Sample Size Calculator: Simple Linear Regression

Hypothesis: Two-Sided Equality  Data Input: (Help) (Example)

 Input Results α σ β ρ σx N σy λ1

Note:

 Variables Descriptions α Probability of type I error β Probability of type II error σx The standard deviation of the independent variable σy The standard deviation of the dependent variable λ1 Slope of the linear regression line σ Standard deviation of the regression errors ρ 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 α, the two-sided confidence level

b)    Value of β, 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:   Top

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 σx=7.5 minutes; the reported standard deviation of the female subjects is σy=4.0kg/m2. We want to determine the sample size with which we can detect a true drop of BMI of λ1=-0.0667 kg/m2 per minute of exercise. Assume α=0.05 and β=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.

Top