Psychology Wiki

Sample size

34,203pages on
this wiki
Add New Page
Talk0 Share

Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |

Statistics: Scientific method · Research methods · Experimental design · Undergraduate statistics courses · Statistical tests · Game theory · Decision theory

Sample size, usually designated N, is the number of repeated measurements in a statistical sample. They are used to estimate a parameter, a descriptive quantity of some population. N determines the precision of that estimate. Larger N gives smaller error bounds of estimation. A typical statement is to say that one can be 95% sure the true parameter is within +or- B of the estimate, where B is an error bound that decreases with increasing N. Such a bounded estimate is refered to as the confidence interval for that parameter.

For example, the simplest rule of thumb for estimating any parameter is the one for a proportion in a population. It is that the maximum bound, B, of a 95% confidence interval for an unknown proportion is 1/sqrt(N). So, N=100 gives B = 10%, N=400 gives B = 5%, N=1000 gives B = ~3%, and N=10000 gives B = 1%. One sees these numbers quoted often in news reports of opinion polls and other sample surveys.

For sufficient N, usually at least 30, the general 95% confidence interval for a population mean or "expected value" is the sample mean +or- B, where B = 2sqrt(V/N) and V is the variance of the sampled variable. Conversely N=4V/B2.

The rule of thumb for maximum B for a proportion derives from the fact that for sufficient N, the estimator of a proportion, X/N, has a binomial distribution and is also the sample mean from a Bernoulli distribution with maximum variance of .25, closely approximating a normal distribution which the Central Limit Theorem says contains ~95% of its values within 2 standard deviations of its population mean. One simply envisions those bounds being shifted from around the population mean to around its estimator. This maximum 95% error bound, twice the standard error of X/N, where X are N are yet to be determined, is B = 2sqrt(.25/N) = 1/sqrt(N). Conversely N=1/B2.

See also Edit

This page uses Creative Commons Licensed content from Wikipedia (view authors).

Ad blocker interference detected!

Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.

Also on Fandom

Random Wiki