E l e m e n t a r y S t a t i s t i c s i n S o c i a l R e s e a r c h Elementary Statistics in Social Research : E Essentials s s e Jack Levin James Alan Fox n t i Third Edition a l s L e v i n F o x T h i r d E d i t ISBN 978-1-29202-718-0 i o n 9 781292 027180 Pearson New International Edition Elementary Statistics in Social Research Essentials Jack Levin James Alan Fox Third Edition International_PCL_TP.indd 1 7/29/13 11:23 AM ISBN 10: 1-292-02718-5 ISBN 13: 978-1-292-02718-0 Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk © Pearson Education Limited 2014 All rights reserved. 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ISBN 10: 1-292-02718-5 ISBN 10: 1-269-37450-8 ISBN 13: 978-1-292-02718-0 ISBN 13: 978-1-269-37450-7 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Printed in the United States of America Copyright_Pg_7_24.indd 1 7/29/13 11:28 AM 111222232579159157921913955533731 P E A R S O N C U S T O M L I B R AR Y Table of Contents 1. Why the Social Researcher Uses Statistics Jack Levin/James Alan Fox 1 2. Organizing the Data Jack Levin/James Alan Fox 23 3. Measures of Central Tendency Jack Levin/James Alan Fox 57 4. Measures of Variability Jack Levin/James Alan Fox 73 5. Probability and the Normal Curve Jack Levin/James Alan Fox 91 6. Samples and Populations Jack Levin/James Alan Fox 119 7. Testing Differences between Means Jack Levin/James Alan Fox 151 8. Analysis of Variance Jack Levin/James Alan Fox 193 9. Nonparametric Tests of Significance Jack Levin/James Alan Fox 219 10. Correlation Jack Levin/James Alan Fox 255 11. Regression Analysis Jack Levin/James Alan Fox 275 12. Nonparametric Measures of Correlation Jack Levin/James Alan Fox 295 13. Appendix: Instructions for Using ABCalc Jack Levin/James Alan Fox 323 I 333323457373 14. Appendix: A Review of Some Fundamentals of Mathematics Jack Levin/James Alan Fox 327 15. Appendix: Tables Jack Levin/James Alan Fox 333 16. Appendix: List of Formulas Jack Levin/James Alan Fox 347 Index 353 II Why the Social Researcher Uses Statistics A little of the social scientist can be found in all of us. Almost daily, we take educated guesses concerning the future events in our lives in order to plan for new situations or ex- periences. As these situations occur, we are sometimes able to confirm or support our ideas; other times, however, we are not so lucky and must face the sometimes unpleasant consequences. Consider some familiar examples: We might invest in the stock market, vote for a political candidate who promises to solve domestic problems, play the horses, take medi- cine to reduce the discomfort of a cold, throw dice in a gambling casino, try to psych out our instructors regarding a midterm, or accept a blind date on the word of a friend. Sometimes we win; sometimes we lose. Thus, we might make a sound investment in the stock market, but be sorry about our voting decision; win money at the craps table, but discover we have taken the wrong medicine for our illness; do well on a midterm, but have a miserable blind date; and so on. It is unfortunately true that not all of our everyday pre- dictions will be supported by experience. The Nature of Social Research Similar to our everyday approach to the world, social scientists attempt to explain and predict human behavior. They also take “educated guesses” about the nature of social re- ality, although in a far more precise and structured manner. In the process, social scien- tists examine characteristics of human behavior called variables—characteristics that differ or vary from one individual to another (for example, age, social class, and atti- tude) or from one point in time to another (for example, unemployment, crime rate, and population). Not all human characteristics vary. It is a fact of life, for example, that the gender of the person who gave birth to you is female. Therefore, in any group of individuals, gender From Chapter 1 of Elementary Statistics in Social Research: The Essentials, 3/e. Jack Levin. James Alan Fox. Copyright © 2011 by Pearson Education. Published by Allyn & Bacon. All rights reserved. 1 Why the Social Researcher Uses Statistics of mother is the constant “female.” A biology text would spend considerable time dis- cussing why only females give birth and the conditions under which birth is possible, but a social scientist would consider the mother’s gender a given, one that is not worthy of study because it never varies. It could not be used to explain differences in the mental health of children because all of their mothers are females. In contrast, a mother’s age, race, and mental health are variables: In any group of individuals, they will differ from person to person and can be the key to a greater understanding of the development of the child. A re- searcher therefore might study differences in the mental health of children depending on the age, race, and mental health of their mothers. In addition to specifying variables, the social researcher must also determine the unit of observation for the research. Usually, social scientists collect data on individual per- sons. For example, a researcher might conduct interviews to determine if the elderly are victimized by crime more often than younger respondents. In this case, an individual re- spondent is the unit to be observed by the social scientist. However, researchers sometimes focus their research on aggregates—that is, on the way in which measures vary across entire collections of people. For example, a researcher might study the relationship between the average age of the population and the crime rate in various metropolitan areas. In this study, the units of observation are metropolitan areas rather than individuals. Whether focusing on individuals or aggregates, the ideas that social scientists have concerning the nature of social reality are called hypotheses. These hypotheses are frequently expressed in a statement of the relationship between two or more vari- ables: at minimum, an independent variable(or presumed cause) and a dependent vari- able (or presumed effect). For example, a researcher might hypothesize that socially isolated children watch more television than children who are well integrated into their peer groups, and he or she might conduct a survey in which both socially isolated and well-integrated children are asked questions regarding the time they spend watching television (social isolation would be the independent variable; TV-viewing behavior would be the dependent variable). Or a researcher might hypothesize that the one- parent family structure generates greater delinquency than the two-parent family struc- ture and might proceed to interview samples of delinquents and nondelinquents to determine whether one or both parents were present in their family backgrounds (fam- ily structure would be the independent variable; delinquency would be the dependent variable). Thus, not unlike their counterparts in the physical sciences, social researchers often conduct research to increase their understanding of the problems and issues in their field. Social research takes many forms and can be used to investigate a wide range of problems. Among the most useful research methods employed by social researchers for testing their hypotheses are the experiment, the survey, content analysis, participant observation, and secondary analysis. For example, a researcher may conduct an experiment to determine if arresting a wife batterer will deter this behavior in the future, a sample survey to investi- gate political opinions, a content analysis of values in youth magazines, a participant ob- servation of an extremist political group, or a secondary analysis of government statistics on unemployment. 2 Why the Social Researcher Uses Statistics Why Test Hypotheses? Social science is often referred to, quite unfairly, as the study of the obvious. However, it is desirable, if not necessary, to test hypotheses about the nature of social reality, even those that seem logical and self-evident. Our everyday commonsense observations are generally based on narrow, often biased preconceptions and personal experiences. These can lead us to accept without criticism invalid assumptions about the characteristics of social phenom- ena and behavior. To demonstrate how we can be so easily misled by our preconceptions and stereotypes, consider what we “know” about mass murderers—those individuals who simultaneously kill at least four victims. According to popular thinking (and media portrayals), mass murderers are typically insane individuals who go berserk or run amok, expressing their anger in a spontaneous and impulsive outpouring of aggression. Moreover, they are usually regarded as total strangers to their victims, who are unlucky enough to be in the wrong place at the wrong time—at a shopping mall, on a commuter train, or in a fast-food restaurant. The foregoing conception of mass murderers may seem clear-cut and obvious. Yet, compiling detailed information from FBI reports about 697 mass killers over the period from 1976 to 1995, Fox and Levin found instead that mass murderers are rarely insane and spontaneous—they know exactly what they are doing and are not driven to kill by voices of demons. Random shootings in a public place are the exceptions; most mass murders occur within families or among acquaintances. Typically, mass murderers target spouses and all of their children, or bosses and their co-workers. Far from being impulsive, most mass killers are methodical and selective. They usually plan their attacks and are quite selective as to the victims they choose to kill. In an office massacre, for example, a mass killer might choose to murder only those co-workers and supervisors whom the murderer blames for losing an important promotion or getting fired. Until recently, even criminologists all but ignored mass killings, perhaps believing that mass murder was merely a special case of homicide (albeit, by definition, yielding a larger body count), explainable by the same theories applied to single-victim incidents and therefore not deserving of special treatment. From this point of view, mass murder occurs in the same places, under the same circumstances, and for the same reasons as single-victim murder. Comparing FBI reports of single-victim homicides with mass murders reveals quite a different pattern. The location of mass murder differs sharply from that of homicides in which a single victim is slain. First, mass murders do not tend to cluster in large cities as do single-victim crimes; rather, mass killings are more likely to occur in small-town or rural settings. Moreover, while the South (and the deep South in particular) is known for its high rates of murder, this does not hold for mass murder. In comparison to single- victim murder, which is highly concentrated in urban inner-city neighborhoods and in the deep South where arguments are often settled through gunfire, mass murder more or less reflects the general population distribution. Not surprisingly, the firearm is the weapon of choice in mass-murder incidents, even more than in single-victim crimes. Clearly, a handgun or rifle is the most effective means of mass destruction. By contrast, it is difficult to kill large numbers of people simultaneously with physical force or even a knife or blunt object. Furthermore, although an explosive 3 Why the Social Researcher Uses Statistics device can potentially cause the death of large numbers of people (as in the 1995 bombing of the Oklahoma City federal building), its unpredictability would be unacceptable for most mass killers who target their victims selectively. In addition, far fewer Americans are profi- cient in the use of explosives, as compared with guns. The findings regarding victim–offender relationships are perhaps as counterintuitive as the weapon-use results may be obvious. Contrary to popular belief, mass murderers in- frequently attack strangers who just happen to be in the wrong place at the wrong time. In fact, almost 40% of these crimes are committed against family members, and almost as many involve other victims acquainted with the perpetrator (for example, co-workers). It is well known that murder often involves family members, but this is especially pronounced among massacres. The differences in circumstance underlying these crimes are quite dramatic. Although more than half of all single-victim homicides occur during an argument between the victim and the offender, it is relatively rare for a heated dispute to escalate into mass murder. Some of the most notable differences between homicide types emerge in the offender data. Compared to those offenders who kill but one, mass murderers are especially likely to be male, are far more likely to be white, and are somewhat older (middle-aged). Typically, the single-victim offender is a young male and slightly more often black than white. Victim characteristics are, of course, largely a function of the offender characteristics, indicating that mass killers generally do not select their victims on a random basis. For ex- ample, the victims of mass murder are usually white simply because the perpetrators to whom they are related or with whom they associate are white. Similarly, the youthfulness and greater representation of females among the victims of mass murder, as compared to single-victim homicide, stem from the fact that a typical mass killing involves the bread- winner of the household who annihilates the entire family—his wife and his children. The Stages of Social Research Systematically testing our ideas about the nature of social reality often demands carefully planned and executed research in which the following occur: 1. The problem to be studied is reduced to a testable hypothesis (for example, “one- parent families generate more delinquency than two-parent families”). 2. An appropriate set of instruments is developed (for example, a questionnaire or an interview schedule). 3. The data are collected (that is, the researcher might go into the field and conduct a poll or a survey). 4. The data are analyzed for their bearing on the initial hypotheses. 5. Results of the analysis are interpreted and communicated to an audience (for exam- ple, by means of a lecture, journal article, or press release). The material presented in this text is most closely tied to the data-analysis stage of research (see number 4 earlier), in which the data collected or gathered by the researcher are analyzed for their bearing on the initial 4 Why the Social Researcher Uses Statistics hypotheses. It is in this stage of research that the raw data are tabulated, calculated, counted, summarized, rearranged, compared, or, in a word, organized, so that the accu- racy or validity of the hypotheses can be tested. Using Series of Numbers to Do Social Research Anyone who has conducted social research knows that problems in data analysis must be confronted in the planning stages of a research project, because they have a bearing on the nature of decisions at all other stages. Such problems often affect aspects of the research design and even the types of instruments employed in collecting the data. For this reason, we constantly seek techniques or methods for enhancing the quality of data analysis. Most researchers would agree on the importance of measurementin analyzing data. When some characteristic is measured, researchers are able to assign to it a series of num- bers according to a set of rules. Social researchers have developed measures of a wide range of phenomena, including occupational prestige, political attitudes, authoritarianism, alienation, anomie, delinquency, social class, prejudice, dogmatism, conformity, achieve- ment, ethnocentrism, neighborliness, religiosity, marital adjustment, occupational mobil- ity, urbanization, sociometric status, and fertility. Numbers have at least three important functions for social researchers, depending on the particular level of measurement that they employ. Specifically, series of numbers can be used to 1. classifyor categorizeat the nominal level of measurement, 2. rankor orderat the ordinal level of measurement, and 3. assign a scoreat the interval/ratio level of measurement. The Nominal Level The nominal level of measurementinvolves naming or labeling—that is, placing cases into categories and counting their frequency of occurrence. To illustrate, we might use a nominal- level measure to indicate whether each respondent is prejudiced or tolerant toward Latinos. As shown in Table 1, we might question the 10 students in a given class and determine that 5 can be regarded as (1) prejudiced and 5 can be considered (2) tolerant. TABLE 1 Attitudes of 10 College Students toward Latinos:Nominal Data Attitude toward Latinos Frequency 1 = prejudiced 5 2 = tolerant 5 Total 10 5