statistics begins as a shadowy mathematical nightmare, followed by a mandatory course or two in college, and is considered a weakness forevermore. Why? The answer is incredibly simple: The way statistics is taught is not the way most people learn, including most methods used to teach the Statistics and Probability domain within the Common Core State Standards Initiative for Grades 6–12. Most people learn easily through impressions and experiences, the qualitative side of life, not through numbers and equations, the quantitative side. This book shows that the fundamental concepts of statistics can be learned through impressions and experiences, too. Simply put, understanding the meaning and worth of statistics does not require the ability to calculate them.
Statistics are ways of understanding more about questions and issues that interest us. The Tao of Statistics is a journey down a path that leads to an intriguing view of the world. The statistical view of the world is of a place where knowledge is neither certain nor random. Statistical portraits are painted in pastel rather than in primary colors. Extremes are understood for the information they contain but are done so in a context of centrality. The Tao of Statistics lays a path to this understanding of the world. The path leads to a view of the subtle patterns in life that were invisible before.
The world has changed. Only a few decades ago, a relative handful of people could manage society’s needs for calculating and interpreting statistics. Now, paradoxically, an even smaller group needs to know how to calculate statistics, because computers have taken over much of the calculation. This may be both a blessing and a curse. Vastly more of us, however, need to understand what statistics are telling us about our work, our communities, our children’s test scores, and even our play, especially in an age where Big Data places governments, financial, communications, medical, insurance, and marketing firms in control of vast amounts of information on our daily lives—from where and what we like to eat, to our favorite colors, flowers, and vacation spots.
Yet the larger group of consumers who now need to understand where and how statistics are developed and used tends to have a more qualitative learning style than statisticians of years ago. This critical difference (i.e., “the rest of us”) has been largely overlooked by writers of textbooks on the topic. Regardless of the prestige of the school or the academic domain, statistics almost universally is taught through equations, hour after brain-breaking hour. What is the point of this traditional chore? Apparently, it is to inculcate an intuitive understanding of statistics that will follow from it. Is there evidence to support this expected outcome? That is, do we live in a nation with a collective intuitive understanding of statistics? I do not think so. More likely, we live in a nation that cringes at the term statistics and is skeptical of their use. It does not have to be this way.
This book introduces readers to the commonly encountered terms and techniques in statistics through verse, graphical illustrations, and accompanying text. No equations are used. The result is an understanding of each concept that is created without having to do math.
This journey is about living a series of experiences, their impressions, and sometimes even their emotions. These experiences lead to a deeper understanding of the world of statistics as we follow the paths of two research-oriented professionals with different careers as they experience the statistical concepts presented herein. Try to experience the concepts with them. Stroll down the path together. Before beginning, though, a few thoughts on statistics themselves might be helpful.
Statistics are filters on how we see the world. They focus our vision, and they help us to see through the fog. In doing so, they also prevent us from seeing some of what else is there. Stay aware of what is being filtered out, too.
You do not need to know how to calculate statistics to understand what they are telling you.
Averages do not exist for most things. They are only ideas. A truly average person does not exist. The idea of an average is what is useful.
The rest of statistics is no more real than averages. Regardless of how technical a statistic sounds, it is still only an idea that can be grasped by all.
The world of statistics has become technically quite complex. When someone produces a statistic that you have never heard of or seen before, simply ask what it does and for an example that demonstrates its usefulness.
Ideas lead to understanding. Experiencing the ideas of statistics motivates us to develop and deepen our understanding of them.
This journey is best experienced in comfortable clothing, in a favorite chair, and in a quiet space.
Take your time.
Breathe deeply and slowly.
Relax.
Let the world pass you by.
For each section, try to open yourself up to the impressions from the verse and from the graphic. Next, try to put yourself in the shoes of each of the two professionals we follow, as they use statistics in their otherwise specialized jobs. Then, reread the verse, pausing for a few moments, and look again at the illustration to deepen your understanding of the concept and help you to anchor it in your long-term memory.
Finally, be ready for a noticeable change. Life never looks quite the same again after being seen through statistical eyes. It is more predictable but less deterministic. Mostly, one acquires a growing sense of wonderment at the patterns and relationships that emerge from the chaos.
If you enjoy this journey, you might also value the result of learning the math behind statistics. With the mathematics comes a much richer appreciation of the statistical view of life. The precision with which it approaches ambiguity is simultaneously humbling and amusing, most typically when conclusions are drawn from sparse data, when much of the needed information is simply not present.
1. The Beginning — The Question
The world is hazy
No clean lines or sharp points
Focus the camera
The world of statistics starts with a question. Many types of statistics exist because questions can be of almost any type, can be about almost anything, and can take place under quite varied conditions. This variety calls for an almost equal number of statistical approaches to answers.
Statistics need data. Data come from measures. Good answers to important questions require good data from relevant measures. Good measures are specific and, through that specificity, are informative. If the selected measures do not directly address the questions, the statistics can be meaningless because they will have lost their context.
Statistics become important when they are about things that people consider important. In this book, we will follow two professionals with different careers as they use statistical concepts to answer questions that are relevant to their own lines of work. The first is a high school principal with questions about differences in quality and other characteristics of the various classes taught at his school. The second is a director of public health with questions about how well the residents of her state are meeting national guidelines for public health issues, such as immunizations, especially for individuals receiving public medical assistance.
The choice of careers and the specific concerns of the related fields really do not matter to the interpretation of statistics. What matters is that
