Random Variables and Sources of Variation - Sampling Error - Non-sampling Variation - Management Assignment Help

Assignment Task:

Learning Objectives
The learning objectives associated with this module are:

• Define and understand the omnipresence of variability by stating major sources and types of variation.
• Define the discipline and science of statistics, and distinguish it from mathematics.
• Define a variable, their major types, and levels of measurement.
• Understand the basics stages of the statistical data investigation process.
• Understand the major types of statistical data investigations, namely, surveys, observational studies and experiments.
• Discuss the idea of statistical inference and how the use of samples give rise to uncertainty.
• Explore the central concepts of variability in a simple statistical data investigation.

Random Variables and Sources of Variation
Statistics, as defined by MacGillivray, Utts and Heckard (2014), is the “discipline and science of obtaining, understanding, modelling, interpreting, and using data in all real and complex systems and processes that involve uncertainty and variation” (p.15). Data, variation, and uncertainty are at the core of statistics. Statistical data refer to variables, which are defined as any characteristic or value of a unit that can change or vary. The idea of a unit is very broad and can refer to a person, a time point, a device, or system. Variation is all around us. This idea is referred to as the “omnipresence of variability” and is the reason why the field of statistics emerged. There are many forms of variation that you need understand. These can be summarised into four main categories.

•    Natural or Real Variation: This refers to inherent, natural variability that is left over when all the other sources of variability are accounted for. Take, for example, a person’s height. Height varies greatly in the population, but there a many other variables that can explain why one person is taller than another. Males tend to be taller than females. Adults are taller than children. However, even if we compared males of a similar age, height will still vary. This is the natural or “real” variability that statistics seeks to measure and understand. Natural variability is what makes the world an interesting place.
•    Explainable Variation: This is the variation in one variable that we can explain by considering another variable. The statistical tests and models that you will learn in this course seek to test relationships and effects that different variables have on each other. You already know heaps of examples of variables that “explain” other variables. For example, you know that height can help explain variation in weight, smoking can help us understand why some people are at a greater risk of lung cancer, gender can explain variation in the risk of heart disease, and the amount of hours spent studying can help explain exam scores.
•    Sampling Error: Take a sample from a population, make a measurement and record the result. Now, repeat the process many times. The sample results will all differ to a certain degree. This type of variability is known as sampling variability. Statistical inference and hypothesis testing, to be introduced in later modules, deals with this specific form of variability and the implications it has on drawing conclusions from our studies. We will also consider this important source of variation in an interesting demonstration at the end of this module.
•    Non-sampling Variation: This refers to any artificial variability induced by the research process. As researchers, you try to understand real variability, while acknowledging, accounting or controlling for induced variability. Induced variability can come from many factors. The following are some common examples:
•    Measurement: Sometimes referred to as observational error, this is the variability associated with how we have measured our variables. All measures of a variable are imperfect. We need to understand the reliability and validity of our measurements to account for measurement variability. 

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