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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