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# Sample size: Confidence Interval for a difference between means

 Command: Sample sizeConfidence Interval estimation & PrecisionDifference between means

## Description

Calculates the required minimum sample size for the estimation of a confidence interval with a required width for a difference between two independent means (Machin et al., 2009).

Note that the calculation does not include a null hypothesis value or a factor for power (1−β). Therefore the estimated sample size does not give a certainty that a particular value will fall inside or outside the confidence interval. The number of cases is only the number required to attain a specified confidence interval width.

## Required input

• Confidence level (%): select the confidence level: 90, 95 or 99%. A 95% confidence level (the value for a 95% Confidence Interval) is the most common selection. You can enter a different confidence level if required.
• Pooled standard deviation: you can find the pooled standard deviation in the output of the Independent samples t-test (see also Independent samples t-test: computational notes).
• Confidence interval width (2-sided): this is the required total width of the confidence interval. For example when a difference is 25 with 95% Confidence Interval 20 to 30, then the confidence interval width is 10.
• Ratio of sample sizes in Group 1 / Group 2: enter 1 for equal sample sizes in both groups. Enter 2 if the number of cases in group 1 must be double of the number of cases in group 2.

## Literature

• Machin D, Campbell MJ, Tan SB, Tan SH (2009) Sample size tables for clinical studies. 3rd ed. Chichester: Wiley-Blackwell.

## Sample Size Tables for Clinical StudiesDavid Machin, Michael J. Campbell, Say-Beng Tan, Sze-Huey Tan

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Sample Sizes for Clinical, Laboratory and Epidemiology Studies includes the sample size software (SSS) and formulae and numerical tables needed to design valid clinical studies. The text covers clinical as well as laboratory and epidemiology studies and contains the information needed to ensure a study will form a valid contribution to medical research.

The authors, noted experts in the field, explain step by step and explore the wide range of considerations necessary to assist investigational teams when deriving an appropriate sample size for their when planned study. The book contains sets of sample size tables with companion explanations and clear worked out examples based on real data. In addition, the text offers bibliography and references sections that are designed to be helpful with guidance on the principles discussed.