Fundamentals of Statistics (2nd Edition)
It is helpful to consider this definition in three parts.The first part of the definition states that statistics involves the collection of information. The second refers to the organization and summarization of information. Finally, the third states that the information is analyzed to draw conclusions or answer specific questions.
What is the information referred to in the definition? The information is data.According to the American Heritage Dictionary, data are “a fact or proposition used to draw a conclusion or make a decision.”Data can be numerical, as in height, or they can be nonnumerical, as in gender. In either case, data describe characteristics of an individual.The reason that data are important in statistics can be seen in this definition: data are used to draw a conclusion or make a decision.
Analysis of data can lead to powerful results. Data can be used to offset anecdotal claims, such as the suggestion that cellular telephones cause brain cancer. After carefully collecting, summarizing, and analyzing data regarding this phenomenon, it was determined that there is no link between cell phone usage and brain cancer.
Because data are powerful, they can be dangerous when misused. The misuse of data usually occurs when data are incorrectly obtained or analyzed. For example, radio or television talk shows regularly ask poll questions in which respondents must call in or use the Internet to supply their vote.The only individuals who are going to call in are those that have a strong opinion about the topic. This group is not likely to be representative of people in general, so the results of the poll are not meaningful.Whenever we look at data, we should be mindful of where the data come from.
Even when data tell us that a relation exists, we need to investigate. For example, a study showed that breast-fed children have higher IQs than those who were not breast-fed. Does this study mean that mothers should breast-feed their children? Not necessarily. It may be that some other factor contributes to the IQ of the children. In this case, it turns out that mothers who breast-feed generally have higher IQs than those who do not.Therefore, it may be genetics that leads to the higher IQ, not breast-feeding. This illustrates an idea in statistics known as the lurking variable. In statistics, we must consider the lurking variables because two variables most often are influenced by a third variable.A good statistical study will have a way of dealing with the lurking variable.
Another key aspect of data is that they vary. To help understand this variability, consider the students in your classroom. Is everyone the same height?
No. Does everyone have the same color hair? No. So, among a group of individuals there is variation. Now consider yourself. Do you eat the same amount of food each day? No. Do you sleep the same number of hours each day? No. So,even looking at an individual there is variation. Data vary. The goal of statistics is to describe and understand the sources of variation.
Because of this variability in data, the results that we obtain using data can vary.This is a very different idea than what you may be used to from your mathematics classes. In mathematics, if Bob and Jane are asked to solve they will both obtain as the solution, if they use the correct procedures. In statistics, if Bob and Jane are asked to estimate the average commute time for workers in Dallas, Texas, they will likely get different answers, even though they both use the correct procedure. The different answers occur because they likely surveyed different individuals, and these individuals have different commute times. Note: The only way Bob and Jane would get the same result is if they both asked all commuters or the same commuters how long it takes to get to work, but how likely is this?
So, in mathematics when a problem is solved correctly, the results can be reported with 100% certainty. In statistics, when a problem is solved, the results do not have 100% certainty. In statistics, we might say that we are 95% confident that the average commute time in Dallas, Texas is 21.5 minutes.While uncertain results may sound disturbing now, it will become more apparent what this means as we proceed through the course.
Without certainty, how can statistics be useful? Statistics can provide an understanding of the world around us because recognizing where variability in data comes from can help us to control it. Understanding the techniques presented in this text will provide you with powerful tools that will give you the ability to analyze and critique media reports,make investment decisions (such as what mutual fund to invest in), or conduct research on major purchases (such as what type of car you should buy). This will help to make you an informed consumer of information and guide you in becoming a critical and statistical thinker.
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