ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500903

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A simple derivation of asymptotic efficiency for the two sample Kolmogorov-Smirnov statistic is given and evaluated for normal location and normal scale alternatives. Using equal samples to simplify the derivation, the limiting efficiency is obtained by letting the type I error α go to zero while the type II error goes to β, 0 < β < 1. For unimodal symmetric location alternatives, the efficiency is the same as that obtained for the Mood and Brown median test. Limits of relative efficiencies for alternatives which approach the null hypothesis are 2/π for normal location alternatives and (πe)−1for normal scale alternatives.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500904

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Wilcoxon's signed rank test and a test based on the uniform minimum variance unbiased estimator ofP(X1+X2<Y1+Y2) are considered as competitors of the Mann-Whitney-Wilcoxon (U) test. The criteria used to compare the tests are Bahadur and Pitman efficiency. For pure translation alternativesUis superior, but both tests compare favorably with respect toUfor certain contamination alternatives.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500905

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

The robustness properties of four estimators of location are studied with respect to eight distribution types. For each type, the probability density function is symmetric about the median and the range of variate is infinite. For the entire class of distributions, the estimator with the highest guaranteed efficiency is the mean of the middle fifty percent of the sample. This study supplements the paper by Crow and Siddiqui (1967).

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500906

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

While distribution-free procedures are often appropriate when testing statistical hypotheses, they may become complicated or involve loss of power when the data are grouped. For rank tests the ties caused by grouping are generally broken either by using a randomization procedure or averaging the tied ranks. In this paper the power loss due to equi-spaced grouping (in terms of Pitman asymptotic relative efficiency) is investigated for some commonly used tests, for each method of tie-breaking. The tests considered are Wilcoxon's and Mood's tests for the two-sample problem, Mann's test for randomness, and Pitman's independence test. It is shown how the power loss depends on the width of the grouping intervals and the distribution of the data, and some numerical studies are given. The results seem to indicate that the power loss is small even for a sizable group interval, and that it may be preferable to break ties by randomization than by averaging ranks.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500907

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Some rejection limits of the absolute normal scores test (K) for symmetry are extended from sample size 10 to 17 and partially to 20, by essentially forming all possible values ofKfor fixed sample size. These limits are compared with normal and Edgeworth approximations, which seem to be quite satisfactory in that the percent error in test size for sample size greater than 20 should be less than 12% for the normal approximation and less than 2% for the Edgeworth approximation (see (3.3)), for test size ≥ .01. The powers of the absolute normal scores (K), Wilcoxon (W), binary (B), sign (S), andt(T) tests are estimated from Monte Carlo trials for shifts of symmetrical hypothesized populations which are normal, logistic, double exponential, and rectangular. The powers ofTandKare usually very close, withTmore powerful for normal shifts and large rectangular shift, andKmore powerful for the others, though the differences may not be substantial. In terms of decreasing power, the tests are ordered as follows, with a comma marking an apparent substantial difference: for normal shiftTKW, B, S;for logistic shiftKTW, S, B;for small double exponential shift and large test sizeSWKT, B;as the shift increases and test size decreasesW, SKT, BandW, KST, B;and for rectangular shiftB, KT, W, S, andB, TK, W, S.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500908

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Returns and findings from three strategies of data collection are compared. Each strategy contains personal interviews, telephone interviews, and mail questionnaires in different combinations—one mainly personal, one mainly telephone, and one mainly mail. All three strategies are based on area probability samples of households in Alameda County, California. The test was made on two separate studies, with identical questionnaires used in all strategies within each study.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500909

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

In surveys of human populations respondents are not likely to participate or tell the truth when the reply may tend to stigmatize them in the eyes of the surveyor. Warner developed a technique for estimating the proportion of persons with such a sensitive characteristic in a binomial situation by having the respondent answer only “Yes” or “No” to one of two questions selected at random. This technique is hereby extended to the case where the population can be divided intotcategories in which at least one and not more than (t− 1) of them are stigmatizing. The case whent= 3 is investigated in detail and the estimates are shown to be unbiased. The variances are larger than those for regular trinomial estimators but this loss may be compensated for by greater cooperation. Under the assumption that respondents may tend to lie under either interviewing method, comparisons are made to determine where the randomizing technique still has an advantage. An example of a field trial is cited where the method was shown to work only with highly skilled interviewers and on more intelligent respondents. Improvements in field technique are also suggested.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500910

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Just as ratio estimators are often indicated when the variableyis positively correlated with an auxiliary variablexso product estimators are indicated whenyis negatively correlated withx.The method of estimation suggested by Olkin [4] is extended to the case where some or all of the auxiliary variables are positively correlated and some or all are negatively correlated withy.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500911

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

In estimating the total of a finite population the minimum variance estimate in a given class of linear unbiased estimates depends on the population values. In such a situation, the criterion of the ‘necessary best estimate’ is proposed by Ajgaonkar [1], in order to choose a serviceable estimate purely from practical point of view; and it was proved by him that in a particular subclass T5of linear estimates of the population total, the well known Horvitz-Thomson estimate, is the ‘necessary best estimate’ in sampling with varying probabilities without replacement. In this paper the result is generalized to the class of all linear estimates of the population total and for any sampling design.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500912

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor