours per week. To answer such questions, an experiment is carried out to collect relevant data. 294 9 Chapter رة ا Ministry of Education 2024-1446 Business Decision Making S1 S2 S3.indb 294 DEFINITION Observational study: A study in which characteristics of a sample selected from one or more existing populations are observed. The goal of an observational study is usually to draw conclusions about the corresponding population or about differences between two or more populations. In a well-designed observational study, the sample is rep- resentative of the population. 30/06/2023 14:28

وزارة التعليم Ministry of Education 2024-1446 Business Decision Making S1 S2 S3.indb 295 DEFINITION Experiment: A study that investigates how a response variable behaves when one or more explanatory variables, also called factors, are manipulated. The usual goal of an experiment is to determine the effect of the explanatory variables (factors) on the response variable. In a well-designed experiment, the composition of the groups that will be exposed to different experimental conditions is determined by ran- dom assignment. 3-2 Variables The value of a response variable (test score in the chemistry example) is recorded under different experimental conditions (three-hour lab and six-hour lab). In an experiment, one or more explanatory variables, also sometimes called factors, define the experimental conditions. A well-designed experiment can result in data that provide evidence for a cause- and-effect relationship. This is an important difference between an observational study and an experiment. In an observational study, it is not possible to draw clear cause-and-effect conclusions because we cannot rule out the possibility that the observed effect is due to some variable other than the explanatory variable being studied. Such variables are called confounding variables. DEFINITION Confounding variable: A variable that is related to both how the experimental groups were formed and the response variable of interest. Consider the role of confounding variables in the following study. Studies have shown that people over the age of 65 who get a flu shot are less likely to die from a flu-related illness during the following year than those who do not get a flu shot. However, research has shown that people over the age of 65 who get flu shots are also less likely to die from any cause during the fol- lowing year than those who don't get flu shots. This has led to the specula- tion that those over the age of 65 who make the effort to get flu shots are generally healthier as a group than those who do not get flu shots. If this is the case, observational studies that compare two groups—those who get flu shots and those who do not—may overestimate the effectiveness of the flu vaccine because general health differs in the two groups. General health is a possible confounding variable in such studies. Using Data to Support the Decision Making Process 295 30/06/2023 14:28

QUICK TIP This idea is the most important part of your data collection: When choosing a sample of data to measure, be very careful to ensure that everything has an equal chance of being the one selected. If you do this, your sample will be very representative of the population as a whole. 3-3 Sampling Many methods introduced in this chapter are based on random selection. The most straightforward sampling method is called simple random sampling. A simple random sample is a sample chosen using a method that ensures that each different possible sample of the desired size has an equal chance of being the one chosen. DEFINITION Simple random sample: A sample chosen using a method that ensures that each different possible sample of the desired size has an equal chance of being chosen. 296 9 Chapter رة ا Ministry of Education 2024-1446 Business Decision Making S1 S2 S3.indb 296 For example, suppose that Nora wants a simple random sample of 10 employees chosen from everyone at a large design firm where she works. For the sample to be a simple random sample, the method used by Nora to select the sample must ensure that each of the many different subsets of 10 employees are equally likely to be selected. A sample taken from only full- time employees would not be a simple random sample of all employees, because someone who works part-time has no chance of being selected. Although a simple random sample may, by chance, include only full-time employees, it must be selected in such a way that each possible sample, and therefore every employee, has the same chance of being selected. A number of different methods can be used to select a simple random sam- ple. One way is to put the name or number of each member of the popula- tion on different but identical slips of paper. The process of thoroughly mixing the slips and then selecting n slips yields a random sample of size n. This method is easy to understand, but it has obvious drawbacks. The mixing must be adequate, and producing the necessary slips of paper can be extremely tedious, even for relatively small populations. A commonly used method for selecting a random sample is to first create a list, called a sampling frame, of the objects or individuals in the population. Each item on the list is identified by a number. A table of random digits or a random number generator can then be used to select the sample. A random number generator is an algorithm that produces a sequence of numbers that satisfies properties associated with the notion of randomness. Most statistics software packages and many calculators include a random number generator. Simple random sampling provides researchers with a sampling method that 30/06/2023 14:28

QUICK TIP Cluster sampling can greatly simplify your data collection. When choosing your clusters, be sure that the cluster mirrors what the overall population looks like. Avoid clusters with different population characteristics. is objective and free of selection bias. In some settings, however, alternative sampling methods may be less costly, easier to implement, and sometimes even more accurate. Sometimes it is easier to select groups of individuals from a population than it is to select individuals themselves. Cluster sampling involves dividing the popula- tion of interest into non-overlapping subgroups, called clusters. Clusters are then selected at random, and then all individuals in the selected clusters are included in the sample. وزارة التعليم Ministry of Education 2024-1446 Business Decision Making S1 S2 S3.indb 297 DEFINITION Cluster sampling: Involves dividing the population of interest into non-overlapping subgroups, or clusters, and clusters are then selected at random. For example, suppose that a large school in Dammam has 600 senior stu- dents, all of whom are enrolled in a first period registration class. There are 24 senior classes, each with approximately 25 students. If school administra- tors wanted to select a sample of about 75 seniors to participate in an evalu- ation of the school and career advising available to students, they might find it much easier to select three of the senior classes at random and then include all the students in the selected classes in the sample. Then, a survey could be administered to all students in the selected classes at the same time-cer- tainly easier to implement than randomly selecting 75 individual seniors and then administering the survey to these students. Because whole clusters are selected, the ideal situation for cluster sampling is when each cluster mirrors the characteristics of the population. When this is the case, a small number of clusters results in a sample that is representative of the population. Systematic sampling is a method that can be used when it is possible to view the population of interest as consisting of a list or some other sequential arrange- ment. A value k is specified (for example, k = 50 or k = 200). Then, one of the first k individuals is selected at random, after which every kth individual in the sequence is included in the sample. A sample selected in this way is called a 1 in k systematic sample. DEFINITION Systematic sampling: A way to randomly select a sample from a population to avoid sampling error. Using Data to Support the Decision Making Process 297 30/06/2023 14:28

QUICK TIP In spite of being a very poor way to form a sam- ple, convenience sampling is commonly used in busi- ness. Sometimes, this is due to restrictions or con- straints. If you have to use a convenience sample, give careful thought to how you can randomize ele- ments of it. For example, a sample of Safiya's customers might be selected from her cli- ent database. One of the first k = 20 customers listed could be selected at random, and then every 20th customer after that on the list would also be included in the sample. This would result in a 1 in 20 systematic sample. The value of k for a 1 in k systematic sample is generally chosen to achieve a desired sample size. For example, in Safiya's customer database scenario just described, if there were 900 customers, the 1 in 20 systematic sample described would result in a sample size of 45. If a sample size of 100 was desired, a 1 in 9 systematic sample could be used (because 900/100 = 9). As long as there are no repeating patterns in the population sequence, system- atic sampling works reasonably well. It is often tempting to resort to convenience sampling—that is, using an easily available or convenient group to form a sample. This is a recipe for disaster! Results from such samples are rarely informative, and it is a mistake to try to gen- eralize from a convenience sample to any larger population. DEFINITION Convenience sampling: Using an easily available or convenient group to form a sample. 298 9 Chapter رة ا Ministry of Education 2024-1446 Business Decision Making S1 S2 S3.indb 298 One common form of convenience sampling is sometimes called voluntary response sampling. Such samples rely entirely on individuals who volunteer to be a part of the sample, often by responding to an advertisement, calling a publicized telephone number to register an opinion, or completing a pop-up online survey. It is extremely unlikely that individuals participating in such voluntary response surveys are representative of any larger population of interest. DEFINITION Voluntary response sampling: A form of convenience sampling. Relies on individuals who volunteer to be part of the sample, e.g., by completing an online survey. 30/06/2023 14:28

YOU TRY IT Research examples of sampling methods online. Using either real examples or hypothetical situations to illustrate your answer, describe an example of each of the following: simple random sampling systematic sampling ⚫ cluster sampling • convenience sampling . voluntary response sampling. For each example, explain the benefits and drawbacks of using that particular sampling method. Explain whether every sampling method is appropriate for every situation. وزارة التعليم Ministry of Education 2024-1446 Business Decision Making S1 S2 S3.indb 299 Using Data to Support the Decision Making Process 299 30/06/2023 14:28

REVIEW QUESTIONS 1. A research study was conducted to identify relationships between physical activity during the teenage years, middle age, and poten- tial cognitive impairment later in life. 9,000 women who were being seen at a large mental-health clinic were asked about their levels of physical activity as teenagers and at ages 30 and 50. Data about the subjects' mental health were also collected as part of the process. A press release about this study generalized the results of this study to all women. In the press release, the researcher who conducted the study is quoted as saying, "Our study shows that women who are regularly physically active at any age have lower risk of cognitive impairment than those who are inactive, but that being physically active as a teenager is most important in preventing cognitive impairment." Answer the following three questions for this observational study. a. What is the population of interest? b. Was the sample selected in a reasonable way? c. Is the sample likely to be representative of the population of interest? 2. For each of the situations described, state whether the sampling procedure is simple random sampling, cluster sampling, system- atic sampling, or convenience sampling. a. All first-year students at a university are enrolled in one of 30 sections of a seminar course. To select a sample of first-years at this university, a researcher selects four sections of the seminar course at random from the 30 sections and all students in the four selected sections are included in the sample. b. To obtain a sample of the seniors at a particular high school, a researcher writes the name of each senior on a slip of paper, places the slips in a box and mixes them, and then selects 10 slips. The students whose names are on the selected slips of paper are included in the sample. c. To obtain a sample of those attending a football game, a researcher selects the 24th person through the door. Then, every 50th person after that is also included in the sample. 300 9 Chapter رة ا Ministry of Education 2024-1446 Business Decision Making S1 S2 S3.indb 300 30/06/2023 14:28