# The Importance of Large Samples

Any experiment may be regarded as forming an individual of a 'population' of experiments which might be performed under the same conditions. A series of experiments is a sample drawn from this population.

Now any series of experiments is only of value in so far as it enables us to form a judgment as to the statistical constants of the population to which the experiments belong. In a great number of cases the question finally turns on the value of a mean, either directly, or as the mean difference between the two qualities.

If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty:— (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals.

## Notes:

Small samples introduce two potential errors.

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**Concepts:**

Statistics (0.981539): dbpedia | freebase | opencyc

Sampling (0.878353): dbpedia | freebase

Sample (0.856009): dbpedia | freebase

Sampling error (0.710830): dbpedia | freebase

Sample size (0.678155): dbpedia

Standard deviation (0.652736): dbpedia | freebase

Probability theory (0.649484): dbpedia | freebase | opencyc

Cluster sampling (0.600976): dbpedia | freebase | yago

**The Probable Error of a Mean**

**Books, Brochures, and Chapters>**

**Book:**Gosset, William Sealy (1908)

*, The Probable Error of a Mean*, Oxford University Press, USA, Biometrika, Retrieved on 2012-05-30

**Folksonomies:**mathematics