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March 27, 2009
Few things annoy the scientist and madden the statistician more than Ns (numbers of cases) which vary mysteriously and inexplicably from table to table. Having been guilty of this offense in our 1948 volume and properly taken to task, we have become meticulous about making explicit the quantities upon which our figures are based. Any variations in N will be noted and explained either in the tables or in the text.
Nevertheless, this study presents some unusual opportunities for confusion, which can be avoided only by recognizing which of our three sorts of Ns are being considered.
N of individuals. This is the number of persons interviewed and used in this study: 477 white males of the control group, 888 white males of the prison group, and 1,356 white males convicted of sex offenses.
N of sex offenses. Since a male may commit more than one offense, this number exceeds the number of individuals. There were 2,274 sex offenses in all.
N of type offenders. This category is the only one hard to grasp. Since a man who commits two or more different types of sex offenses is counted as a member of each sex-offender category, the number of such “type offenders” (to coin a term) exceeds the number of actual individuals. For instance, a man is counted both as an exhibitionist and a rapist if he has been convicted on both charges. However, a man is counted only once within each offender type category: a peeper convicted a score of times for peeping still counts as one peeper. Adding up all the individuals represented in each category, one comes out with a total of 1,685. Within each offender type no confusion exists—the N of type offenders and the N of actual individuals are synonymous. For instance, the offenders vs. children category consists of 199 men, all of whom were convicted one or more times of an offense against a child; the fact that some of these men also committed other sorts of sex offenses is another matter and one that is dealt with separately. The confusion and apparent discrepancy arises only when one tries to add the Ns of the individual categories. For example, while there are 96 homosexual offenders vs. children, 136 homosexual offenders vs. minors, and 199 homosexual offenders vs. adults, there are not 431 homosexual offenders in all because some men have been counted in two or more categories. Fortunately this N of “type offenders” is seldom employed.
The discussion of Ns naturally should include our attitude toward the size of the groups with which we deal. While validity decreases with decrease in sample size, we have been surprised at how even tiny samples exhibit value in special situations. If a tiny sample is in line with a trend established by large samples, that tiny sample is meaningful, and suitably qualified inferences may be drawn from it. In other instances small samples may be said to support one another. For example, both the aggressors vs. children and the aggressors vs. minors are groups with relatively few members (25 and 27 respectively), and if only one group ranked high in some particular respect, little significance could be attributed to this; however, if both ranked high, and especially if the two groups were contiguous in the rank-order, the joint evidence is great that, regardless of the small number of people involved, high ranking in this particular item is a trait of aggressors. To have two groups of a tripartite larger group contiguous in a seriation is not likely to be the result of chance even with a small number of individuals involved.
Another consideration is the known or assumed incidence of the behavior in question. Five cases of some common type of sex offense such as statutory rape would not warrant publication, but five cases of a rare type constitute an important body of data, publication on which is obligatory. In many respects, this small N problem boils down to one’s philosophy, and we feel that some information is better than none. Only the most impractical purist would maintain that a deliberately preserved ignorance is preferable to running the risk of being misled by a small sample.
Note regarding tables and figures. In tables, calculations based on Ns of ten to 19 are in italics, and in charts they are indicated by one asterisk. Calculations based on Ns of nine or less are italicized in tables and enclosed within parentheses; in charts they are indicated by two asterisks.
When data have not been calculated a blank space appears in the tables; three dots indicate that there are no applicable data. In addition, when calculations of means and medians would have been based on nine or fewer cases no figure has been expressed,
*4\161\2*
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