Adjustment

Adjustment is the process by which the anticipated effect of a variable in which there is no primary interest is quantitatively removed from the relationship of primary interest. There are several well-accepted procedures by which this is accomplished.

The need for adjustment derives from the observation that relationships between variables that capture the complete attention of an investigator also have relationships with other variables in which there is no direct interest. The relationship between ethnicity and death from acquired immunodeficiency syndrome (AIDS) may be of the greatest interest to the researcher, but it must be acknowledged that death rates from this disease are also influenced by several other characteristics of these patients (e.g., education, acculturation, and access to health care). A fundamental question that confronts the researcher is whether it is truly ethnicity that is related to AIDS deaths or whether ethnicity plays no real role in the explanation of AIDS deaths at all. In the second circumstance, ethnicity serves merely as a surrogate for combinations of these other variables that, among themselves, truly determine the cumulative mortality rates. Thus, it becomes important to examine the relationship between these other explanatory variables (or covariates) and that of ethnicity and death from AIDS.

Three analytic methods are used to adjust for the effect of a variable: (a) control, (b) stratification, and (c) regression analysis. In the control method, the variable whose effect is to be adjusted for (the adjustor) is not allowed to vary in an important fashion. This is easily accomplished for dichotomous variables. As an example, if it is anticipated that the relationship between prison sentence duration and age at time of sentencing is affected by gender, then the effect is removed by studying the relationship in only men. The effect of gender has been neutralized by fixing it at one and only one value.

The process of stratification adds a layer of complication to implementing the control procedure in the process of variable adjustment. Specifically, the stratification procedure uses the technique of control repetitively, analyzing the relationship between the variables of primary interest on a background in which the adjustor is fixed at one level and then fixed at another level. This process works very well when there area relatively small number of adjust or variable levels. For example, as in the previous example, the analysis of prison sentence duration and age can be evaluated in (a) only men and (b) only women. This evaluation permits an examination of the role that gender plays in modifying the relationship between sentence duration and age. Statistical procedures permit an evaluation of the relationship between the variables of interest within each of the strata, as well as a global assessment of the relationship between the two variables of interest across all strata. If the adjusting variable is not dichotomous but continuous, then it can be divided into different strata in which the strata definitions are based on a range of values for the adjustor.

The procedure of adjustment through regression analysis is somewhat more complex but, when correctly implemented, can handle complicated adjustment operations satisfactorily. Regression analysis itself is an important tool in examining the strength of association between variables that the investigator believes may be linked in a relationship. However, this regression model must be carefully engineered to be accurate. We begin with a straightforward model in regression analysis, the simple straight-line model. Assume we have collected n pairs of observations (xi,yi), i = 1to n. The investigator's goal is to [Page 8]demonstrate that individuals with different values of x will have different values of y in a pattern that is best predicted by a straight-line relationship. Write the simple linear regression model for regressing y on x as follows:

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