Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T05:26:18.691Z Has data issue: false hasContentIssue false

28 - THE LAW OF GREAT NUMBERS

from V - THE FOUNDATIONS OF STATISTICAL INFERENCE

Published online by Cambridge University Press:  05 November 2012

Get access

Summary

Natura quidem suas habet consuetudines, natas ex reditu causarum, sed non nisi ὡς ἐπί τὸ πολύ. Novi morbi inundant subinde humanum genus, quodsi ergo de mortibus quotcunque experimenta feceris, non ideo naturae rerum limites posuisti, ut pro futuro variare no possit.

Leibniz in a letter to Bernoulli, 3 December 1703.

1. It has always been known that, while some sets of events invariably happen together, other sets generally happen together. That experience shows one thing, while not always a sign of another, to be a usual or probable sign of it, must have been one of the earliest and most primitive forms of knowledge. If a dog is generally given scraps at table, that is sufficient for him to judge it reasonable to be there. But this kind of knowledge was slow to be made precise. Numerous experiments must be carefully recorded before we can know at all accurately how usual the association is. It would take a dog a long time to find out that he was given scraps except on fast days, and that there was the same number of these in every year.

The necessary kind of knowledge began to be accumulated during the seventeenth and eighteenth centuries by the early statisticians. Halley and others began to construct mortality tables; the proportion of the births of each sex were tabulated; and so forth. These investigations brought to light a new fact which had not been suspected previously—namely, that in certain cases of partial association the degree of association, i.e. the proportion of instances in which it existed, shows a very surprising regularity, and that this regularity becomes more marked the greater the number of the instances under consideration.

Type
Chapter
Information
Publisher: Royal Economic Society
Print publication year: 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×