# [R] quadratic trends and changes in slopes

Martin Michlmayr tbm at cyrius.com
Mon Jan 20 01:12:02 CET 2003

```I'd like to use linear and quadratic trend analysis in order to find
out a change in slope.  Basically, I need to solve a similar problem as
discussed in http://www.gseis.ucla.edu/courses/ed230bc1/cnotes4/trend1.html

My subjects have counted dots: one dot, two dots, etc. up to 9 dots.
The reaction time increases with increasing dots.  The theory is that
1 up to 3 or 4 points can be counted relatively fast (a process known
as "subiziting") but that is becomes slower at around 5 dots ("counting").
The question is when the slope changes.  Most papers in the literature
determine this by checking when it changes from being a linear trend to
a quadratric trend. i.e deviation from linearity is seen as evidence
that the second, slower process is used.

I'd like to test the ranges 1-2, 1-3, 1-4, 1-5, 1-6, etc and see when
a qudratric trend is significant.  However, although I have read some
literature and done many google searches, I cannot figure out how to
do this with R.  Can anyone show me a simple example of how to do
this. (Either with the method described above or with a different
method -- but please note that I only have 9 data points, tho; 1:9).

Any help is appreciated.

Thanks.

FWIW, here's the description from one paper using this method:

"For both conditions, the subitizing range for each group was established
using quadratic trend tests on the aggregated RT data for numerosities 1-3,
1-4, and so on (Akin and Chase, 1978; Chi and Klahr, 1975; Pylyshyn,
1993). For both groups the first appearance of a quadratic trend was in
the N=1-5 range (t(9) = 7.33, p< .001 for the control group, and t(5) =
5.35, p = .005 for the Turner group). This indicates a subitizing range
of 4 for both groups. This divergence from a linear increase in RT
suggests the deployment of a new process for the last numerosity added."

--
Martin Michlmayr
tbm at cyrius.com

```