Sample Size Calculator: Simple Linear Regression

Hypothesis: Two-Sided Equality



Data Input: (Help) (Example)

Input

 

Results

α

 

£m

£]

£l

£mx

 

N

£my

 

 

£f1

 

 

 

Note:

Variables

Descriptions

£\

Probability of type I error

£]

Probability of type II error

£mx

The standard deviation of the independent variable

£my

The standard deviation of the dependent variable

£f1

Slope of the linear regression line

£m

Standard deviation of the regression errors

£l

Correlation

N

Sample size

Help Aids Top

Application: This section illistrates how to determine the minimum sample size for simple linear regression.

Procedure:

  1. Enter

a)    Value of £\, the two-sided confidence level

b)    Value of £], the type II error (1-power)

c)    Standard deviations of independent and dependent variables

d)    Slope of the linear regression line

  1. Click the button ¡§Calculate¡¨ to obtain

a)    The standard deviation of the regression errors, correlation and sample size.

  1. Click the button ¡§Reset¡¨ for a new calculation

Formulae:


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Example

A dieting program encourages patients to follow a specific diet and to exercise regularly. We want to determine whether the actual average time per day spent exercising is related to BMI after 6 months on this program. Previous study suggests that exercise time of female participants has a standard deviation of £mx=7.5 minutes; the reported standard deviation of the female subjects is £my=4.0kg/m2. We want to determine the sample size with which we can detect a true drop of BMI of £f1=-0.0667 kg/m2 per minute of exercise. Assume £\=0.05 and £]=0.2.

N = [(1.960+0.842)*3.9686/(-0.1251*7.5)]2= 494

Therefore, 494 female participant is required.

Reference: Dupont, W.D. and Plummer, W.D. Power and Sample Size Calculations for Studies Involving Linear Regression. New York, 1998. Print.

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