Statistics Translated, Second Edition: A Step-by-Step Guide to Analyzing and Interpreting Data Second Edition

Book Preface

Many Students Do Not Know What They’re Getting Into
The first thing I have discovered is most people do not really know the definition of  statistics. To me, it seems odd they would be sitting in a class where they do not know  what they are about to study, but it occurs all the time. Although we will cover this  topic in great detail later in the book, let me give you a simple definition for now: „ The science of statistics is nothing more than the use of arithmetic tools to  help us examine numeric data we have collected and make decisions based  on our examination. The first of these tools, descriptive statistics, helps  us understand our data by giving us the ability to organize and summarize  it. Inferential statistics, the second tool, helps us make decisions or make  inferences based on the data.

Second, I’ve found that students greatly overestimate the proficiency in math they  need in order to calculate or comprehend statistics. Whenever I find people worrying about their math skills, I always ask them, “Can you add, subtract, multiply, and  divide? Can you use a calculator to determine the square root of a number?” Often,  their answer is “yes” so I tell them, “That is great news! You have all the math background you need to succeed!” I’ve found that many people, when I tell them this,  breathe a big sigh of relief!
Next, I’ve discovered that a class in statistics isn’t nearly as bad as people anticipate if they approach it with an open mind and learn a few basic rules. Since most  people want to be able to use statistics to plan research, analyze its results, and make  sound statistically based decisions, they want to become consumers of statistics rather  than statisticians per se. As consumers, they want to be able to make decisions based  on data, as well as understand decisions others have made. With that in mind, this  book will help you; all you must do is approach it with an open mind and learn a few, easily understood steps.

Fourth, I have found that students get confused by all the terminology thrown  around in a statistics course. For instance, for a given statistical problem you could  find the correct answer by using procedures such as the Scheffé test, Tukey’s HSD test,  or the Bonferroni procedure. The truth is, you could use any one of these techniques  and get very similar answers. I was recently at a meeting where a very prominent statistician jokingly said we do this “to confuse graduate students”; there certainly seems  to be a lot of truth in what he said! These types of terms, as well as the ambiguity of  having many terms that mean basically the same thing, seem to intimidate students  sometimes. Knowing that, I like to stick to what students need to know most of the  time. We can deal with the exceptions on an “as needed” basis.

Along these same lines, I’ve discovered many instructors try to cover far too much  in an introductory statistics class, especially when they are dealing with people who  want to be consumers of statistics. Research shows that 30 to 50% of studies published  in prestigious research journals use a small set of common descriptive and inferential  statistics. My experience, however, is that the average student tends to use the same  basic statistical techniques about 90% of the time. Knowing that, we are left with a  manageable problem: we need to be able to identify when to use a given statistical test,  use it to analyze data we have collected, and interpret the results. To help you do that,  I have developed a set of six steps to guide you. Using these steps, you will be able to  work with the statistics you need most of the time.

A Few Simple Steps

You may be asking yourself, “Why are these steps so important? How could something  so important be so easy? Exactly what are these steps?” If so, we can begin to answer  your questions with a short story: Do you remember back in high school when you took beginning algebra? Can  you remember what you did the first few days of class? If you can’t, let me refresh your  memory.

You spent the first few class sessions learning about the basic rules of algebra.  These included topics such as the commutative property, the associative property, the  distributive property, and other things that seemed really boring at the time. If you  were like me, you probably questioned spending valuable time worrying about rules  that did not seem to apply to algebra. If you were really like me, you didn’t pay attention since you were saving your energy and attention until it could be used for “real” math.

Unfortunately, for many of us, our plan backfired. We soon discovered that learning algebra was a linear process and we had tried to start in the middle of the line;  learning those boring rules was important if we were going to succeed. At that point,  in order to understand what was going on, we found it necessary to go back and learn  what we should have already learned. Some of us went back and learned; some of us  didn’t.

We can apply this analogy to my steps for statistics. In the beginning we will  spend a lot of time discussing these six steps and the fundamentals of statistical decision making. After we get through the basics, we will move into the “real statistics.” For now, just read through these steps and the brief description of what each step entails.

Identify the Problem

At the outset, researchers need to understand both the problem they are investigating and why investigating it is significant.
They may begin by asking questions such as “How do I know  this is a problem?”, “Why is investigating this problem important?”, “What causes this type of problem?”, and “What can  possibly be done to address this problem?” In other cases, researchers may not face a  specific problem; rather they may have an opportunity to conduct or expand research  in a given field. Either way, once they have answered those questions, they need to  develop their problem statement. In this step, they are identifying “what” we are going  to investigate; the remaining five steps will help us understand “how” to investigate it.

State a Hypothesis

A hypothesis is a researcher’s beliefs about what will be found  or what will occur when he or she investigates a problem. For  example, let’s suppose that our school is faced with lower than  average scores on a statewide math test. We have heard that it is  possible that the problem may be based on gender; apparently  males do not perform as well in math as their female classmates, and this may cause  the classes’ overall average to be lower. Since we have considerably more males than  females in our school, we then must ask ourselves, “How can I find out if this is true?”  Or, if we plan on using some type of intervention to increase the achievement of our  male students, we could ask, “What do I think will occur based on what I do?” These  questions lead us to make a statement regarding our beliefs about what will occur. As  I said earlier, stating the hypothesis is the first step in understanding “how” we can  investigate the problem.

Identify the Independent Variable

When statisticians state a hypothesis, they must identify what  they believe causes an event to occur. The first major part of the  hypothesis is called the independent variable and is the “cause”  we want to investigate. In most instances, the independent variable will contain two or more levels. In our preceding example,  our independent variable was gender, and it had two levels, male and female. In other  cases, we may be investigating a problem that has more than one independent variable; the levels of each independent variable will still be identified in the manner we have just described.

Identify and Describe the Dependent Variable

Once researchers identify what they believe will cause an event  to occur, they then must determine what they will use to measure its effect. This second major part of the hypothesis is called  the dependent variable. The researcher will collect data about the  dependent variable and then use descriptive statistics to begin to  understand what effect, if any, the independent variable had on it. In our example, we  are interested in student achievement—our dependent variable. Again, as we said, a  hypothesis may have more than one dependent variable.

Choose the Right Statistical Test

Although there are many different inferential statistical tests,  information about the independent variable, the dependent
variable, and the descriptive statistics will, in most instances,  tell the researcher exactly which statistical test to use. We will  learn to compute both the descriptive and inferential statistics  manually and we will also see examples of computer software that can assist us in  becoming good consumers of statistics.

Use Data Analysis Software to Test the Hypothesis

The manual computations, or the results from statistical software, will give the researcher the information necessary to test a  hypothesis. Based on this, the decision can be made as to whether  the independent variable had any effect on the dependent variable.