# Sample size determination

**sample sizeSampling sizessamplenumber of shotssample sizessizeestimating sample sizesestimating sufficient sample sizesfinite sampleonly 22 Bulldogs**

Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample.wikipedia

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### Power (statistics)

**statistical powerpowerpowerful**

In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power.

Power analysis can be used to calculate the minimum sample size required so that one can be reasonably likely to detect an effect of a given size.

### Confidence interval

**confidence intervalsconfidence levelconfidence**

For example, if a proportion is being estimated, one may wish to have the 95% confidence interval be less than 0.06 units wide.

A major factor determining the length of a confidence interval is the size of the sample used in the estimation procedure, for example, the number of people taking part in a survey.

### Accuracy and precision

**accuracyprecisionaccurate**

Larger sample sizes generally lead to increased precision when estimating unknown parameters.

For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy.

### Statistical hypothesis testing

**hypothesis testingstatistical teststatistical tests**

Such considerations can be used for the purpose of sample size determination prior to the collection of data.

### Estimation theory

**parameter estimationestimationestimated**

Larger sample sizes generally lead to increased precision when estimating unknown parameters.

:where m is the sample maximum and k is the sample size, sampling without replacement.

### Replication (statistics)

**replicationreplicatereplicates**

Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample.

### Survey sampling

**surveyssampleSample Survey**

In complicated studies there may be several different sample sizes: for example, in a stratified survey there would be different sizes for each stratum.

### Stratified sampling

**stratificationstratifiedstratified random sampling**

In complicated studies there may be several different sample sizes: for example, in a stratified survey there would be different sizes for each stratum.

For an efficient way to partition sampling resources among groups that vary in their means, variance and costs, see "optimum allocation".

### Estimator

**estimatorsestimateestimates**

The estimator of a proportion is, where X is the number of 'positive' observations (e.g. the number of people out of the n sampled people who are at least 65 years old).

A consistent sequence of estimators is a sequence of estimators that converge in probability to the quantity being estimated as the index (usually the sample size) grows without bound.

### Proportionality (mathematics)

**proportionalinversely proportionalproportion**

The estimator of a proportion is, where X is the number of 'positive' observations (e.g. the number of people out of the n sampled people who are at least 65 years old). A relatively simple situation is estimation of a proportion.

### Central limit theorem

**Lyapunov's central limit theoremlimit theoremscentral limit**

Several fundamental facts of mathematical statistics describe this phenomenon, including the law of large numbers and the central limit theorem.

### Standard error

**SEstandard errorsstandard error of the mean**

When estimating the population mean using an independent and identically distributed (iid) sample of size n, where each data value has variance σ 2, the standard error of the sample mean is:

### Sample (statistics)

**samplesamplesstatistical sample**

Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample.

### Effect size

**Cohen's deffect sizesmagnitude**

Cohen's d is frequently used in estimating sample sizes for statistical testing.

### Standard deviation

**standard deviationssample standard deviationSD**

This so-called range rule is useful in sample size estimation, as the range of possible values is easier to estimate than the standard deviation.

### Opinion poll

**opinion pollingpollapproval rating**

These numbers are quoted often in news reports of opinion polls and other sample surveys.

### Statistical significance

**statistically significantsignificantsignificance level**

### Stepwise regression

**Backward eliminationforward selectionStepwise**

For additional consideration, when planning an experiment, computer simulation, or scientific survey to collect data for this model, one must keep in mind the number of parameters, P, to estimate and adjust the sample size accordingly.

### Thematic analysis

A tool akin to a quantitative power calculation, based on the negative binomial distribution, has been suggested for thematic analysis.

For example, Fugard and Potts offered a prospective, quantitative tool to support thinking on sample size by analogy to quantitative sample size estimation methods.

### Degrees of freedom (statistics)

**degrees of freedomdegree of freedomEffective degrees of freedom**

All the parameters in the equation are in fact the degrees of freedom of the number of their concepts, and hence, their numbers are subtracted by 1 before insertion into the equation.

### Design of experiments

**experimental designdesignExperimental techniques**

### Statistical inference

**inferential statisticsinferenceinferences**

The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample.

### Statistical population

**populationsubpopulationsubpopulations**

The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample.

### Census

**UK censuscensusespopulation census**

In a census, data is sought for an entire population, hence the intended sample size is equal to the population.