Sample Size Calculator: Linear Regression Comparing Two slopes

Hypothesis: Two-Sided Equality

Data Input: (Help) (Example)

Input

 

Results

α

 

Ncases

]

Ncontrol

mx1

 

Ntotal

mx2

 

 

 

mp

 

 

 

f1

 

 

 

f2

 

 

 

r

 

 

 


Note:

Variables

Descriptions

\

Probability of type I error

]

Probability of type II error

mx1

The standard deviation of unexposed group

mx2

The standard deviation of exposed group

f1

Slope of the first linear regression line

f2

Slope of the second linear regression line

mp

Standard deviation from pooled variance

r

Ratio of unexposed to exposed



Help Aids Top

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

Procedure:

  1. Enter

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

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

c)    Standard deviations for unexposed group and exposed group

d)    Standard deviations from pooled variance

e)    Slope of the first linear regression line

f)    Slope of the second linear regression line

g)    Ratio of unexposed to exposed

  1. Click the button Calculate to obtain

a)    The required sample size.

  1. Click the button Reset for a new calculation

Formulae:


Top

Example

From the Armitage and Berry's cadmium exposure study, 28 cadmium industry workers with less than 10 years of cadmium exposure and 44 workers never exposed to cadmium. The standard deviations of the ages of those unexposed and exposed were 12.0 and 9.19 respectively. Regressing vital capacity on age in the two groups yielded slope of -0.0306 and 0.0465 liters per year of life in unexposed and exposed workers. The standard errors for the slopes are 0.00754 and 0.0113; the residual mean squares from the unexposed and exposed regressions are 0.352 and 0.293. The pooled estimate of the error variance from both groups is s2=0.329. Suppose we want to recruit sufficient workers to detect a true difference of -0.0159 in the two groups with 80%, type I error of 0.05, and ratio of unexposed to exposed workers m=44/28=1.57.

z\/2=1.960

z1-]=0.842

mx1=12

mx2=9.19

mp=0.574

f1=-0.0306

f2=-0.0465

r=44/28=1.57

Nexposed = 167

Nunexposed = 263

Therefore, 430 cadmium worker is required.

Reference:

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

Armitage P, Berry G. Statistical Methods in Medical Research 3rd ed. Oxford, UK: Blackwell Scientific 1994. Print.

Top