Leslie Kish

A Procedure for Objective Respondent Selection within the Household

Abstract In modern survey methods growing emphasis is placed on the objective selection of the sample. For surveys of the general population, increasing use is made of area sampling to obtain probability samples of households. Heretofore, scant attention has been given to the question of how to make an objective selection among the members of the household. A procedure for selecting objectively one member of the household is given as used in four surveys of the adult population. Demographic data as found in the sample are compared with outside sources for available factors. * Presented at the 107th Annual Meeting of the American Statistical Association, New York City, December 30, 1947.

Balanced Repeated Replications for Standard Errors

Abstract Balanced repeated replications (BRR) is a general method for computing standard errors. It is useful when mathematical distribution theory is impractical or lacking, and especially for analytical statistics based on complex samples where clustering destroys the independence of observations. Presented are results of methods used to measure standard errors of regression coefficients for several multivariate techniques. The basic designs of the several samples comprised two primary selections (PS) per stratum. Each replication was a half-sample, created by selecting one PS from each stratum. The variance of the coefficient , estimated from the entire sample, is measured by , where bj is the same estimator based on a half-sample. To increase the precision of the variance estimate, select k repeated replications and obtain the mean of the k computed variances, . Balanced repeated replications reduce the number of repetitions needed; e.g., 48 balanced replications sufficed for 47 strata in our samples....

FAMILY LIFE CYCLE AS AN INDEPENDENT VARIABLE

degree of urbanization controlled, white delinquents have a comparatively smaller proportion of girls and pre-adolescents than Negro delinquents. For example, in the highly urbanized counties, the pre-adolescent delinquency rate is 36 per cent of the adolescent delinquency rate for white boys; the corresponding statistic is 55 per cent for Negro boys. Similarly, the adolescent delinquency rate for white girls is 18 per cent of the adolescent delinquency rate for white boys, whereas the corresponding statistic for Negroes is 30 per cent. Within each group of counties, three Negro-white comparisons are possible, twelve in all. All twelve show male adolescents bulking larger among whites.

Studies of Interviewer Variance for Attitudinal Variables

Abstract We studied the effects of the variable biases of interviewers on responses to a variety of items, mostly attitudinal, included in two surveys. Not satisfied with “testing statistical significance,” we measured this interviewer variance as a component of the total variance per respondent; thus s 2 =s a 2 + s b 2, where s a 2 is the “between interviewer” and s b 2 the “within interviewer” component; ρ = s a 2/s 2 is the proportion of the interviewer effect. The contribution of the interviewer variance to total survey errors is examined for its implications for the planning and interpretation of survey statistics. Among these we included subclass means and comparisons among pairs of subclasses. The data yielded important results: (1) We can obtain responses with low or moderate interviewer variance on highly “ambiguous” and “critical” attitudinal questions. The range of ρs was mostly 0 to .07 in the first study, 0 to .05 in the second and their average is about .01 or .02; these effects are not gen...

Controlled Selection—A Technique in Probability Sampling

Abstract A sampling technique is defined as introducing control into the selection of n out of N sampling units when it increases the probabilities of selection for preferred combinations of units (and decreases the probabilities for non-preferred combinations). Methods used in the past have by no means exhausted the possibilities of controlled selection, however. Procedures are developed by which the probabilities of selection for preferred combinations are sharply increased and the theoretical basis for the methods is stated. The methods are applied to a specific problem and the procedures are described in detail. It it found that as a result the variances of estimates for several important items are reduced as compared with the corresponding variances for stratified random sampling. * Presented at the 108th Annual Meeting of the American Statistical Association, Cleveland, December 29, 1948.

CONFIDENCE INTERVALS FOR CLUSTERED SAMPLES

1. It minimizes the likelihood that the investigator will present to himself and the world a prematurely coherent set of propositions in which contradictory propositions, however plausible, are ignored. The procedure requires that a range of contradictory propositions be made explicit before the empirical investigation, and it should conduce to theoretical humility after the fact. Projects are less likely to culminate in particularistic interpretations in terms of a single theory. 2. This procedure increases the likelihood of the researchers building into his researchdesign provisions for the test of a variety of theoretical interpretations of a number of possible empirical findings. 3. The proposed procedure makes the researcher more aware of the total significance of his empirical findings. Where, as in the usual procedure, the investigator is concerned with upholding or refuting a particular theory, he may be completely unaware of the fact that his empirical findings actually add confirmation, or doubt, as the case may be, to numerous other theoretical propositions extant in the area or in related areas. 4. The procedure employed here makes for continuity of research. At the present state of theoretical development in sociology it is rare that clear-cut, unambiguous interpretations are possible after a single research project. Where there is little in the way of theory to guide interpretation, subsequent empirical investigations of alternative interpretations are often necessary. Where alternate interpretations are made explicit from the beginning of the project, they are more likely to survive as alternatives after the fact of investigation: the present procedure encourages research programs rather than isolated projects.8

A Biometrics Invited Paper. Estimation for Small Domains

Timely and complete health, social and economic data can be obtained from samples, but usually only for snajor geographic areas and large subgroups of the population. Small domain estimates are available from censuses, but only infrequently and then only for a few variables. Efffiective planning of health services and other governmental activities cannot depend on traditional data sources, the data must be more current and more complete than these sources provide. Since estimates are needed for a great diversity of domains, a definition and classification of domains is presented to clarify the direction of this review. The existing small domain estimation techniques are split into several distinct approaches and reviewed separately. The basic methodologies of these techniques are presented together with their data requirements and limitations. The existing techniques are briefly assessed in regard to their performance and their potential for further application. Current research approaches are also reviewed and possible lines for future advances are indicated.

Some efficient random imputation methods

Imputation methods that assign a selection of respondents’ values for missing i tern nonresponses give rise to an addd,tional source of sampling variation, which we term imputation varLance , We examine the effect of imputation variance on the precision of the mean, and propose four procedures for sampling the rEespondents that reduce this additional variance. Two of the procedures employ improved sample designs through selection of respc,ndents by sampling without replacement and by stratified sampl;lng. The other two increase the sample base by the use of multiple imputations.

Retaining Units aFter Changing Strata and Probabilities

Abstract Survey samples are often based on primary sampling units selected from initial strata with probabilities pj proportional to initial measures. However, later samples can be better served with new strata and new probabilities, Pj, based on new information. The differences between the initial and new strata and measures may be due to changes either in population distributions or in survey objectives. It is efficient to retain in the new sample the maximum permissible number of initial selections. Procedures are presented first for changing measures within fixed strata, then for strata with changed units. Modifications, improvements and simplifications are also introduced.

Multivariate and Multipurpose Stratification

Abstract The number of strata L = II i Li (i = 1, 2, …, k) depends on the number of stratifying variables k and the number of classes Li from each; but strata are limited by cost restrictions on the number of selections, especially when these are primary selections in cluster sampling. Several stratifying variables often seem desirable both to reduce variances and to create domains. We quantify the gains of multivariate stratification in tables for 12 multivariate normal structures, with L = 12 and 36 and for three empirical studies. Even greater gains are shown for multipurpose designs, which are most common in surveys.