Hi
In general, patterns that hold within groups need NOT hold between groups
(problem of ecological correlations), which can also produce seeming paradoxes
for within versus aggregate correlations, as in Marie's case.
Note, for example, in the means that were posted, there is a strong negative
association between X and Y. Blue is lower than Red on X but higher than Red
on Y. This between-group effect presumably over-rides the within-group
positive association. Difficult to interpret without knowing what X/Y and
Red/Blue represent, but there is nothing inherently "impossible" about the
result. Imagine X is aptitude and Y is gpa, and Red is brighter students
taking more difficult courses and Blue is weaker aptitude students (lower X)
taking easier courses (higher Y). Within Red and Blue, positive r to be
expected, but could turn out to be negative in the aggregate.
Red Blue
X 2.9469 2.2219
Y 3.0952 4.3140
Depending on how you are analyzing these data, I would do a single scatterplot
with both groups represented by distinct symbols and fit lines to separate
groups, and combined groups. Should clarify the pattern in the data, if not
the interpretation.
Take care
Jim
James M. Clark
Professor of Psychology
204-786-9757
204-774-4134 Fax
[email protected]
>>> "Helweg-Larsen, Marie" <[email protected]> 27-Feb-12 11:07 AM >>>
Doesn't look like there are outlier issues. Both X and Y are measured on 5
point scales. Here are the means and standard deviations:
Descriptive Statisticsa
Mean
Std. Deviation
N
Var X
2.9469
.84347
113
Var Y
3.0952
.70281
112
a. Red Group
Descriptive Statisticsa
Mean
Std. Deviation
N
Var X
2.2219
.79934
196
Var Y
4.3140
.55183
198
a. Blue Group
Descriptive Statistics
Mean
Std. Deviation
N
Var X
2.4871
.88631
309
Var Y
3.8737
.84584
310
Blue and Red Group Combined
Any outliers when the full set is combined? That has the possibility of
changing the direction of the relationship.
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From: Helweg-Larsen, Marie
[mailto:[email protected]]<mailto:[mailto:[email protected]]>
Sent: Monday, February 27, 2012 11:31 AM
To: Teaching in the Psychological Sciences (TIPS)
Subject: [tips] Statistical question-correlations
Now what doesn't make sense to me that two groups individually have positive
and significant correlations but the two groups combined can have a negative
and significant correlation.
So you stats tipsters. Is that statistically possible?
I have checked everything I possibly can in terms of errors in the data or the
analyses and have found none. Some suggestions about what I ought to look at?
Marie
Marie Helweg-Larsen, Ph.D.
Associate Professor l Department of Psychology
Kaufman 168 l Dickinson College
Phone 717.245.1562 l Fax 717.245.1971
Office Hours: Mondays and Tuesdays 2:00-3:30
http://users.dickinson.edu/~helwegm/index.html
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