Chapter 11 Making Sense of Data: First Steps

Chapter 11 Making Sense of Data: First Steps

In chapter 11 of the text, we began the study of applied statistical analysis. The main goal of this study is to introduce some tools that can be used to summarize a batch of numbers and make inferences. These tools will help you in your coursework, in conducting your own research projects, and in interpreting statistics in the media. Furthermore, political science leads to quite a few interesting and exciting career opportunities, and many of these jobs require at least a rudimentary knowledge of quantitative research methods. Think, for example, of someone working for a nongovernmental organization like the World Health Organization. In all likelihood, her or his ability to interpret and apply statistics would be quite useful in analyzing health projects around the world. Or suppose you have an internship at a government agency. You may be of greater assistance to your employers if you can provide a modest amount of technical advice about reports they are receiving or information the agency supplies to the public. So there are lots of reasons for studying at least a few quantitative methods, no matter how far removed from the world of politics they seem to be.

Many students are initially put off by having to learn statistics, but our experience tells us that this aversion often results from unfamiliarity with the subject, not its inherent difficulty. So even if you are one who says, “I stink at math,” at least attempt to keep an open mind because you may find that these concerns are misplaced.

Here are a few tips:

Keep up. Unlike some subjects that may seem to lend themselves to cramming, statistics is best learned step by step; you should make sure you understand each concept reasonably well before moving on to the next one. And since the ideas are possibly daunting at first sight, it is easy to get lost if you try to learn everything all at once. This is, in short, one course where it pays to stay on top of the readings and assignments.

Learn by doing. You cannot get into good physical shape by reading articles on conditioning. You have to work out regularly. In the same way and for essentially the same reasons, data analysis has to be learned actively. It is crucial that you perform your own analysis. Simply reading about how it is done will not give you the functional understanding that makes statistics so useful. The exercises in this workbook are designed to do just that: give you actual training in data analysis.

Keep substance over method. Whenever possible think about the substantive context of a problem. You may be asked to calculate a mean or standard deviation, for example. But what is important is not the numbers per se (although they do have to be correct) but rather what they say about the problem at hand. For example, instead of just writing, “The average is ten,” you should write, “The average is ten thousand dollars,” to keep firmly in mind that you are working on a concrete issue and not an abstract algebra problem.

Be neat and orderly. Yes, this advice sounds peevish. Yet we have found that a huge number of mistakes and misconceptions arise simply from disorderly note taking and hand calculations. It is always a good idea to have plenty of scrap paper handy and to work in a top-down fashion rather than jump all around the page putting intermediate calculations here and there in no logical order. It should be possible for you or anyone else to reconstruct your thought processes by following your calculations from beginning to end. That way errors and misunderstandings can be spotted and corrected.

A computer is only a tool. Computers can compute answers to statistics problems and analyze data very quickly. Computers, however, cannot tell you what you need to solve a problem. When you begin analysis work on the computer, take a few moments to contemplate exactly what you need to complete a problem or an analysis. What do you need to find out? What procedure will give you the answers?

In these assignments we ask you to examine one variable at a time. The idea is to summarize a possibly large batch of numbers with a few indicators of a distribution’s central tendency, dispersion, and shape. We have also appended a brief set of guidelines for preparing your own data for analysis.

Exercise 11-1. In this first exercise, you should consider some of the basic terms that are key to understanding chapter 11. Some of these terms can sound too similar to differentiate or appear too complex to understand at first glance. For each pair of terms below, first define each term then explain the important differences between them.

1. Relative frequency and cumulative frequency
2. Frequency and proportion
3. Central tendency and dispersion
4. Range and interquartile range
5. Frequency distribution and normal distribution

Exercise 11-2. Measures of central tendency describe the typical value of a variable—the average, middle, or most frequently observed value. Below you will find variables that might arise in political science research, as well as a measure of central tendency. For each pairing explain why you think the selected measure would be appropriate or inappropriate. If you think it would be inappropriate, explain why you think a different measure would be a better choice. When answering the questions, make sure to consider levels of measurement and the possibilities of outliers or skewed data.

1. Variable: type of political system: indicates the political system in a country (democracy, dictatorship, monarchy, etc.)

Measure of central tendency: mean

1. Variable: marital status: indicates whether respondent is single, married, separated, divorced, widow(er)

Measure of central tendency: mode

1. Variable: AIDS-related deaths: number of AIDS-related deaths in a country in a year

Measure of central tendency: median

1. Variable: annual household income: dollar amount earned by each household in a year

Measure of central tendency: mean

1. Variable: Environmental Performance Index: a 0-to-100 score that measures 180 countries’ performance across ten issue categories covering environmental health and ecosystem vitality

Measure of central tendency: median

4. Variable: Internet connection speed: indicates the average Internet connection speed in a country (1 = 0 to 4 Mbps; 2 = 4.1–8 Mbps; 3 = greater than 8 Mbps)

Measure of central tendency: mode

Exercise 11-4. In table 11-2 you will find estimated AIDS-related deaths in Central African countries in 2017 in the frequency column. Complete the table by calculating the proportion, percentage, and cumulative percentage.

Exercise 11-10. Figure 11-1 contains two distributions, A and B.

In this graph, the X axis shows values from -50 to 250 with an interval of 50. There are two distribution curves A and B: “A” is a normal line and “B” is a dotted line. Curve “A” begins at the value “50,” and shows steep increase and reaches its highest peak at the value “100,” then decreases before “150.” Curve “B” begins before “-50” and gradually increases from “-25” and reaches its maximum height at the value “100”, and then gradually decreases in a similar way it increased, ending after “250.” Curve “A” has a higher peak than curve “B”.

1. Which distribution has the greater variation?
2. Which distribution has the smaller standard deviation?
3. How do measures of central tendency for distributions A and B differ, if they differ at all?
4. What are the mean and the median of distribution A?
5. What are the mean and the median of distribution B?

Exercise 11-12. Define as clearly as possible the following statistics. Try to explain each term in plain language.

1. The sample standard deviation
2. The median
3. The mode
4. The trimmed mean
5. The interquartile range