Hi,

I've made a research about how to compare two regression line slopes

(of y versus x for 2 groups, "group" being a factor ) using R.

I knew the method based on the following statement :

t = (b1 - b2) / sb1,b2

where b1 and b2 are the two slope coefficients and sb1,b2 the pooled

standard error of the slope (b)

which can be calculated in R this way:

> df1 <- data.frame(x=1:3, y=1:3+rnorm(3))

> df2 <- data.frame(x=1:3, y=1:3+rnorm(3))

> fit1 <- lm(y~x, df1)

> s1 <- summary(fit1)$coefficients

> fit2 <- lm(y~x, df2)

> s2 <- summary(fit2)$coefficients

> db <- (s2[2,1]-s1[2,1])

> sd <- sqrt(s2[2,2]^2+s1[2,2]^2)

> df <- (fit1$df.residual+fit2$df.residual)

> td <- db/sd

> 2*pt(-abs(td), df)

[1] 0.9510506

However, I also found a procedure in Wonnacott & Wonnacott, that is

based on the use of a mute variable D that will have a binary value

according to the group to which a given point belongs (group : D=0;

group 2: D=1). Then the equation that is computed is as follow:

y = b0 + b1.x + D.b2.x

which can be computed in R with:

> fit <- lm(y ~ group + x + x:group)

where y is the response of the 2 groups.

The p-value of x:group gives the probability for the two slopes to be

different, and the estimated values of parameters are these of both

populations.

These two methods have already been described in the mailing list but

not confronted and discussed.

So, my questions are:

- are these methods different ?

- which one should be preferentially used ?

This is not really a question about R but more about statisticsâ€¦

I don't think I'm really clear and I know I'm not rigorous at all in

my descriptions, but I hope someone will understand me.

Thanks,

Etienne

-------------------------------------------------------------------

Etienne Toffin, PhD Student

Unit of Social Ecology

UniversitĂ© Libre de Bruxelles, CP 231

Boulevard du Triomphe

B-1050 Brussels

Belgium

Tel: +32(0)2/650.55.30

Fax: +32(0)/650.59.87

Skype: etienne_titou

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