《统计学通俗指南》第三版：清晰理解数据科学

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"《统计学通俗英语第三版》(Statistics In Plain English 3rd)是由Timothy C. Urdan撰写的一本深入浅出的统计学教材。该书旨在帮助读者理解和应用统计概念，而不局限于专业术语和复杂的数学公式。作者W.L. Warrick\& Co. 是一位知名的统计学教育者，他的作品通过Routledge出版社发行，隶属于Taylor&Francis Group。这本书的第三版在2010年出版，包含了丰富的实例和实用的解释，使读者能够轻松地掌握统计的基本原理。它覆盖的主题广泛，从概率、数据分布、假设检验、回归分析到更高级的统计技术，都用通俗易懂的语言进行阐述。书中强调了统计在日常生活、商业决策以及科学研究中的实际应用，适合对统计有初步了解或希望提升统计技能的读者阅读。《统计学通俗英语》的特点是注重实用性，避免了专业领域的行话和冗长的理论推导，而是以故事化的方式呈现知识，帮助读者快速理解并掌握统计的核心概念。此外，书中还提供了详细的步骤指导，使得即使是统计初学者也能跟随学习，并且为了方便版权管理，读者在使用部分内容时需要通过Copyright Clearance Center获取许可。本书的国际标准书号(ISBN)为978-0-415-87291-1（平装版），并由Routledge在纽约和霍夫分别发行。对于组织和个人欲复制或电子使用书中的材料，需遵循版权规定，可通过www.copyright.com或联系版权所有者获得相应的授权。《统计学通俗英语》是一部理想的入门读物，帮助非专业背景的人们克服对统计学的畏惧，提升他们的数据分析能力，使其在日常生活中更好地运用统计学原理做出明智的决策。"

Introduction to Social Science Research Principles and Terminology

■

about the characteristics of the larger population that the sample is supposed to represent.

Although researchers are sometimes interested in simply describing the characteristics of a

sample, for the most part we are much more concerned with what our sample tells us about the

population from which the sample was drawn. In the depression study, the researcher does not

care so much about the depression levels of her sample per se. Rather, she wants to use the data

from her sample to reach some conclusions about the depression levels of adolescents in general.

But to make the leap from sample data to inferences about a population, one must be very clear

about whether the sample accurately represents the population. An important ﬁrst step in this

process is to clearly deﬁne the population that the sample is alleged to represent.

Sampling Issues

ere are a number of ways researchers can select samples. One of the most useful, but also the

most diﬃcult, is random sampling. In statistics, the term random has a much more speciﬁc

meaning than the common usage of the term. It does not mean haphazard. In statistical jargon,

random means that every member of a population has an equal chance of being selected into

a sample. e major beneﬁt of random sampling is that any diﬀerences between the sample

and the population from which the sample was selected will not be systematic. Notice that in

the depression study example, the sample diﬀered from the population in important, systematic

(i.e., nonrandom) ways. For example, the researcher most likely systematically selected adoles-

cents who were more likely to be depressed than the average adolescent because she selected

those who had visited mental health service providers. Although randomly selected samples may

diﬀer from the larger population in important ways (especially if the sample is small), these dif-

ferences are due to chance rather than to a systematic bias in the selection process.

Representative sampling is a second way of selecting cases for a study. With this method,

the researcher purposely selects cases so that they will match the larger population on speciﬁc

characteristics. For example, if I want to conduct a study examining the average annual income

of adults in San Francisco, by deﬁnition my population is “adults in San Francisco.” is popula-

tion includes a number of subgroups (e.g., diﬀerent ethnic and racial groups, men and women,

retired adults, disabled adults, parents and single adults, etc.). ese diﬀerent subgroups may

be expected to have diﬀerent incomes. To get an accurate picture of the incomes of the adult

population in San Francisco, I may want to select a sample that represents the population well.

erefore, I would try to match the percentages of each group in my sample that I have in my

population. For example, if 15% of the adult population in San Francisco is retired, I would

select my sample in a manner that included 15% retired adults. Similarly, if 55% of the adult

population in San Francisco is male, 55% of my sample should be male. With random sampling,

I may get a sample that looks like my population or I may not. But with representative sam-

pling, I can ensure that my sample looks similar to my population on some important variables.

is type of sampling procedure can be costly and time-consuming, but it increases my chances

of being able to generalize the results from my sample to the population.

Another common method of selecting samples is called convenience sampling. In conve-

nience sampling, the researcher generally selects participants on the basis of proximity, ease-of-

access, and willingness to participate (i.e., convenience). For example, if I want to do a study

on the achievement levels of eighth-grade students, I may select a sample of 200 students from

the nearest middle school to my oﬃce. I might ask the parents of 300 of the eighth-grade stu-

dents in the school to participate, receive permission from the parents of 220 of the students,

and then collect data from the 200 students that show up at school on the day I hand out my

survey. is is a convenience sample. Although this method of selecting a sample is clearly less

labor-intensive than selecting a random or representative sample, that does not necessarily make

it a bad way to select a sample. If my convenience sample does not diﬀer from my population of

■

Statistics in Plain English, Third Edition

interest in ways that inﬂuence the outcome of the study, then it is a perfectly acceptable method of

selecting a sample.

Types of Variables and Scales of Measurement

In social science research, a number of terms are used to describe diﬀerent types of variables.

A variable is pretty much anything that can be codiﬁed and has more than a single value

(e.g., income, gender, age, height, attitudes about school, score on a meas ure of depression). A

constant, in contrast, has only a single score. For example, if every member of a sample is male,

the “gender” category is a constant. Types of variables include quantitative (or continuous)

and qualitative (or categorical). A quantitative variable is one that is scored in such a way that

the numbers, or values, indicate some sort of amount. For example, height is a quantitative (or

continuous) variable because higher scores on this variable indicate a greater amount of height.

In contrast, qualitative variables are those for which the assigned values do not indicate more or

less of a certain quality. If I conduct a study to compare the eating habits of people from Maine,

New Mexico, and Wyoming, my “state” variable has three values (e.g., 1 = Maine, 2 = New

Mexico, 3 = Wyoming). Notice that a value of 3 on this variable is not more than a value of 1 or

2—it is simply diﬀerent. e labels represent qualitative diﬀerences in location, not quantitative

diﬀerences. A commonly used qualitative variable in social science research is the dichotomous

variable. is is a variable that has two diﬀerent categories (e.g., male and female).

Most statistics textbooks describe four diﬀerent scales of meas ure ment for variables: nomi-

nal, ordinal, interval, and ratio. A nominally scaled variable is one in which the labels that

are used to identify the diﬀerent levels of the variable have no weight, or numeric value. For

example, researchers often want to examine whether men and women diﬀer on some variable

(e.g., income). To conduct statistics using most computer software, this gender variable would

need to be scored using numbers to represent each group. For example, men may be labeled “0”

and women may be labeled “1.” In this case, a value of 1 does not indicate a higher score than a

value of 0. Rather, 0 and 1 are simply names, or labels, that have been assigned to each group.

With ordinal variables, the values do have weight. If I wanted to know the 10 richest people

in America, the wealthiest American would receive a score of 1, the next richest a score of 2, and

so on through 10. Notice that while this scoring system tells me where each of the wealthiest 10

Americans stands in relation to the others (e.g., Bill Gates is 1, Oprah Winfrey is 8, etc.), it does

not tell me how much distance there is between each score. So while I know that the wealthiest

American is richer than the second wealthiest, I do not know if he has one dollar more or one

billion dollars more. Variables scored using either interval and ratio scales, in contrast, contain

information about both relative value and distance. For example, if I know that one member of

my sample is 58 inches tall, another is 60 inches tall, and a third is 66 inches tall, I know who

is tallest and how much taller or shorter each member of my sample is in relation to the others.

Because my height variable is measured using inches, and all inches are equal in length, the

height variable is measured using a scale of equal intervals and provides information about both

relative position and distance. Both interval and ratio scales use measures with equal distances

between each unit. Ratio scales also include a zero value (e.g., air temperature using the Celsius

scale of meas ure ment). Figure 1.2 provides an illustration of the diﬀerence between ordinal and

interval/ratio scales of meas ure ment.

Research Designs

ere are a variety of research methods and designs employed by social scientists. Sometimes

researchers use an experimental design. In this type of research, the experimenter divides the

cases in the sample into diﬀerent groups and then compares the groups on one or more variables

Introduction to Social Science Research Principles and Terminology

■

of interest. For example, I may want to know whether my newly developed mathematics cur-

riculum is better than the old method. I select a sample of 40 students and, using random

assignment, teach 20 students a lesson using the old curriculum and the other 20 using the new

curriculum. en I test each group to see which group learned more mathematics concepts. By

applying students to the two groups using random assignment, I hope that any important dif-

ferences between the two groups get distributed evenly between the two groups and that any

diﬀerences in test scores between the two groups is due to diﬀerences in the eﬀectiveness of the

two curricula used to teach them. Of course, this may not be true.

Correlational research designs are also a common method of conducting research in the

social sciences. In this type of research, participants are not usually randomly assigned to

groups. In addition, the researcher typically does not actually manipulate anything. Rather, the

researcher simply collects data on several variables and then conducts some statistical analyses

to determine how strongly diﬀerent variables are related to each other. For example, I may be

interested in whether employee productivity is related to how much employees sleep (at home,

not on the job). So I select a sample of 100 adult workers, meas ure their productivity at work,

and meas ure how long each employee sleeps on an average night in a given week. I may ﬁnd that

there is a strong relationship between sleep and productivity. Now logically, I may want to argue

that this makes sense, because a more rested employee will be able to work harder and more

eﬃciently. Although this conclusion makes sense, it is too strong a conclusion to reach based on

my correlational data alone. Correlational studies can only tell us whether variables are related

to each other—they cannot lead to conclusions about causality. After all, it is possible that being

more productive at work causes longer sleep at home. Getting one’s work done may relieve stress

and perhaps even allows the worker to sleep in a little longer in the morning, both of which

create longer sleep.

Experimental research designs are good because they allow the researcher to isolate speciﬁc

independent variables that may cause variation, or changes, in dependent variables. In the

example above, I manipulated the independent variable of a mathematics curriculum and was

able to reasonably conclude that the type of math curriculum used aﬀected students’ scores on

the dependent variable, test scores. e primary drawbacks of experimental designs are that they

are often diﬃcult to accomplish in a clean way and they often do not generalize to real-world

situations. For example, in my study above, I cannot be sure whether it was the math curricula

that inﬂuenced test scores or some other factor, such as preexisting diﬀerence in the mathemat-

ics abilities of my two groups of students or diﬀerences in the teacher styles that had nothing to

Ordinal Interval/Ratio

Finish Line

0.25 seconds

5 seconds

3 seconds

0.30 seconds

2 seconds

FIGURE 1.2 Diﬀerence between ordinal and interval/ratio scales of meas ure ment.

■

Statistics in Plain English, Third Edition

do with the curricula, but could have inﬂuenced test scores (e.g., the clarity or enthusiasm of the

teacher). e strengths of correlational research designs are that they are often easier to conduct

than experimental research, they allow for the relatively easy inclusion of many variables, and

they allow the researcher to examine many variables simultaneously. e principle drawback of

correlational research is that such research does not allow for the careful controls necessary for

drawing conclusions about causal associations between variables.

Making Sense of Distributions and Graphs

Statisticians spend a lot of time talking about distributions. A distribution is simply a collec-

tion of data, or scores, on a variable. Usually, these scores are arranged in order from smallest

to largest and then they can be presented graphically. Because distributions are so important in

statistics, I want to give them some attention early in the book and show you several examples

of diﬀerent types of distributions and how they are depicted in graphs. Note that later in this

book there are whole chapters devoted to several of the most commonly used distributions in

statistics, including the normal distribution (Chapters 4 and 5), t distributions (Chapter 9 and

parts of Chapter 7), F distributions (Chapters 10, 11, and 12), and chi-square distributions

(Chapter 14).

Let’s begin with a simple example. Suppose that I am conducting a study of voter’s attitudes

and I select a random sample of 500 voters for my study. One piece of information I might

want to know is the political aﬃliation of the members of my sample. So I ask them if they are

Republicans, Democrats, or Independents. I ﬁnd that 45% of my sample identify themselves

as Democrats, 40% report being Republicans, and 15% identify themselves as Independents.

Notice that political aﬃliation is a nominal, or categorical, variable. Because nominal variables

are variables with categories that have no numerical weight, I cannot arrange my scores in this

distribution from highest to lowest. e value of being a Republican is not more or less than the

value of being a Democrat or an Independent—they are simply diﬀerent categories. So rather

than trying to arrange my data from the lowest to the highest value, I simply leave them as sepa-

rate categories and report the percentage of the sample that falls into each category.

ere are many diﬀerent ways that I could graph this distribution, including pie charts, bar

graphs, column graphs, diﬀerent sized bubbles, and so on. e key to selecting the appropriate

graphic is to keep in mind that the purpose of the graph is to make the data easy to understand.

For my distribution of political aﬃliation, I have created two diﬀerent graphs. Both are ﬁne

choices because both of them oﬀer very clear and concise summaries of this distribution and

are easy to understand. Figure 1.3 depicts this distribution as a column graph, and Figure 1.4

presents the data in a pie chart. Which graphic is best for these data is a matter of personal

preference. As you look at Figure 1.3, notice that the x-axis (the horizontal one) shows the party

Percentage

Republicans

Political Aﬃliation

Independents

Democrats

FIGURE 1.3 Column graph showing distribution of Republicans, Democrats, and Independents.

Introduction to Social Science Research Principles and Terminology

■

aﬃliations: Democrats, Republicans, and Independents. e y-axis (the vertical one) shows the

percentage of the sample. You can see the percentages in each group and, just by quickly glanc-

ing at the columns, you can see which political aﬃliation has the highest percentage of this

sample and get a quick sense of the diﬀerences between the party aﬃliations in terms of the per-

centage of the sample. e pie chart in Figure 1.4 shows the same information, but in a slightly

more striking and simple manner, I think.

Sometimes, researchers are interested in examining the distributions of more than one vari-

able at a time. For example, suppose I wanted to know about the association between hours

spent watching television and hours spent doing homework. I am particularly interested in how

this association looks across diﬀerent countries. So I collect data from samples of high school

students in several diﬀerent countries. Now I have distributions on two diﬀerent variables across

5 diﬀerent countries (the United States, Mexico, China, Norway, and Japan). To compare these

diﬀerent countries, I decide to calculate the average, or mean (see Chapter 2) for each country on

each variable. en I graph these means using a column graph, as shown in Figure 1.5 (note that

these data are ﬁctional—I made them up). As this graph clearly shows, the disparity between

the average amount of television watched and the average hours of homework completed per day

is widest in the United States and Mexico and nonexistent in China. In Norway and Japan, high

school students actually spend more time on homework than they do watching TV according to

my fake data. Notice how easily this complex set of data is summarized in a single graph.

Another common method of graphing a distribution of scores is the line graph, as shown in

Figure 1.6. Suppose that I selected a random sample of 100 college freshpeople who have just

completed their ﬁrst term. I asked them each to tell me the ﬁnal grades they received in each

40%

45%

Republicans

Democrats

Independents

15%

FIGURE 1.4 Pie chart showing distribution of Republicans, Democrats, and Independents.

Japan

Hours

Country

HoursTV

Hourshomework

U.S. MexicoChina Norway

FIGURE 1.5 Average hours of television viewed and time spent on homework in ﬁve countries.

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《统计学通俗指南》第三版：清晰理解数据科学

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