Advertisement

Der Vergleich unabhängiger Stichproben gemessener Werte

  • Lothar Sachs

Zusammenfassung

Wissen wir einiges über die zu erwartende Heterogenität innerhalb der Grundgesamtheit, die wir untersuchen wollen, dann gibt es wirksamere Verfahren als die Auswahl zufälliger Stichproben. Wichtig ist die Verwendung geschichteter oder stratifizierter Stichproben; hier wird die Grundgesamtheit in relativ homogene Teilgrundgesamtheiten, Schichten oder Strata unterteilt, und zwar jeweils nach den Gesichtspunkten, die für das Studium der zu untersuchenden Variablen von Bedeutung sind. Geht es um die Voraussage von Wahlergebnissen, dann wird man die Stichprobe so wählen, daß sie ein verkleinertes Modell der Gesamtbevölkerung darstellt. Dabei werden in erster Linie Altersschichtung, das Verhältnis zwischen Männern und Frauen und die Einkommensgliederung berücksichtigt. Stratifizierung verteuert meist die Stichprobenerhebung, ist jedoch ein wichtiges Hilfsmittel.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. Ailing, D.W.: Early decision in the Wilcoxon two-sample test. J. Amer. Statist. Assoc. 58 (1963), 713–720.MathSciNetGoogle Scholar
  2. Anscombe, F.J.: Rejection of outliers. Technometrics 2 (1960), 123–166.MathSciNetzbMATHGoogle Scholar
  3. Banerji, S.K.: Approximate confidence interval for linear functions of means of k populations when the population variances are not equal. Sankhya 22 (1960), 357 + 358.Google Scholar
  4. Bauer, R.K.: Der „Median-Quartile-Test“: Ein Verfahren zur nichtparametrischen Prüfung zweier unabhängiger Stichproben auf unspezifizierte Verteilungsunterschiede. Metrika 5 (1962), 1–16.MathSciNetzbMATHGoogle Scholar
  5. Behrens, W.-V.: Ein Beitrag zur Fehlerberechnung bei wenigen Beobachtungen. Landwirtschaftliche Jahrbücher 68 (1929), 807–837.Google Scholar
  6. Belson, I., and Nakano, K.: Using single-sided non-parametric tolerance limits and percentiles. Industrial Quality Control 21 (May 1965), 566–569.Google Scholar
  7. Bhapkar, V.P., and Deshpande, J. V.: Some nonparametric tests for multisample problems. Technometrics 10 (1968), 578–585.Google Scholar
  8. Birnbaum, Z. W., und Hall, R. A.: Small sample distribution for multisample statistics of the Smirnov type. Ann. Math. Stat. 31 (1960), 710–720 [vgl. auch 40 (1969), 1449-1466].MathSciNetzbMATHGoogle Scholar
  9. Bowker, A.H., and Lieberman, G.J.: Engineering Statistics. (Prentice-Hall) Englewood Cliffs, N.J. 1959.Google Scholar
  10. Box, G.E.P.: Non-normality and tests on variances. Biometrika 40 (1953), 318–335.MathSciNetzbMATHGoogle Scholar
  11. Box, G.E.P., and Andersen, S.L.: Permutation theory in the derivation of robust criteria and the study of departures from assumption. With discussion. J. Roy. Statist. Soc., Ser. B 17 (1955), 1–34.zbMATHGoogle Scholar
  12. Boyd, W.C.: A nomogramm for the “Student”-Fisher t test. J. Amer. Statist. Assoc. 64 (1969), 1664–1667.Google Scholar
  13. Bradley, J.V.: Distribution-Free Statistical Tests. (Prentice-Hall, pp.388) Englewood Cliffs, N.J. 1968, Chapters 5 and 6.Google Scholar
  14. Bradley, R.A., Martin, D.C., and Wilcoxon, F.: Sequential rank-tests I. Monte Carlo studies of the two-sample procedure. Technometrics 7 (1965), 463–483.MathSciNetGoogle Scholar
  15. Bradley, R.A., Martin, D.C., Merchant, S.D. and Wilcoxon, F.: Sequential rank tests II. Modified two-sample procedures. Technometrics 8 (1966), 615–623.Google Scholar
  16. Breny, H.: L’état actuel du problème de Behrens-Fisher. Trabajos Estadist. 6 (1955), 111–131.MathSciNetzbMATHGoogle Scholar
  17. Burrows, G.L.: (1) Statistical tolerance limits — what are they? Applied Statistics 12 (1963), 133-144. (2) One-sided normal tolerance factors. New tables and extended use of tables. Mimeograph, Knolls Atomic Power Lab., General Electric Company, USA 1964.Google Scholar
  18. Cacoullos, T.: A relation between t and F-distributions. J. Amer. Statist. Assoc. 60 (1965), 528–531.MathSciNetzbMATHGoogle Scholar
  19. Cadwell, J.H.: (1) Approximating to the distributions of measures of dispersion by a power of chi-square. Biometrika 40 (1953), 336–346. (2) The statistical treatment of mean deviation. Biometrika 41 (1954), 12-18.MathSciNetzbMATHGoogle Scholar
  20. Carnal, H. and Riedwyl, H.: On a one-sample distribution-free test statistic V. Biometrika 59 (1972), 465–467.MathSciNetzbMATHGoogle Scholar
  21. Chacko, V.J.: Testing homogeneity against ordered alternatives. Ann. Math. Statist. 34 (1963), 945–956.MathSciNetzbMATHGoogle Scholar
  22. Chakravarti, I. M.: Confidence set for the ratio of means of two normal distributions when the ratio of variances is unknown. Biometrische Zeitschr. 13 (1971), 89–94.MathSciNetzbMATHGoogle Scholar
  23. Chun, D.: On an extreme rank sum test with early decision. J. Amer. Statist. Assoc. 60 (1965), 859–863.Google Scholar
  24. Cochran, W.G.: (1) Some consequences when the assumptions for the analysis of variance are not satisfied. Biometrics 3 (1947), 22–38. (2) Modern methods in the sampling of human populations. Amer. J. Publ. Health 41 (1951), 647-653. (3) Query 12, Testing two correlated variances. Technometrics 7 (1965), 447-449.MathSciNetGoogle Scholar
  25. Cochran, W.G., Mosteller, F., and Tukey, J.W.: Principles of sampling. J. Amer. Statist. Assoc. 49 (1954), 13–35.Google Scholar
  26. Cohen, J.: Statistical Power Analysis for the Behavioral Sciences. (Academic Press, pp.416) New York 1969.Google Scholar
  27. Conover, W. J.: Two k-sample slippage tests. J. Amer. Statist. Assoc. 63 (1968), 614–626.Google Scholar
  28. Croarkin, Mary C.: Graphs for determining the power of Student’s t-test. J. Res. Nat. Bur. Stand. 66 B (1962), 59–70 (vgl. Errata: Mathematics of Computation 17 (1963), 83 [334]).MathSciNetGoogle Scholar
  29. D’Agostino, R.B.: (1) Simple compact portable test of normality: Geary’s test revisited. Psychol. Bull. 74 (1970), 138–140 [vgl. auch 78 (1972), 262-265]. (2) An omnibus test of normality for moderate and large size samples. Biometrika 58 (1971), 341-348. (3) Small sample probability points for the D test of normality. Biometrika 59 (1972), 219-221 [vgl. auch 60 (1973), 169-173] Danziger, L., and Davis, S.A.: Tables of distribution-free tolerance limits. Ann. Math. Statist. 35 (1964), 1361-1365.Google Scholar
  30. Darling, D.A.: The Kolmogorov-Smirnov, Cramér-von Mises tests. Ann. Math. Statist. 28 (1957), 823–838.MathSciNetzbMATHGoogle Scholar
  31. Davies, O. L.: The Design and Analysis of Industrial Experiments. London 1956, p. 614.Google Scholar
  32. Dietze, Doris: t for more than two. Perceptual and Motor Skills 25 (1967), 589–602.Google Scholar
  33. Dixon, W.J.: (1) Analysis of extreme values. Ann. Math. Statist. 21 (1950), 488–506. (2) Processing data for outliers. Biometrics 9 (1953), 74-89. (3) Rejection of Observations. In Sarhan, A. E., and Greenberg, B. G. (Eds.): Contributions to Order Statistics. New York 1962, pp. 299-342.Google Scholar
  34. Dixon, W.J., and Tukey, J.W.: Approximate behavior of the distribution of Winsorized t (trimming/Winsorization 2). Technometrics 10 (1968), 83–98.MathSciNetGoogle Scholar
  35. Edington, E. S.: The assumption of homogeneity of variance for the t-test and nonparametric tests. Journal of Psychology 59 (1965), 177–179.Google Scholar
  36. Faulkenberry, G.D., and Daly, J.C.: Sample size for tolerance limits on a normal distribution. Technometrics 12 (1970), 813–821.zbMATHGoogle Scholar
  37. Fisher, R. A.: (1) The comparison of samples with possibly unequal variances. Ann. Eugen. 9 (1939), 174–180. (2) The asymptotic approach to Behrens’s integral, with further tables for the d test of significance. Ann. Eugen. 11 (1941), 141-172.Google Scholar
  38. Fisher, R.A., and Yates, F.: Statistical Tables for Biological, Agricultural and Medical Research, 6th ed., London 1963.Google Scholar
  39. Geary, R.C.: (1) Moments of the ratio of the mean deviation to the standard deviation for normal samples. Biometrika 28 (1936), 295–305 (vgl. auch 27, 310/32 und 34, 209/42). (2) Tests de la normalité. Ann. Inst. Poincaré 15 (1956), 35-65.zbMATHGoogle Scholar
  40. Gibbons, J.D.: On the power of two-sample rank tests on the equality of two distribution functions. J. Roy. Statist. Soc. B 26 (1964), 293–304.MathSciNetzbMATHGoogle Scholar
  41. Glasser, G. J.: A distribution-free test of independence with a sample of paired observations. J. Amer. Statist. Assoc. 57 (1962), 116–133.MathSciNetzbMATHGoogle Scholar
  42. Goldman, A.: On the Determination of Sample Size. (Los Alamos Sci. Lab.; LA-2520; 1961) U.S. Dept. Commerce, Washington 25, D.C. 1961 [vgl. auch Biometrics 19 (1963), 465–477].zbMATHGoogle Scholar
  43. Granger, C.W. J., and Neave, H.R.: A quick test for slippage. Rev. Inst. Internat. Statist. 36 (1968), 309–312.zbMATHGoogle Scholar
  44. Graybill, F.A., and Connell, T.L.: Sample size required to estimate the ratio of variances with bounded relative error. J. Amer. Statist. Assoc. 58 (1963), 1044–1047.MathSciNetzbMATHGoogle Scholar
  45. Grubbs, F.E.: Procedures for detecting outlying observations in samples. Technometrics 11 (1969), 1–21 [vgl. auch 527-550 und 14 (1972), 847-854; 15 (1973), 429].Google Scholar
  46. Guenther, W.C.: Determination of sample size for distribution-free tolerance limits. The American Statistician 24 (Febr. 1970), 44–46.MathSciNetGoogle Scholar
  47. Gurland, J., and McCullough, R.S.: Testing equality of means after a preliminary test of equality of variances. Biometrika 49 (1962), 403–417.MathSciNetzbMATHGoogle Scholar
  48. Guttmann, I.: Statistical Tolerance Regions. Classical and Bayesian. (Griffin, pp. 150) London 1970.Google Scholar
  49. Haga, T.: A two-sample rank test on location. Annals of the Institute of Statistical Mathematics 11 (1960), (211–219).MathSciNetzbMATHGoogle Scholar
  50. Hahn, G.J.: Statistical intervals for a normal population. Part I and II. J. Qual. Technol. 2 (1970), 115–125 and 195-206 [vgl. auch 168-171, Biometrika 58 (1971), 323-332 sowie J. Amer. Statist. Assoc. 67 (1972), 938-942].Google Scholar
  51. Halperin, M.: Extension of the Wilcoxon-Mann-Whitney test to samples censored at the same fixed point. J. Amer. Statist. Assoc. 55 (1960), 125–138.MathSciNetzbMATHGoogle Scholar
  52. Harmann, A. J.: Wilks’ tolerance limit sample sizes. Sankhya A 29 (1967), 215–218.Google Scholar
  53. Harter, H. L.: Percentage points of the ratio of two ranges and power of the associated test. Biometrika 50 (1963), 187–194.MathSciNetzbMATHGoogle Scholar
  54. Herrey, Erna M. J.: Confidence intervals based on the mean absolute deviation of a normal sample. J. Amer. Statist. Assoc. 60 (1965), 257–269 (vgl. auch 66 [1971], 187 + 188).MathSciNetzbMATHGoogle Scholar
  55. Hodges, J.L., Jr., and Lehmann, E.L.: (1) The efficiency of some nonparametric competitors of the t-test. Ann. Math. Statist. 27 (1956), 324–335. (2) A compact table for power of the t-test. Ann. Math. Statist. 39 (1968), 1629-1637. (3) Basic Concepts of Probability and Statistics. 2nd ed. (Holden-Day, pp.401) San Francisco 1970.MathSciNetzbMATHGoogle Scholar
  56. Jacobson, J. E.: The Wilcoxon two-sample statistic: tables and bibliography. J. Amer. Statist. Assoc. 58 (1963), 1086–1103.MathSciNetzbMATHGoogle Scholar
  57. Johnson, N.L., and Welch, B.L.: Applications of the noncentral t-distribution. Biometrika 31 (1940), 362–389.MathSciNetzbMATHGoogle Scholar
  58. Kendall, M.G.: The treatment of ties in ranking problems. Biometrika 33 (1945), 239–251.MathSciNetzbMATHGoogle Scholar
  59. Kim, P. J.: On the exact and approximate sampling distribution of the two sample Kolmogorov-Smirnov criterion D mn, mn. J. Amer. Statist. Assoc. 64 (1969), 1625–1637 [vgl. auch. Ann. Math. Statist. 40 (1969), 1449-1466].MathSciNetGoogle Scholar
  60. Kolmogoroff, A.N.: Sulla determinazione empirica di una legge di distribuzione. Giornale Istituto Italiano Attuari 4 (1933), 83–91.Google Scholar
  61. Krishnan, M.: Series representations of the doubly noncentral t-distribution. J. Amer. Statist. Assoc. 63 (1968), 1004–1012.zbMATHGoogle Scholar
  62. Kruskal, W.H.: A nonparametric test for the several sampling problem. Ann. Math. Statist. 23 (1952), 525–540.MathSciNetzbMATHGoogle Scholar
  63. Kruskal, W.H., and Wallis, W. A.: Use of ranks in one-criterion variance analysis. J. Amer. Statist. Assoc. 47 (1952), 583–621 und 48 (1953), 907-911.zbMATHGoogle Scholar
  64. Krutchkoff, R.G.: The correct use of the sample mean absolute deviation in confidence intervals for a normal variate. Technometrics 8 (1966), 663–674.MathSciNetGoogle Scholar
  65. Kühlmeyer, M.: Die nichtzentrale t-Verteilung. Grundlagen und Anwendungen mit Beispielen. Lect. Notes Op. Res., Vol. 31 (Springer, 106 S.) Berlin, Heidelberg, New York 1970 (Druckfehlerliste kostenlos beim Autor erhältlich).Google Scholar
  66. Laan, P. van der: Simple distribution-free confidence intervals for a difference in location. Philips Res. Repts. Suppl. 1970, No. 5, pp.158.Google Scholar
  67. Levene, H.: Robust tests for equality of variances. In I. Olkin and others (Eds.): Contributions to Probability and Statistics. Essays in Honor of Harold Hotelling, pp. 278-292. Stanford 1960.Google Scholar
  68. Lieberman, G.J.: Tables for one-sided statistical tolerance limits. Industrial Quality Control 14 (Apr. 1958), 7–9.Google Scholar
  69. Lienert, G.A., und Schulz, H.: Zum Nachweis von Behandlungswirkungen bei heterogenen Patientenstichproben. Ärztliche Forschung 21 (1967), 448–455.Google Scholar
  70. Lindgren, B.W.: Statistical Theory. New York 1960, p. 401.Google Scholar
  71. Lindley, D.V., East, D.A. and Hamilton, P.A.: Tables for making inferences about the variance of a normal distribution. Biometrika 47 (1960), 433–437.MathSciNetzbMATHGoogle Scholar
  72. Linnik, Y. V.: Latest investigation on Behrens-Fisher-problem. Sankhya 28 A (1966), 15–24.MathSciNetzbMATHGoogle Scholar
  73. Lord, E.: (1) The use of range in place of standard deviation in the t-test. Biometrika 34 (1947), 41–67. (2) Power of the modified t-test (u-test) based on range. Biometrika 37 (1950), 64-77.MathSciNetzbMATHGoogle Scholar
  74. Mace, A.E.: Sample-Size Determination. (Reinhold; Chapman and Hall; pp.226) New York; London 1964.Google Scholar
  75. MacKinnon, W. J.: Table for both the sign test and distribution-free confidence intervals of the median for sample sizes to 1,000. J. Amer. Statist. Assoc. 59 (1964), 935–956.MathSciNetzbMATHGoogle Scholar
  76. Mann, H. B., and Whitney, D. R.: On a test of whether one of two random variables is stochastically larger than the other. Ann. Math. Statist. 18 (1947), 50–60.MathSciNetzbMATHGoogle Scholar
  77. Massey, F.J., Jr.: (1) The distribution of the maximum deviation between two sample cumulative step functions. Ann. Math. Statist. 22 (1951), 125–128. (2) Distribution table for the deviation between two sample cumulatives. Ann. Math. Statist. 23 (1952), 435-441.MathSciNetzbMATHGoogle Scholar
  78. McCullough, R.S., Gurland, J., and Rosenberg, L.: Small sample behaviour of certain tests of the hypothesis of equal means under variance heterogeneity. Biometrika 47 (1960), 345–353.zbMATHGoogle Scholar
  79. McHugh, R.B.: Confidence interval inference and sample size determination. The American Statistician 15 (April 1961), 14–17.Google Scholar
  80. Mehta, J. S.: On the Behrens-Fisher problem. Biometrika 57 (1970), 649–655.zbMATHGoogle Scholar
  81. Meyer-Bahlburg, H.F.L.: A nonparametric test for relative spread in k unpaired samples. Metrika 15 (1970), 23–29.zbMATHGoogle Scholar
  82. Miller, L.H.: Table of percentage points of Kolmogorov statistics. J. Amer. Statist. Assoc. 51 (1956), 113–115.Google Scholar
  83. Milton, R.C.: An extended table of critical values for the Mann-Whitney (Wilcoxon) two-sample statistic. J. Amer. Statist. Assoc. 59 (1964), 925–934.MathSciNetzbMATHGoogle Scholar
  84. Minton, G.: (1) Inspection and correction error in data processing. J. Amer. Statist. Assoc. 64 (1969), 1256–1275 [vgl. auch 67 (1972), 943-950]. (2) Some decision rules for administrative applications of quality control. J. Qual. Technol. 2 (1970), 86-98 [vgl. auch 3 (1971), 6-17].Google Scholar
  85. Mitra, S.K.: Tables for tolerance limits for a normal population based on sample mean and range or mean range. J. Amer. Statist. Assoc. 52 (1957), 88–94.MathSciNetzbMATHGoogle Scholar
  86. Moore, P.G.: The two sample t-test based on range. Biometrika 44 (1957), 482–489.MathSciNetzbMATHGoogle Scholar
  87. Mosteller, F.: A k-sample slippage test for an extreme population. Ann. Math. Stat. 19 (1948), 58–65 (vgl. auch 21 [1950], 120-123).MathSciNetzbMATHGoogle Scholar
  88. Neave, H. R.: (1) A development of Tukeys quick test of location. J. Amer. Statist. Assoc. 61 (1966), 949–964. (2) Some quick tests for slippage. The Statistician 21 (1972), 197-208.MathSciNetzbMATHGoogle Scholar
  89. Neave, H.R., and Granger, C.W.J.: A Monte Carlo study comparing various two-sample tests for differences in mean. Technometrics 10 (1968), 509–522.Google Scholar
  90. Nelson, L.S.: (1) Nomograph for two-sided distribution-free tolerance intervals. Industrial Quality Control 19 (June 1963), 11–13. (2) Tables for Wilcoxon’s rank sum test in randomized blocks. J. Qual. Technol. 2 (Oct. 1970), 207-218.Google Scholar
  91. Neyman, J.: First Course in Probability and Statistics. New York 1950.Google Scholar
  92. Owen, D.B.: (1) Factors for one-sided tolerance limits and for variables sampling plans. Sandia Corporation, Monograph 607, Albuquerque, New Mexico, March 1963. (2) The power of Student’s t-test. J. Amer. Statist. Assoc. 60 (1965), 320–333 and 1251. (3) A survey of properties and applications of the noncentral t-distribution. Technometrics 10 (1968), 445-478.MathSciNetzbMATHGoogle Scholar
  93. Owen, D.B., and Frawley, W.H.: Factors for tolerance limits which control both tails of the normal distribution. J. Qual. Technol. 3 (1971), 69–79.Google Scholar
  94. Parren, J.L. Van der: Tables for distribution-free confidence limits for the median. Biometrika 57 (1970), 613–617.zbMATHGoogle Scholar
  95. Pearson, E.S., and Stephens, M.A.: The ratio of range to standard deviation in the same normal sample. Biometrika 51 (1964), 484–487.MathSciNetzbMATHGoogle Scholar
  96. Penfield, D.A., and McSweeney, Maryellen: The normal scores test for the two-sample problem. Psychological Bull. 69 (1968), 183–191.Google Scholar
  97. Peters, C.A.F.: Über die Bestimmung des wahrscheinlichen Fehlers einer Beobachtung aus den Abweichungen der Beobachtungen von ihrem arithmetischen Mittel. Astronomische Nachrichten 44 (1856), 30 + 31.Google Scholar
  98. Pierson, R.H.: Confidence interval lengths for small numbers of replicates. U.S. Naval Ordnance Test Station. China Lake, Calif. 1963.Google Scholar
  99. Pillai, K.C.S., and Buenaventura, A.R.: Upper percentage points of a substitute F-ratio using ranges. Biometrika 48 (1961), 195 + 196.MathSciNetGoogle Scholar
  100. Potthoff, R. F.: Use of the Wilcoxon statistic for a generalized Behrens-Fisher problem. Ann. Math. Stat. 34 (1963), 1596–1599.MathSciNetzbMATHGoogle Scholar
  101. Pratt, J. W.: Robustness of some procedures for the two-sample location problem. J. Amer. Statist. Assoc. 59 (1964), 665–680.MathSciNetGoogle Scholar
  102. Proschan, F.: Confidence and tolerance intervals for the normal distribution. J. Amer. Statist. Assoc. 48 (1953), 550–564.MathSciNetzbMATHGoogle Scholar
  103. Quesenberry, C.P., and David, H.A.: Some tests for outliers. Biometrika 48 (1961), 379–390.zbMATHGoogle Scholar
  104. Raatz, U.: Eine Modifikation des White-Tests bei großen Stichproben. Biometrische Zeitschr. 8 (1966), 42–54.Google Scholar
  105. Reiter, S.: Estimates of bounded relative error for the ratio of variances of normal distributions. J. Amer. Statist. Assoc. 51 (1956), 481–488.MathSciNetzbMATHGoogle Scholar
  106. Rosenbaum, S.: (1) Tables for a nonparametric test of dispersion. Ann. Math. Statist. 24 (1953), 663–668. (2) Tables for a nonparametric test of location. Ann. Math. Statist. 25 (1954), 146-150. (3) On some two-sample non-parametric tests. J. Amer. Statist. Assoc. 60 (1965), 1118-1126.MathSciNetzbMATHGoogle Scholar
  107. Rytz, C.: Ausgewählte parameterfreie Prüfverfahren im 2-und k-Stichproben-Fall. Metrika 12 (1967), 189–204 und 13 (1968), 17-71.Google Scholar
  108. Sachs, L.: Statistische Methoden. Ein Soforthelfer. 2. neubearb. Aufl. (Springer, 105 S.) Berlin, Heidelberg, New York 1972, S. 52-55, 72 und 94-96.Google Scholar
  109. Sandelius, M.: A graphical version of Tukey’s confidence interval for slippage. Technometrics 10 (1968), 193 + 194.MathSciNetGoogle Scholar
  110. Saw, J.G.: A non-parametric comparison of two samples one of which is censored. Biometrika 53 (1966), 599–602.MathSciNetzbMATHGoogle Scholar
  111. Scheffé, H.: Practical solutions of the Behrens-Fisher problem. J. Amer. Statist. Assoc. 65 (1970), 1501–1508.MathSciNetzbMATHGoogle Scholar
  112. Scheffé, H., and Tukey, J.W.: Another Beta-Function Approximation. Memorandum Report 28, Statistical Research Group, Princeton University 1949.Google Scholar
  113. Shorack, G.R.: Testing and estimating ratios of scale parameters. J. Amer. Statist. Assoc. 64 (1969), 999–1013.Google Scholar
  114. Siegel, S.: Nonparametric Statistics for the Behavioral Sciences. New York 1956, p. 278.Google Scholar
  115. Siegel, S., and Tukey, J.W.: A nonparametric sum of ranks procedure for relative spread in unpaired samples. J. Amer. Statist. Assoc. 55 (1960), 429–445.MathSciNetGoogle Scholar
  116. Smirnoff, N.W.: (1) On the estimation of the discrepancy between empirical curves of distribution for two independent samples. Bull. Université Moskov. Ser. Internat., Sect A 2. (2) (1939), 3-8. (2) Tables for estimating the goodness of fit of empirical distributions. Ann. Math. Statist. 19 (1948), 279–281.Google Scholar
  117. Stammberger, A.: Über einige Nomogramme zur Statistik. (Fertigungstechnik und Betrieb 16 [1966], 260-263 oder) Wiss. Z. Humboldt-Univ. Berlin, Math.-Nat. R. 16 (1967), 86–93.Google Scholar
  118. Sukhatme, P.V.: On Fisher and Behrens’s test of significance for the difference in means of two normal samples. Sankhya 4 (1938), 39–48.Google Scholar
  119. Szameitat, K., und Koller, S.: Über den Umfang und die Genauigkeit von Stichproben. Wirtschaft u. Statistik 10 NF (1958), 10–16.Google Scholar
  120. Szameitat, K., und K.-A. Schäffer: (1) Fehlerhaftes Ausgangsmaterial in der Statistik und seine Konsequenzen für die Anwendung des Stichprobenverfahrens. Allgemein. Statist. Arch. 48 (1964), 1–22. (2) Kosten und Wirtschaftlichkeit von Stichprobenstatistiken. Allgem. Statist. Arch. 48 (1964), 123-146.Google Scholar
  121. Szameitat, K., and R. Deininger: Some remarks on the problem of errors in statistical results. Bull. Int. Statist. Inst. 42, I (1969), 66-91 [vgl. 41, II (1966), 395-417 u. Allgem. Statist. Arch. 55 (1971), 290–303] Thöni, H.P.: Die nomographische Lösung des t-Tests. Biometrische Zeitschr. 5 (1963), 31-50.Google Scholar
  122. Thompson jr., W.A., and Endriss, J.: The required sample size when estimating variances. The American Statistician 15 (June 1961), 22 + 23.Google Scholar
  123. Thompson, W.A., and Willke, T.A.: On an extreme rank sum test for outliers. Biometrika 50 (1963), 375–383.MathSciNetzbMATHGoogle Scholar
  124. Tiku, M.L.: Tables of the power on the F-test. J. Amer. Statist. Assoc. 62 (1967), 525–539 [vgl. auch 63 (1968), 1551 u. 66 (1971), 913-916 sowie 67 (1972), 709 + 710].MathSciNetzbMATHGoogle Scholar
  125. Trickett, W.H., Welch, B.L., and James, G.S.: Further critical values for the two-means problem. Biometrika 43 (1956), 203–205.MathSciNetzbMATHGoogle Scholar
  126. Tukey, J. W.: (1) A quick, compact, two-sample test to Duckworth’s specifications. Technometrics 1 (1959), 31–48. (2) A survey of sampling from contaminated distributions. In I. Olkin and others (Eds.): Contributions to Probability and Statistics. Essays in Honor of Harold Hotelling. pp. 448-485, Stanford 1960. (3) The future of data analysis. Ann. Math. Statist. 33 (1962), 1-67, 812 Waerden, B.L., van der: Mathematische Statistik. 2. Aufl., Berlin-Heidelberg-New York 1965, S. 285/95, 334/5, 348/9.MathSciNetGoogle Scholar
  127. Walter, E.: Über einige nichtparametrische Testverfahren. Mitteilungsbl. Mathem. Statist. 3 (1951), 31–44 und 73-92.zbMATHGoogle Scholar
  128. Weiler, H.: A significance test for simultaneous quantal and quantitative responses. Technometrics 6 (1964), 273–285.MathSciNetGoogle Scholar
  129. Weiling, F.: Die Mendelschen Erbversuche in biometrischer Sicht. Biometrische Zeitschr. 7 (1965), 230–262, S. 240.Google Scholar
  130. Weir, J.B. de V.: Significance of the difference between two means when the population variances may be unequal. Nature 187 (1960), 438.zbMATHGoogle Scholar
  131. Weissberg, A., and Beatty, G.H.: Tables of tolerance-limit factors for normal distributions. Technometrics 2 (1960), 483–500 [vgl. auch J. Amer. Statist. Assoc. 52 (1957), 88-94 u. 64 (1969), 610-620 sowie Industrial Quality Control 19 (Nov. 1962), 27 + 28].MathSciNetzbMATHGoogle Scholar
  132. Welch, B. L.: (1) The significance of the difference between two means when the population variances are unequal. Biometrika 29 (1937), 350–361. (2) The generalization of “Student’s” problem when several different population variances are involved. Biometrika 34 (1947), 28-35.Google Scholar
  133. Wenger, A.: Nomographische Darstellung statistischer Prüfverfahren. Mitt. Vereinig. Schweizer. Versicherungsmathematiker 63 (1963), 125–153.MathSciNetzbMATHGoogle Scholar
  134. Westlake, W. J.: A one-sided version of the Tukey-Duckworth test. Technometrics 13 (1971), 901–903.Google Scholar
  135. Wilcoxon, F.: Individual comparisons by ranking methods. Biometrics 1 (1945), 80–83.Google Scholar
  136. —, Katti, S.K., and Wilcox, Roberta A.: Critical Values and Probability Levels for the Wilcoxon Rank Sum Test and the Wilcoxon Signed Rank Test. Lederle Laboratories, Division Amer. Cyanamid Company, Pearl River, New York, August 1963.Google Scholar
  137. Wilcoxon, F., Rhodes, L.J., and Bradley, R.A.: Two sequential two-sample grouped rank tests with applications to screening experiments. Biometrics 19 (1963), 58–84 (vgl. auch 20 [1964], 892).MathSciNetzbMATHGoogle Scholar
  138. —, and Wilcox, Roberta A.: Some Rapid Approximate Statistical Procedures. Lederle Laboratories, Pearl River, New York 1964.Google Scholar
  139. Wilks, S.S.: (1) Determination of sample sizes for setting tolerance limits. Ann. Math. Statist. 12 (1941), 91–96 [vgl. auch The American Statistician 26 (Dec. 1972), 21]. (2) Statistical prediction with special reference to the problem of tolerance limits. Ann. Math. Statist. 13 (1942), 400-409.MathSciNetGoogle Scholar
  140. Winne, D.: (1) Zur Auswertung von Versuchsergebnissen: Der Nachweis der Übereinstimmung zweier Versuchsreihen. Arzneim.-Forschg. 13 (1963), 1001–1006. (2) Zur Planung von Versuchen: Wieviel Versuchseinheiten? Arzneim.-Forschg. 18 (1968), 1611-1618.Google Scholar

Lehrbücher der Stichprobentheorie

  1. Billeter, E.P.: Grundlagen der repräsentativen Statistik. Stichprobentheorie und Versuchsplanung. (Springer, 160 S.) Wien und New York 1970.Google Scholar
  2. Cochran, W.G.: Sampling Techniques. 2nd ed., New York 1963 (Übersetzung erschien 1972 bei de Gruyter, Berlin und New York).Google Scholar
  3. Conway, Freda: Sampling: An Introduction for Social Scientists. (G. Allen and Unwin, pp.154) London 1967.Google Scholar
  4. Deming, W.E.: Sampling Design in Business Research. London 1960.Google Scholar
  5. Desabie, J.: Théorie et Pratique des Sondages. Paris 1966.Google Scholar
  6. Raj, D.: (1) Sampling Theory. (McGraw-Hill, pp.225) New York 1968. (2) The Design of Sample Surveys. (McGraw-Hill, pp.416) New York 1972.Google Scholar
  7. Hansen, M. H., Hurwitz, W.N., and Madow, W.G.: Sample Survey Methods and Theory. Vol. I and II (Wiley, pp.638, 332) New York 1964.Google Scholar
  8. Kellerer, H.: Theorie und Technik des Stichprobenverfahrens. Einzelschriften d. Dtsch. Statist. Ges. Nr. 5, 3. Aufl., München 1963.Google Scholar
  9. Kish, L.: Survey Sampling. New York 1965.Google Scholar
  10. Menges, G.: Stichproben aus endlichen Gesamtheiten. Theorie und Technik, Frankfurt/Main 1959.Google Scholar
  11. Murthy, M.N.: Sampling Theory and Methods. (Statistical Publ. Soc., pp.684) Calcutta 1967.Google Scholar
  12. Parten, Mildred: Surveys, Polls, and Samples: Practical Procedures. (Harper and Brothers, pp.624) New York 1969 (Bibliography pp. 537/602).Google Scholar
  13. Sampford, M.R.: An Introduction to Sampling Theory with Applications to Agriculture. London 1962.Google Scholar
  14. Statistisches Bundesamt Wiesbaden (Hrsg.): Stichproben in der amtlichen Statistik. Stuttgart 1960.Google Scholar
  15. Stenger, H.: Stichprobentheorie. (Physica-Vlg., 228 S.) Würzburg 1971.Google Scholar
  16. Stuart, A.: Basic Ideas of Scientific Sampling. (Griffin, pp.99) London 1969.Google Scholar
  17. Sukhatme, P.V., and Sukhatme, B.V.: Sampling Theory of Surveys With Applications. 2nd rev. ed. (Iowa State Univ. Press; pp.452) Ames, Iowa 1970.Google Scholar
  18. United Nations: A short Manual on Sampling. Vol. I. Elements of Sample Survey Theory. Studies in Methods Ser. F No. 9, rev. 1, New York 1972.Google Scholar
  19. Yamane, T.: Elementary Sampling Theory. (Prentice-Hall, pp.405) Englewood Cliffs, N.J. 1967.Google Scholar
  20. Zarkovich, S.S.: Sampling Methods and Censuses. (Fao, UN, pp. 213) Rome 1965.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Lothar Sachs

There are no affiliations available

Personalised recommendations