A magyar korona országainak betegsegélyző pénztárai 1898-ban = Die Krankenkassen der Länder der ungarischen Krone im Jahre 1898

An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 890185476

URN:: urn:nbn:de:zbw-retromon-7558

Document type:: Monograph

Title:: A magyar korona országainak betegsegélyző pénztárai 1898-ban = Die Krankenkassen der Länder der ungarischen Krone im Jahre 1898

Place of publication:: Budapest

Publisher:: Pester Buchdruckerei-Actien-Gesellschaft

Year of publication:: 1901

Scope:: 1 Online-Ressource (164, 131 Seiten)

Digitisation:: 2017

Collection:: Economics Books

Usage license:: Get license information via the feedback formular.

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: I. Allgemeiner Bericht

Collection:: Economics Books

LE THEORY OF STATISTICS. The association between inoculation and protection from attack is positive for each estate, but for only one of the tables is the value of P so small that we can say the result is wery unlikely to have arisen as a fluctuation of sampling. Adding up the values of x2, the total is 28-40, and entering the column for n'=7 (one more than the number of tables considered), we find P 0 23 000094 29 000061 whence by interpolation the value of P is ‘000081, i.e. we should only expect to get a total of x%s as great as or greater than this, on random sampling, 81 times in 1,000,000 trials. We can therefore regard the results as significant with a high degree of confidence. We may, I think, go further: for all the observed associations are positive, and in six cases there are 2% or 64 possible permuta- tions of sign. We should therefore only expect to get an equal or greater total value of x2 and tables all showing positive associa- tion, not 81 times in 1,000,000 trials but 81/64 or, roundly, 1-3 times. P for the observed event (3(x?)=28'4 and all associations positive) is therefore only ‘0000013. Experimental Illustrations of the General Case.—The formule for the general case, as for the special case in which the frequencies with which comparison is made are given a prior, can be checked by experiment. The numbers of beans counted in each of the sixteen compart- ments of the revolving circular tray mentioned on p. 374 above were entered as the frequencies of a table (1) with 4 rows and 4 columns, (2) with 2 rows and 8 columns, and the value of x? computed for each table for divergence from independence. For the two cases we have w=(3x3)+1=10 and n'=(1x7)+1=38 respectively. Differencing the columns for P corresponding to these two values of n’, we obtain the theoretical frequency-distri- butions given in the columns headed “Expectation” in Table A, The observed distributions of the values of x? in 100 experimental tables are given in the columns headed “ Observation.” It will be seen that the agreement between expectation and observation is excellent for so small a number of observations. If the goodness of fit be tested by the x2 method, grouping together the frequencies from x2=15 upwards, so that n’ is 4, x* is found to be 2-27 for the 4 x 4 tables and 4:36 for the 2 x 8 tables, giving P=052 in the first case and 0:22 in the second. 184

Access restriction

Copyright

fullscreen: An Introduction to the theory of statistics

Monograph

Chapter

Table of contents

Download

Monograph

This page

Image fragment

Citation links

Citation recommendation