Gudmund R. Iversen

Recovering Individual Data in the Presence of Group and Individual Effects

The ecological fallacy of relating variables on the group level, when the individual-level relationship is desired, can only be avoided by using individual-level data. This paper gives some conditions for occasions when individual-level data can successfully be recovered from grouped data. Such a recovery is illustrated using data on urban or rural residence and participation or not in the labor force as an example. The conditions are given in terms of the distinction between individual-and group-level effects of one variable on another. Recovering individual data, on the one hand, and the study of individual and group-level effects, on the other hand, epresent two separate areas of thought that have received considerable attention. Here a link is made between the two lines of development to facilitate the recovery of individual-level data. Some consequences of the models for research design and recovery of historical data are explored.

Decomposing Chi-Square A Forgotten Technique

According to the statistical properties of the chi-square distribution, a variable which is distributed according to the chi-square distribution with p degrees of freedom can be written as the sum ofp chi-square variables, each with one degree of freedom. This means that a contingency table which gives rise to a chi-square with p degrees of freedom can be decomposed into as many as p smaller tables. The magnitudes of the chi-squares for these smaller tables will often give a better understanding of the relationship between the two variables than was possible to obtain from the overall chi-square for the original table. This paper gives explicit rules for how to decompose a table into smaller tables, and the rules are illustrated with an example from a content analysis of value orientations in different maga zines.

Statistics in Liberal Arts Education

Abstract Statistics has not been a part of the typical liberal arts curriculum. After an examination of some central features of both liberal arts education and statistics, it is argued that statistics can play a strong role in liberal arts education, in part because of the advances that have taken place in computer technology.

Decomposing Chi-Square

According to the statistical properties of the chi-square distribution, a variable which is distributed according to the chi-square distribution with p degrees of freedom can be written as the sum ofp chi-square variables, each with one degree of freedom. This means that a contingency table which gives rise to a chi-square with p degrees of freedom can be decomposed into as many as p smaller tables. The magnitudes of the chi-squares for these smaller tables will often give a better understanding of the relationship between the two variables than was possible to obtain from the overall chi-square for the original table. This paper gives explicit rules for how to decompose a table into smaller tables, and the rules are illustrated with an example from a content analysis of value orientations in different maga zines.

Anova: Analysis of Variance for a Categorical and a Metric Variable

In this chapter we focus on one particular kind of crime—violent crime: murder, forcible rape, robbery, and aggravated violent crime. We address the question of whether the chances of being a victim of violent crime are the same from one part of the country to another. Then, if we do find that the number of violent crimes is not the same in different parts of the country, where are the high and low incidences of violent crime? These questions are more than theoretical. Insult and injury are at stake.

Statistics: Randomness and Regularity

You probably are reading this book because you think it is important to know something about the subject of statistics. At the same time, you may suspect that studying statistics won’t be the pleasantest task you have ever undertaken. We have seen too many reluctant students to think statistics courses are automatically crowd pleasers. We know some of you would prefer to analyze a poem, sing a ballad, or dissect a frog. But we think we have enough knowledge of student temperament to speak to all of you, eager and less than eager.

Collection of Data

To answer these questions and an enormous number of other ones, information must be gathered. In these instances, we need to know many things, from sexual habits to recycling practices. At first glance it seems easy to get this information. One needs only to go out and ask people or do an experiment to see how things work. But then the quandaries begin: Who should do the asking—you, me, unemployed college students, retired executives? And who should be asked? Can we afford to ask everyone concerned with the problem? For the first question, that would be the entire population of Los Angeles! Well, if not everyone, how about people who walk by a certain store at the mall on Saturday afternoon? Or those buying beer at the baseball stadium? Or do you think a presumably fairer way should be found?

Drawing Conclusions Estimation

Survey results and other statistical reports are often presented in newspapers and magazines and on television news. Statistical studies show, among many varied results, what percentages of African Americans in a sample prefer “African American” to “Black” as a name for their race (26%; 1989 telephone poll taken by Yankelovich Partners, Inc., for Time/CNN); what percentage of white Americans say they do not have enough money to buy food (13%; 1989 Gallup poll); what the mean age of female gymnasts equals (12.3 years; G. E. Theintz, et al., “Evidence for a reduction of growth potential in adolescent female gymnasts,” Journal of Pediatrics, vol. 122 (1993), pp. 306–313); what percentage of their time people spend sleeping (30.9; The New York Times, Tuesday, September 6, 1995, p. C6).

Regression and Correlation for Two Metric Variables

Questions about relationships between metric variables with well-defined units of measurement, such as food calories and fat content, gas mileage and vehicle weight, are answered using the statistical methods know as regression analysis and correlation analysis. Regression and correlation analyses represent two major and complementary aspects of the analysis of the relationship between metric variables.

Statistics in Everyday Life

Often, when we are blazing a trail through the woods in unfamiliar territory, we get so caught up in cutting through the surrounding brambles that we lose track of the bigger forest in which we are (possibly) lost. Now that we have arrived at a clearing and have survived the challenge of finding our way, we can take stock of what we have accomplished and look forward to future prospects.