From: Steve Adams <steve_adams_sd_at_yahoo.com>

Date: Tue 26 Apr 2005 - 09:16:14 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Apr 26 09:19:19 2005

Date: Tue 26 Apr 2005 - 09:16:14 EST

If the treatment contrast is used, the p value for x1
is testing whether the slope at the reference level of
x2 is equal to 0 (think about the model y~x1*x2 as
fitting 2 straight lines, one for the reference level
of x2, and one for the other level of x2). I am not
quite sure about what it tests when the helmert
contrast is used, my guess is it tests whether the
slope at the mid-level (?) of the x2 is equal to 0.
maybe other experts can comment on this.

Steve

: -----Original Message-----

*: From: r-help-bounces@stat.math.ethz.ch
**: [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf
*

Of array chip

: Sent: Saturday, 23 April 2005 2:32 PM

*: To: r-help@stat.math.ethz.ch
**: Subject: [R] ANOVA with both discreet and continuous
*

variable

*:
**:
*

: Hi all,

*:
**: I have dataset with 2 independent variable, one (x1)
**: is continuous, the other (x2) is a categorical
**: variable with 2 levels. The dependent variable (y)
*

is

: continuous. When I run linear regression y~x1*x2, I

*: found that the p value for the continuous
*

independent

: variable x1 changes when different contrasts was

used

: (helmert vs. treatment), while the p values for the

*: categorical x2 and interaction are independent of
*

the

: contrasts used. Can anyone explain why?

Because the hypotheses the corresponding test
statistics

are testing are invariant with respect to the choice
of

contrast matrices you have considered. (This is NOT
true

if your factor has more than two levels, by the way.)

: I guess the p

*: value for x1 is testing different hypothesis under
**: different contrasts?
*

The tests are for different null hypotheses, yes.

: If the interaction is NOT

*: significant, what contrast should I use to test the
**: hypothesis that x1 is not significantly related with
**: y?
*

There is no choice of contrast matrix that will give
the

test statistic associated with the linear term x1 this

meaning. Your question only specifies a null
hypothesis,

a significance test requires a null and an alternative
hypothesis. Both matter. In the context you have set
up below the way I would go about addressing what I
think is your question would be something like:

M0 <- lm(y ~ x2) ## Null hypthesis with no x1 M1 <- lm(y ~ x1*x2) ## outer hypothesis as belowanova(M0, M1)

*:
**:
*

: x1<-rnorm(50,9,2)

*: x2<-as.factor(as.numeric(runif(50)<0.35))
**: y<-rnorm(50,30,5)
**:
**: options(contrasts=c('contr.treatment','contr.poly'))
**: summary(lm(y~x1*x2))
**:
**: options(contrasts=c('contr.helmert','contr.poly'))
**: summary(lm(y~x1*x2))
*

:

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Apr 26 09:19:19 2005

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