Using Real Life Examples to Teach Abstract Statistical Concepts
Summary
This article provides real life examples that can be used to explain statistical concepts. It does not attempt to be exhaustive, but rather, provide a few examples for selected concepts based on what students should know after taking a statistics course.
INTRODUCTION
Efforts in statistics education reform have focused on statistical thinking and conceptual understanding rather than mere knowledge of procedure.
Statistics is not an easy subject to teach. Almost every statistics beginner experiences difficulties understanding the topic. There is a consensus among statisticians that statistics education should focus on data and on statistical reasoning rather than on either the presentation of as many methods as possible or the mathematical theory of inference. Generally, the goal of statistics education is to answer ‘real world’ questions. The student should develop sufficient competence to understand and draw accurate meaning from a statistical argument. Examples, therefore, should be presented in the context of real-world problems. Recommendations for statistics courses from the GAISE (Guidelines for Assessment and Instruction in Statistics Education) Report (Garfield et al. 2005) include the following:
Emphasize statistical literacy and develop statistical thinking.
Use real data.
Stress conceptual understanding rather than mere knowledge of procedures.
Foster active learning in the classroom.
Use technology for developing conceptual understanding and analyzing data.
Use assessments to improve and evaluate student learning.
Furthermore, the guidelines are given in the GAISE
The report suggests designing statistics courses that teach students to communicate results of a statistical analysis and do so in context. In addition, students should develop skills to read and critique news stories and journal articles that include statistical information. That is, they should have statistical reasoning skills as well as statistical understanding.
This goal of applying statistics to everyday life is reiterated by Gal and Ginsburg (1994).
It is sometimes difficult for students to relate statistical concepts presented in class to real world problems and everyday situations. Therefore, teaching introductory statistics requires the instructor not only to transmit knowledge but also to enhance students’ motivation and attention (Symanzik and Vukasinovic 2006). From our experiences in teaching statistics, what we have found helpful is to relate the statistical concepts to real life situations. In most cases, this strategy helps lower the students’ statistical anxiety. The impact of statistics anxiety on student learning is well documented (e.g. Benson
1989; Dillon 1982; Roberts and Bilderback 1980; Roberts and Saxe 1982).
Researchers (e.g. Everson et al. 2008) have provided some ideas for putting the GAISE guidelines into practice in the statistics classroom. Interactivity, hands-on exercises, visualization of statistical concepts and well-documented real-life examples are some of the features of a statistical course that help stimulate the student’s activity in class, ease understanding of statistical concepts and make the whole course more attractive and fun for the student.
In this article, we discuss certain real life examples that we normally use to explain statistical concepts.
We do not attempt to cover all the statistical concepts, but rather, we just provide a few examples that are popular with students. Each of the concepts discussed can be linked directly to the goals suggested in the GAISE Report.
REAL LIFE EXAMPLES:
If the field of statistics could be described in one word, that word would be variability. In almost all cases we are attempting to explain variance or apportion variance. We use models (samples) as a representation of the real world so it should not be surprising that there is variability in whatever characteristics we study. As the GAISE Report suggests, students should understand that variability is natural and is also predictable and quantifiable.
The weather reports we hear on the news every day provide an illustration of the value of variability. While two regions can have the same average temperature of, say, 55°F, we get a better understanding of the weather in these regions by considering the variation in temperature. For instance, a region that is near the coast is more likely to have a narrower range than one further inland. That is, the average temperature of 55°F for the inland region may have highs of 75°F and lows of 35°F, while in the coastal region the highs might be 60°F with lows of 50°F. Although the regions have the same average temperature, the higher standard deviation means that predictions are less reliable for the temperature of the inland region.
A similar phenomenon can be found in sports. In sports, trying to predict which teams will win, on any given day, may include looking at the standard deviations of the team ratings in various categories.
In such ratings, anomalies can match strengths versus weaknesses in an attempt to understand which factors are the stronger indicators of eventual scoring outcomes. For instance, there will be teams that excel in some aspects of the sport and perform poorly in others. Teams may have a great offense and a weak defense or vice versa. Furthermore, teams with higher standard deviations will be more unpredictable. It is important, of course, to consider the mean with the standard deviation in making predictions. A team that is constantly good in most categories will have a low standard deviation but so will a team that is consistently bad.
It is important that students understand the concept of a sampling distribution and how it applies to making statistical inferences. Sampling distributions are important because inferential statistics is based on them. Inferential statistics is about drawing conclusions about the population based on sample data.
An example of this is the polling done prior to elections. At the end of August 2008, two of the polls conducted to predict the winner of the US presidential race provided somewhat different results (see table 1). Looking at these results provides an opportunity to discuss what happens when different samples are drawn from the same population.
Although the samples may have been drawn from the same population they may provide different estimates. Furthermore, individual sample statistics do not always match the true population value but vary around it. At this point, the instructor can discuss the distribution of sample statistics
(e.g. means being approximately normal).
This demonstration can also naturally lead to a discussion of the margin of error as it is computed in political polls and to confidence intervals (Baumann and Danielson 1997). Examining the formula for the margin of error can also lead to a discussion of the effect of sample size and variability in the sampling statistics. Students can see that larger samples correspond to smaller sampling variation and smaller margins of error and that population size is not a factor in the margin of error. With these ideas clarified, students can turn to applications such as projecting winners in elections or comparing the responses of subgroups such as men and women.
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The paper published by:
Nyaradzo Mvududu Seattle Pacific University, Washington, USA. e-mail: [email protected]
Gibbs Y. Kanyongo Duquesne University, Pittsburgh, Pennsylvania, USA. e-mail: [email protected]