[R-sig-ME] P value value for a large number of degree of freedom in lmer

Joshua Wiley jwiley.psych at gmail.com
Wed Nov 24 01:51:47 CET 2010

```On Tue, Nov 23, 2010 at 4:09 PM, Jonathan Baron <baron at psych.upenn.edu> wrote:
> For the record, I have to register my disagreement.  In the
> experimental sciences, the name of the game is to design a
> well-controlled experiment, which means that the null hypothesis will
> be true if the alternative hypothesis is false.  People who say what
> is below, which includes almost everyone who responded to this post,
> have something else in mind.  What they say is true in most
> disciplines.  But when I hear this sort of thing, it is like someone
> is telling me that my research career as an EXPERIMENTAL psychologist
> has been some sort of delusion.

I would not take it that way.  I agree there is a difference between
some arbitrary null of no difference and a well designed control, but
no matter what case, the null is a specific hypothesis.  Given a
continuous distribution, if you the probability of any constant
occurring to an infinite decimal place is infinitely small.  With only
100,000 observations:

> dt(.49, df = 10^5) - dt(.5, df = 10^5)
[1] 0.001747051

Your career as an experimental psychologist is not a delusion, null
hypothesis statistical testing is---even with a perfect control, we
set up an unrealistic hypothesis.  Now if we could set up the null as
an interval....

>
> If you have a very large sample and you are doing a correlational
> study, yes, everything will be significant.  But if you do the kind of
> experiment we struggle to design, with perfect control conditions, you
> won't get significant results (except by chance) if your hypothesis is
> wrong.

I agree that this is typically a bigger problem for correlational
studies, but if it became practical to run well-controlled experiments
on millions of participants, I suspect p-values would be disregarded
awfully quickly.  Even then, the study was not pointless or a
delusion, that kind of precision lets you confidently talk about the
control, and would give any applied person or practitioner a great
guide what to expect if they implemented it in the field.

x <- rnorm(10^6, mean = 0)
y <- rnorm(10^6, mean = .01)
t.test(x, y, var.equal = TRUE)

Best regards,

Josh (fan of experiments, correlational studies, & psychology...not so
much of NHST, but you use what you have)

>
> Jon
>
> On 11/24/10 07:59, Rolf Turner wrote:
>>
>> It is well known amongst statisticians that having a large enough data set will
>> result in the rejection of *any* null hypothesis, i.e. will result in a small
>> p-value.  There is no ``bias'' involved.
>
> --
> Jonathan Baron, Professor of Psychology, University of Pennsylvania
> Editor: Judgment and Decision Making (http://journal.sjdm.org)
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

--
Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://www.joshuawiley.com/

```