When the sample is small, the observed values of the random variables are not grouped. Therefore, in computing correlation equations here, one has to deal with nonuniformly spaced values of the quantities being investigated. Due to this, the usual methods of finding the requisite moments turn out to be inadequate, and it becomes necessary to develop techniques which would be applicable to small samples. We shall consider these techniques as applied in various examples.

Zusammenfassung

Die vorliegende Arbeit befaßt sich mit der Darstellung des Prozesses der Einkommensentstehung und Einkommensverwendung, einer der Hauptaufgaben der Wirtschaftsstatistik, im allgemeinen Rahmen der Volkswirtschaftlichen Gesamtrechnung. Ausgangspunkt sind die institutionelle und die funktionale Fragestellung. Für beide werden die Hauptprobleme der Volkswirtschaftlichen Gesamtrechnung erörtert, insbesondere Fragen des Aufbaus des Kontenplans sowie die der Auswahl und Bewertung der Transaktionen. Anschließend folgt eine kurze Diskussion über Nomenklaturen, Systematiken und über die statistischen Einheiten. Schließlich werden einige wichtige Probleme der Integration der beiden entwickelten Systeme behandelt.

The binomial distribution is the most important of the non-normal distributions. Its most widely used application is estimating the ‘fraction defective’ in industry (the fraction defective is the proportion of articles which fail to meet a given standard, e.g. screws nominally of one inch length may be classed as defective if they are less than 63/64 in. or greater than 65/64 in. long). It is used in public opinion polls to estimate the proportion of the population who hold a certain opinion (e.g. who will vote for a certain political party), and has many other applications.

Summary

A class of c-sample (cε2) non-parametric tests for the homogeneity of location or scale parameters is proposed and their various properties studied. These tests are based on a family of congruent interquantile numbers, and may be regarded as the c-sample extension of a class of two sample tests, proposed and studied by Sen [15]. A useful theorem on the asymptotic distribution of the proposed class of statistics is established. With the aid of this result, the asymptotic power-efficiency of the proposed class of test is studied and comparison is made with other test procedures. Location-free scale tests are also considered.

If we have a finite number of articles or plants and wish to select some at random, then care must be taken. For example, selecting by eye has been proved unsatisfactory, particularly for plants. Even the most careful experimenter seems to have a bias in some direction, and, unconsciously, tends to select those which are larger, or smaller, or greener, etc.