Sampling: Introduction

In the Sampling menu, you can calculate the required sample size for some common problems, taking into account the magnitude of differences and the probability to make a correct or a false conclusion.

When you perform a statistical test, you will make a correct decision when you

• reject a false null hypothesis, or
• accept a true null hypothesis.

On the other hand you can make two errors:

• you can reject a true null hypothesis, or
• you can accept a false null hypothesis.

These four situations are represented in the following table.

	Null hypothesis = TRUE	Null hypothesis = FALSE
Reject null hypothesis	Type I error	Correct decision
Accept null hypothesis	Correct decision	Type II error

For example, when you have rejected the null hypothesis in a statistical test (because P<0.05), and therefore conclude that a difference between samples exists, you can either:

• have done so correctly, and uncovered a difference where one exists;
• have rejected the null hypothesis when in fact it is true, and uncovered a difference where in fact none exits. In this case you make a Type I error. is the (two-sided) probability of making a Type I error.

You can avoid making a Type I error by selecting a lower significance level of the test, e.g. by rejecting the null hypothesis when P<0.01 instead of P<0.05.

On the other hand, when you accept the null hypothesis in a statistical test (because P>0.05), and conclude that there is no difference between samples, you can either:

• have correctly concluded that there is no difference;
• have accepted the null hypothesis when in fact it is false, and therefore you have failed to uncover a difference where such a difference really exists. In this case you make a Type II error. is the probability of making a Type II error.

The power of a test is 1-, this is the probability to uncover a difference when there really is one. For example when is 0.10, then the power of the test is 0.90 or 90%.

You can avoid making a Type II error, and increase the power of the test to uncover a difference when there really is one, mainly by increasing the sample size.

To calculate the required sample size, you must decide beforehand on:

• the required probability of a Type I error, i.e. the required significance level (two-sided);
• the required probability of a Type II error, i.e. the required power 1- of the test;
• a quantification of the study objectives, i.e. decide what difference is biologically or clinically meaningful and worthwhile detecting.

In addition, you will sometimes need to have an idea about expected sample statistics such as e.g. the standard deviation. This can be known from previous studies.

See also

• Sampling menu
• Sampling: Single mean
• Sampling: Single proportion
• Sampling: Comparison of two means
• Sampling: Comparison of two proportions
• Sampling: Correlation coefficient
• Sampling: Area under ROC curve
• Sampling: Comparison of two ROC curves

External links

• Sample size on Wikipedia.
• Statistical power on Wikipedia.